But MAGA seems to never have been anything but an empty and meaningless abstraction.

I don't think this is entirely true. While the movement has been quite inchoate, it has had a steady position of immigration: "we want less of it." This is notable because this is the common thread across far-right populist movements across the West.

The other stable characteristic is a general reaction against "PC" or "Wokeness" in the abstract, and particularly against race/gender/sexual orientation/etc. specific efforts at redistributive justice.

You can see this coming to a head in the current Twitter civil war in MAGA. The old guard GOP and the "tech bro" coalition tend support high rates of immigration as a means to allow employers to access a larger talent pool (and arguably to avoid investment in workers). The MAGA core is pretty much entirely against high rates of immigration. Not any immigration per se mind you, just "high rates."

I think this is worth pointing out because, as I said, it's the main thread across a diffuse set of populist movements and it is also notably absent from those advanced economies that have not allowed high levels of immigration (e.g. Japan). Israel is an interesting example here because it has not allowed high rates of immigration for non-Jews, and as such most immigrants share an important sort of identity.

Eco is pretty interesting on this point, although I don't know if I'd totally recommend Kant and the Platypus. He starts off by granting the advocates of the linguistic turn and post-moderns most of their premises, and TBH I found the recap of all their points a bit tedious, particularly since some of these premises seem fairly dubious.

It is one thing to say the philosophizing is primarily done with language, it is another to simply assume that language is posterior to being because all talk of being involves language. The assumption seems to require that those without language simply cannot think, which seems a bit much. This is the old reduction of reason to ratio I mentioned earlier, except now ratio is confined to language (and perhaps to isolated, sui generis "language games").

I wouldn't be willing to cede these points. Similarly, one could argue that the senses are that through which we know not what we know. So too do it seem plausible that language is that through which we articulate thought (which is not to say that we don't sometimes use language to think) and another means through which we know, not thought itself and what we know. In the semiotic tradition Eco is advocating for, the sign vehicle is what joins the object and interpretant in an irreducibly triadic relationship (a gestalt perhaps), it is the mediator of a union, and it's a bit tedious to allow it to instead become an inscrutable and insurmountable barrier, only to try to work one's way back from this assumption.

Likewise, it seems unwise to me to leave unchallenged the presumption that truth is primarily in sentences, in syllables and symbols, and not primarily something that relates to the intellect.

Plus, some of the modeling exercise stuff he does could certainly benefit from advances in information theory and the philosophy of information. Although there is certainly still good stuff there. Perhaps the exercise is worthwhile. It is worth pointing out that in the "continua," (his term for "bare" experience prior to language/naming) there are limits. One can suppose that we can go about naming things in many different ways, but we cannot proceed arbitrarily on pain of being corrected on our errors. That there might be many ways to say things need not entail that all are equally correct. One might challenge the notion of genus and species, but if one tries to mate a cat to a dog one shall find a limit on how our conventions might develop.

Still, to me this smacks of the old empiricist view you find in Locke. A sort of atomization at odds with how learning actually occurs. Even brutes have a grasp on wholes. Sheep need not be exposed to many wolves in order to piece together "bundles of sensation" into an "abstracted image" of some whole. The sheep sees or smells their first wolf a bolts, and it is quite good for it that it has this capacity (St. Thomas makes this point in the commentary on De Anima).

This critique of the article seems to me to be more a disagreement of definitions. "That's not true science, true science is methodology..."

No doubt, it's something worth pointing out. However, I don't think the problems related to the assumptions of smallism and reductionism, what the authors label "scientific materialism," are in any way illusory. This is certainly how "what science says the world is like" was presented to me throughout my education, and one sees this view invoked quite regularly in popular and scientific texts.

Actually, it's no surprise that one author here is a cosmologist because in popular cosmology and physics reductionism and smallism frequently come in for withering criticism. That seems to be more the norm. However, in the special sciences, particularly neuroscience, smallism and reductionism still seem quite dominant. I find that even scientists who pay lip service to rejecting them often slip back into them.

I've long thought this was a consequence of the state of these respective fields (see below):

I am of the opinion that the heavy preferencing of reductionism in biology and particularly in neuroscience comes from the dearth of good "top down" explanations of phenomena. There is no good theory of conciousness, so of course the field looks to what is better understood to explain things. Whereas, it seems like reductionism is far less popular in the physical sciences, and this makes sense given they have very many good "top-down," explanations and because unifications—the explanation of disparate phenomena in terms of more general principles— seem to have been far more common over the last century than reductions. You can even see this in the goals of the fields. In physics, the goal is "grand unification," whereas in neuroscience the goal itself is generally seen as involving some sort of reduction. The idea of emergence is particularly hard to grapple with if you only understand parts relatively well, whereas if you understand the behavior of the whole better than the parts (certainly true in chemistry), the idea of emergence is not so unsettling.

Part of the problem here is perhaps that both analytic and continental philosophy of science has become so divorced from how scientists tend to think of their work that it has become largely irrelevant to scientific practices. The extreme skepticism and general anti-realism one finds in a lot of philosophy of science seems contained largely to the philosophers.

But you need a philosophy of science. It is all well and good to say science is a methodology, but this position needs to be justified. Which methodology? Why are these tools appropriate? This would seem to require giving some sort of metaphysical explanation of the sciences, else the proper methodology is "whatever we think works," in which case, one cannot complain if others takes the inability of science to explain consciousness as evidence that the current methodology is defective.

Plus, a focus on methodology doesn't really resolve these issues. Charges of "pseudoscience" are common, and they are often applied to research that ends up being extremely influential or even paradigm defining (e.g. pretty much the whole of quantum foundations up until the late 90s). These charges are normally made on methodological grounds though. Atoms, quarks, etc. were initially rejected by some precisely because they were considered "unfalsifiable" for instance.



I think that post really undersells the concerns of the advocates of the "view from nowhere." Their concerns don't tie in to difficulties in spacial perspective, but are rather related to how our entire perceptual and cognitive apparatus biases our understanding of the world. I'm certainly no advocate of this view, since I think it leads to the incoherence that "what the world is really like is the way it is conceived of without a mind,"but the problems of spatial perspective are sort of a trivial instances.

And if that is so, then perspective is not an attribute of the world, but of how we say things about the world. We can rephrase things in ways that do not depend on where we are standing...."

I don't see how you've shown this at all. In your example, perspective absolutely is an attribute of the world. "How we say things" is a consequence of how we experience them, and how we experience them says something about how the world is (else we need to write off empiricism). "How we say things" isn't something that is arbitrarily related to how the world is, nor do our practices of speech just happen to be what they are. Terms for perspective are universal across all languages because perspective is universal.

We pick up on them, we become aware that they are there, just as we become aware that these four apples still exist -as four apples, not merely as a non-numerical bunch of fruit-, when no one is in the house.

Apples are a good example, but cats or whole apple trees might be a better. Are there no discrete individual, whole plants or animals in the world such that they make up a multitude? Organisms are only organic unities as ens ratonis - in our minds? This sounds pretty implausible. And likewise, we have our own thoughts and sensations, not other people's, and so, barring solipsism, this is a fairly obvious instance of multiplicity.

In a debate with Richard Rorty, Umberto Eco tried to press the point that things cannot be pragmatism and convention "all the way down." A screwdriver, in some sense, shapes what we choose to do with it. Rorty disagreed and gave the unfortunate counter example that we could just as well scratch our ear with a screwdriver. Except we wouldn't, because of what a screwdriver is and what we are (or, if the point isn't clear enough, consider a razor sharp hunting knife). The world, and truth, imposes itself on how we deal with things.

I've seen this done in a few places actually. Normally the metaphor people use is one of a number line. You have 0 in the middle and positive and negative numbers extending in either direction, out to infinity. To get the imaginary numbers, imagine the real numbers as the x axis on a 2D graph. The imaginary numbers are the Y axis of the complex plain, they are pivoted orthogonal to the reals.

Just say that something has "a certain, je ne sais quoi. When you say it in French it becomes ineffable!

When Moore holds up a hand and says "Here is a hand" he is performing an act, making a declaration

One that requires having a hand no doubt.

It depends on what you mean by "empirical claim". Direct observations are obviously corroborable, whereas claims to have experienced God are not

That depends on the experience. The most famous theophanies, the Incarnation (and events related to it, such as the Resurrection, Transfiguration, and various miracles) as well as the Pillar of Fire over the Tent of Meeting all involved appearances to multiple individuals (in the latter case, an entire community). Hence, for those involved, they were corroborable.

They aren't corroborable for us, at least not in the direct sense that we can go back in time to the Sinai and see the Pillar of Fire traveling alongside the Hebrews and the Glory of the LORD filling their tent. At the same time, this is also true for virtually all historical facts. One cannot go back to 1492 to see if Columbus really did "sail the ocean blue," and we certainly cannot run multiple independent experiments to confirm this fact. Corroboration always involves piecing together signs and testimony.

Why not?

Why not what? Read them that way? Well, I suppose that if they are right, then one is missing out on something terribly important if one reads them in that sort of detached manner. Indeed, according to them what is most important.

If the question is: "why can't we take them seriously if we disregard what they are saying as being true in the sense in which they claim it is?" then IDK, that seems like the definition of not taking them seriously. When the Patristics claim that we are deluded and enslaved to sin until we turn our mind to God, that this alone is our true telos, etc. etc., it doesn't seem possible to say "well that's just a sentiment for their times," and still be "taking them seriously."

One need not be a Sufi to take Rumi seriously, but it hardly seems like one can be an atheist. Likewise, an atheist might find much to enjoy in Dante or Plotinus, but they have to at least allow them the courtesy of being deluded and wrong in order to take them seriously.

Arguments for God based on personal experience are arguments to the best hypothesis.

Yes, and I'd also add that there are different generally socially accepted criteria for what counts as "best explanation" in different societies and times and milieus.

How exactly does this differ from any empirical claims?

I just want to point out that these two views are not the same. You can indeed move on from inexpressibility to a demonstration or showing of what can't be expressed. But first (or conjointly) you can also say why, as Wayfarer suggests. Or would the claim be that inexpressibility itself can only be demonstrated, not justified?

It depends on what is meant by "justified." Plato, in Letter VII, says of "teaching" metaphysics that: There neither is nor ever will be a treatise of mine on the subject. For it does not admit of exposition like other branches of knowledge; but after much converse about the matter itself and a life lived together, suddenly a light, as it were, is kindled in one soul by a flame that leaps to it from another, and thereafter sustains itself.

But note, Plato does attempt to convey such things, and to justify them. Indeed, he produces a 2,000+ page corpus of exquisitely crafted dialogues to do so. St. Augustine has a similar view on metaphysics and a more dismal view of man's unaided reason, and yet he produced 35,000 pages of collected works, much of which deals with these same topics. Dante's Divine Comedy might be the greatest example in world literature of the attempt to convey what escapes language in image.

But if justification is taken to be synonymous with demonstration, (which is obviously a temptation if reason is just ratio) then obviously such efforts will involve "speaking where one ought to be silent." Or they would involve "art" primarily enjoyed for amusement, and not philosophy.

↪Tom Storm It's likes the arts— leads nowhere except to novel and perhaps inspiring experiences.

This denotes a very particular approach to the tradition Wayfarer is talking about though. One cannot take a Meister Eckhart, a Rumi, or a Dogen as simply conveying "novel and perhaps inspiring experiences" and take their claims seriously. Indeed, since such "experiences" generally involve the apprehension of truth, and so demand to be taken exclusively, this would be sort of a contradiction in terms. (Dante, for his part, doesn't even allow those who won't take a stand the dignity of a place in Hell; they will spend eternity following a banner that moves relentlessly and arbitrarily about the outskirts of Hell).

If these authors are simply conveying novel experiences to be surfed through, then they are, in some deep sense, fundamentally deluded. Which doesn't mean they cannot be interesting, but it does mean they cannot be right.

Well, we could always ask: "could good historical epochs always have been better if there was more prudence, justice, fortitude, and temperance, as well as faith, hope, and love?"

I think the answer is yes. There is no need to make vices into virtues.

This is an astute observation that most people don't seem to acknowledge anymore. Nietzsche pointed this out, correctly, that all good things in human history have been the product of bloody and gruesome events. That's not to say we should keep doing it for because of that, but it is worth acknowledging.

It seems to me that you could just as easily make the case that good things have overwhelmingly involved cooperation, loyalty, trust, and love. It's a selective history.

At any rate, you might enjoy Dante. He takes a lot from Aristotle, but he also has a very developed philosophy of history and sees a major unifying role for empire. He has De Monarchia, which is an explicit apology for world-empire, but these ideas are also all over the Commedia.

Hegel would be another good example, and he has some ideas about balancing particularism (perhaps through federalism and strong local governance) and a strong state. However, given he is writing in the long shadow of the Thirty Years War, he cannot seem to find it in himself to discard the post-Westphalian state system, even though his thought would seem to suggest a world-state.

But suppose we run an experiment! We offer people two choices: they can have their favorite entree from their favorite restaurant, or they can eat a plate of dog feces. People choose option A 100% of the time. Clearly, the dog feces has made their choice for them, ergo one cannot ever freely choose not to eat dog feces. QED. :cool:

I find Harris to be very interesting because there is a lot I think he gets right and a lot I think he gets woefully wrong. Of course, "goodness" relates to desires, and so to "well-being," "happiness," or "flourishing." He's right to dismiss Hume's guillotine as more or less begging the question.

But he has to ground all of morality in neuroscience because he has a pretty naive/myopic conception of metaphysics. So, for him, because we need neurons to experience good things and well-being, "goodness" is a principle of neuroscience. To my mind this is a bit like hoping to explain flight by an appeal to an in-depth analysis of the cells in the wings of animals. Sure, they need those cells to fly, but flight is not best explained in this way. Plus, the entire enviornment is equally relevant to both flight and perception, nothing generates lift or consciousness in a vacuum.

I suspect that part of the problem is that the "mythos" of scientism has long been packaged with notions of reductionism and smallism. At least for me, my education tended to always lump them more or less together. And I think this baggage follows us around long after we have decided to dismiss it, and it can often act as a barrier to understanding ideas that fall outside the confines of our model.

I recall seeing a Quora post of someone who was confused about Plato's metaphysics of eidos because "red is just light of a certain wavelength which is just photons." We might certainly find problems with Plato, but I think the move to immediately start thinking of things in this sort of way (i.e. "what are the physical parts involved.") can often be unhelpful.

If Free Will is the case, and a person's thoughts and thoughts to act come into existence at one moment in time, not having any prior cause, then this is an example of spontaneous self-causation, a metaphysical problem difficult to justify.

I am not sure if this is a helpful way to think about free action. If something is uncaused then it occurs for "no reason at all." However, are we free when we act according to what is uncaused and random?

When we act freely, we tend to think we act not only for reasons, but due to reasons we understand. If a German soldier in WWII refuses to execute civilians because it is "the right thing to do," then clearly this act must involve what lies prior to their choice: their understanding of the situation they are in, the consequences of disobedience, all that has shaped their notions of right and wrong, what they think about the innocence of the civilians, etc.

Yet their perception of the innocence of the civilians is prior to their refusal to execute them.

What is self-determining is not undetermined.

While it’s interesting to me to note that truth in other languages can hold a somewhat different set of denotations and connotations (e.g., the Ancient Greek “alethes” meaning un-concealment or un-forgotten—to my knowledge hence not easily specifying something like “the arrow’s aim was true”), I so far do think that the English notion of truth does hold the univocal general meaning just specified: conformity to the actual, and this either as a) the process of remaining aligned to that which is actual or b) the state of being absolutely conformant and hence identical to that which is actual (such that (b) can be found to be a perfected form of (a)).

Well, you mention true crime. Consider evidence, which is a sign of the truth or falsehood of various hypotheses. Likewise, for the belief that "Bonaventure is at home," we could consider signs such as "the lights at his house are on," the "car is in the driveway," etc. But for Aristotle the when we predicate the same term of some sign of a term, and of what most properly has this term (i.e. beings), we are involved in an analogy of attribution. For instance, "tuna fish is healthy" because it produces health in man. Man most fully possesses health, and food/bloodwork/etc. is related to man's health as a contributing agent, sign, etc. In one sense, the tuna is very unhealthy, having been killed and canned, but vis-a-vis man's health it is "healthy."



Yes, I think that all makes sense. Potency is "shaped" by act and we have many "levels" of act and potency. All act is in some way form. The one counterexample would be prime matter, which is said to be sheer indeterminate potency. But even for thinkers who will countenance prime matter, it is generally said to never exist on its own. It is a concept, ens rationis. So we could say all truth relates to act, although I might stick with "being" simply because it captures the same idea without ambiguity vis-a-vis potency.

What do you mean by modern thought? Presumably you're restricting to philosophers? Anglo-American philosophers? And over what time period?

I think it's a trend that you can pick up from late medieval nominalism on TBH, but 20th and 21st century Anglo-American analytic thought it probably the strongest example. Certainly it isn't a universal tendency.

From the point of view of science and particularly of AI, and over the last 40 years I've seen things move the other way. I am quite baffled by the idea that you have somebody to argue against.

I'm baffled that you're baffled. The things you mention are all still overwhelmingly underpinned by classical logic. Bayesian probability doesn't involve abandoning classical logic for instance.

This means that a parameter value which was regarded as having a true but unknown value is now regarded as having a prior distribution which is subjective. This is away from a univocal value for the parameter and quite likely a move away from the binary {True, False} to a subjective probability distribution over [0,1].

Can you explain what you mean by the bolded here? I don't get how a statistical value cannot be univocal. Surely it isn't equivocal or analogous?

To me this just seems like an inadequate mathematical model of some aspect of reality. You should be using a number to represent a degree of illumination, not a boolean value. If you want to consider the illumination in different parts of one room then you need a vector of numbers. Progress in science often follows this path. Here you can see the binary {male, female} being transformed into a nine dimensional entity.

I was not claiming that mathematical models all employ binary values. That seems to be the confusion here. I am speaking to notions of truth in the logic that underpins such models. For instance, how computation is formally defined.

Reducing knowledge to a continuous mathematical variable is still reducing it to a mathematical variable.

When was your class?

2023. But I think the problem here is miscommunication. You are speaking of non-binary variables at play in mathematical models involved in AI, not notions of truth in logic. This was a class on the philosophy of AI, not AI models.

So Aquinas talks about univocal predication and then analogical predication, and then at the end of the corpus of the article he talks about truth as it exists in intellects and truth as it exists in things. The former is univocal and the latter is analogical. But we are talking about truth as it exists in the intellect, not truth as it exists in things. It is mistaken to say that Aquinas thinks truth is analogical. Aquinas thinks that its proper nature has to do with univocal predication, "If therefore we speak of truth, as it exists in the intellect, according to its proper nature..."

Yes, truth in the intellect is most properly truth. How does it follow then that truth in arrangements of stipulated signs or formal systems, which are artifacts is also primarily truth? Aquinas speaks specifically of truth in the sense that people's words (or products of the productive arts) are adequate to their intellect for instance. This is not the same thing as truth-as-adequacy-of-intellect-to-being.

You seem to think that there are no univocal predications. You seem to think that if a monkey is an animal and a dog is an animal, then we must be using "animal" analogically, because monkeys are different than dogs. This is strange.

I don't. Is your contention that beauty is said univocally of Beethoven and horses?

Suppose a man wants to buy 100 pounds of potatoes. The farmer's scale is broken, but he and the farmer eyeball a cartload of potatoes and agree on a price fit for 100 pounds. The man gets home and weighs them. They weigh 98 pounds. "Close enough," he says. The claim is mostly true.

And at this point you interject and say, "See, this proves that weight is analogical, or is being predicated in an analogical manner." But it doesn't prove that.

I think you are largely misreading what I am saying. This is not an example where we have truth being predicated analogously. Truth is predicated analogously when we are moving in and out of the intellect, from the intellect to things, from the intellect to stipulated sign systems, etc. The ambiguity surrounding the truth value propositions such as: "the room is dark" is a result of the fact that the truth of a utterance is not the same as the truth of the intellect.

It's important to note that truth involve contrary opposition because we can say that: "Frodo is tall' is false, because hobbits are short, without thereby implying that Frodo 2D plane lacking in any height. And this is because our words are merely signs of truth in the intellect. Second, we have another dimension of truth when we speak of how well our words (or models, arts, etc.) conform to our intellect.

ou seem to think, "When 'animal' is predicated of each species of animal, it is predicated analogically because each species is not identical." Or, "When 'health' is predicated of kangaroos and daffodils, it is predicated analogically, because kangaroos are not daffodils."

I've said that one might predicate "health" of different species univocally. I said the relationship is analogical. If it weren't, then there must be a single measure by which all healthy things are healthy. Yet the measure of a healthy flower is a healthy flower, and the measure of a healthy tiger a healthy tiger, not a sort of Platonic health participated in by all healthy things.

Of course it gets tricky when we compare uncreated truth to created truth, but I have never found it helpful on these atheistic forums to stray too far into theology. I am happy to say that truth is analogical vis-a-vis the uncreated truth of the divine intellect, but when we are talking about truth on TPF we are almost certainly not talking about that. Instead we are talking about, in Aquinas' language, the correspondence between human intellects and reality. And that (created) truth is univocal.

Analogy isn't only involved in theology, except in later deflations of the notion. But I think the larger issue is that truth is predicated primarily of the divine intellect, not of all intellects. The proper measure of the human intellect is things. Thomas explains what it would mean to deny this; we end up with Protagoras, the human intellect becomes the measure of truth.

IMO, if one cuts out the divine intellect it would be better to describe truth as existing first in things virtually, as time exists in nature fundamentally but not actually for Aristotle and St. Thomas.

But see also ST I.85.5 and ST I.85.8. Aquinas certainly thinks that we understand indivisible wholes, but only through a process of composition and division. Even the act of recognizing that one's apprehension fits the reality is for Aquinas a form of combining (i.e. recognizing that one's intellectual conception is true).

Right, but the order of knowing is the opposite of the order of being. What is "best known to us" is not "what is best known in itself." I don't see Thomas as diverging radically from the tradition he is a part of (St. Augustine, St. Bonaventure, Avicenna, Liber de Causis, Boethius, etc.). Discursive ratio is the means of progressing towards knowledge, it is not the measure of knowledge. Indeed, it moves towards knowledge (and so truth) by moving from the multiplicity in the senses towards unity.

I think it’s fair to say that Habermas sees rationality as procedural, and the procedure necessarily involves language.

A pretty common position. I think Robert Sokolowski does a good job explaining the intuitions that support this position, and demonstrating the centrality of the role of language in the "Human Conversation" (our collective pursuit of knowledge), without running into the problem of reducing reason to language alone (or worse something like computation, symbol manipulation, etc.).

At any rate, such a conception of reason would seem to risk loading the dice against mathematical platonism (and Platonism for that matter) to some degree. All the problems of the "linguistic turn" come up. One cannot "get outside language" or "outside the linguistic community." If these are problems that are assumed as essentially axiomatic, then it hardly seems that one can step outside the sensible world and attain a noetic apprehension of mathematical objects when "notetic apprehension" just is something to do with language (which is grounded in communities, etc.).

By comparison:

Intellectus is the higher, so that if we call it ' understanding', the Coleridgean distinction which puts 'reason' above ' understanding' inverts the traditional order. Boethius, it will be remembered, distinguishes intelligentia from ratio; the former being enjoyed in its perfection by angels. Intellectus is that in man which approximates most nearly to angelic intelligentia; it is infact obumbrata intelligentia, clouded intelligence, or a shadow of intelligence. Its relation to reason is thus described by Aquinas: 'intellect (intelligere) is the simple (i.e. indivisible, uncompounded) grasp of an intelligible truth, whereas reasoning (ratiocinari) is the progression towards an intelligible truth by going from one understood (intellecto) point to another. The difference between them is thus like the difference between rest and motion or between possession and acquisition.

We are enjoying intellectus when we 'just see' a self-evident truth; we are exercising ratio when we proceed step by step to prove a truth which is not self-evident. A cognitive life in which all truth can be simply ' seen' would be the life of an intelligentia, an angel. A life of unmitigated ratio where nothing was simply ' seen' and all had to be proved, would presumably be impossible; for nothing can be proved if nothing is self-evident. Man's mental life is spent in laboriously connecting those frequent, but momentary, flashes of intelligentia which constitute intellectus.

When ratio is used with this precision and distinguished from intellectus, it is, I take it, very much what we mean by 'reason' today; that is, as Johnson defines it, 'The power by which man deduces one proposition from another, or proceeds from premises to consequences'.

C.S. Lewis - The Discarded Image

That is, reason has become merely ratio. And if intellectus survives, it survives as a grasp of simple axioms, the principle of non-contradiction, etc. In fact though, this is still extremely different because the idea was that all wholes could be "grasped as wholes" and that there might be gradations to a sort of noetic understandings (not the understanding had through discursive demonstrations). The sequestering of intellectus to merely the realm of axioms and "hinge propositions" is sort of the flip side of the reduction of reason to ratio.

Anyhow, the following paragraphs are less relevant but I find the application to literature interesting:

But, having so defined it, he gives as his first example, from Hooker, 'Reason is the director of man's will, discovering in action what is good'. There would seem to be a startling discrepancy between the example and the definition. No doubt, if A is good for its own sake, we may discover by reasoning that, since B is the means to A, therefore B would be a good thing to do. But by what sort of deduction, and from what sort of premises, could we reach the proposition 'A is good for its own sake' ?

This must be accepted from some other source before the reasoning can begin; a source which has been variously identified-with 'conscience' (conceived as the Voice of God), with some moral 'sense' or 'taste', with an emotion ('a good heart'), with the standards of one's social group, with the super-ego.Yet nearly all moralists before the eighteenth century regarded Reason as the organ of morality. The moral conflict was depicted as one between Passion and Reason, not between Passion and 'conscience', or ' duty', or ' goodness'. Prospero, in forgiving his enemies, declares that he is siding, not with his charity or mercy, but with'his nobler reason' (Tempest, v, i, 26). The explanation is that nearly all of them believed the fundamental moral maxims were intellectually grasped. If they had been using the strict medieval distinction, they would have made morality an affair not of ratio but of intellectus.

...The belief that to recognise a duty was to perceive a truth-not because you had a good heart but because you were an intellectual being-had roots in antiquity. Plato preserved the Socratic idea that morality was an affair of knowledge; bad men were bad because they did not know what was good. Aristotle, while attacking this view and giving an important place to upbringing and habituation, still made 'right reason' ( 6p6os Myos) essential to good conduct. The Stoics believed in a Natural Law which all rational men, in virtue of their rationality, saw to be binding on them. St Paul has a curious function in this story. His statement in Romans (ii. 14 sq.) that there is a law ' written in the hearts' even of Gentiles who do not know 'the law', is in full conformity with the Stoic conception, and would for centuries be so understood.

Nor, during those centuries, would the word hearts have had merely emotional associations. The Hebrew word which St Paul represents by Kap5ia would be more nearly translated ' Mind' ; and in Latin, one who is cordatus is not a man of feeling but a man of sense. But later, when fewer people thought in Latin, and the new ethics of feeling were corning into fashion, this Pauline use of hearts may well have seemed to support the novelty.

The importance of all this for our own purpose is that nearly every reference to Reason in the old poets will be in some measure misread if we have in mind only ' the power by which man deduces one proposition from another'. One of the most moving passages in Guillaume de Lorris' part of the Romance of the Rose (5813 sq.) is that where Reason, Reason the beautiful, a gracious lady,a humbled goddess, deigns to plead with the lover as a celestial mistress, a rival to his earthly love. This is frigid if Reason were only what Johnson made her. You cannot turn a calculating machine into a goddess. But Raison la bele is 'no such cold thing'. She is not even Wordsworth's personified Duty; not even-though this brings us nearer-the personified virtue of Aristotle's ode, ' for whose virgin beauty men will die' (o-O:s TIEpt, 1rap6eve, J.!Opcpas) .She is intelligentia obumbrata, the shadow of angelic naturein man. So again in Shakespeare's Lucrece we need to know fully who the 'spotted princess' (719-28) is: Tarquin' s Reason, rightful sovereign of his soul, nowmaculate.

Many references to Reason in Paradise Lost need the same gloss. It is true that we still have in our modern use of ' reasonable' a survival of the old sense, for when we complain that a selfish man is unreasonable we do not mean that he is guilty of a non sequitur or an undistributed middle. But it is far too humdrum and jejune to recall much of the old association.

Anyhow, a question philosophy of language has generally ignored (often deciding it belongs to some other field) is: "Why do we feel compelled to speak? Why speak at all, and why of this and not that?"

This is the question Umberto Eco puts front in center in Kant and the Platypus. I think it's also the question that comes front and center when it comes to mathematical objects (or at least if one wants to attempt to explain them in terms of language).

There is the historical question of: "why did disparate cultures all come up with terms for magnitude and multitude?" but also the more immediate question of "why do people feel impelled to use these terms so often?" The platonists seems to have some sort of answer. The more compelling rebuttal would seem to require not only showing problems with the platonists' position, but showing how else these questions might be answered.

Science, similarly to religion may be embedded in mythic understanding. What do you think, especially in relation to the concept of myth?

Sure, Charles Taylor speaks of this in A Secular Age. A dominant narrative, particularly with atheists, is that contemporary secular culture and scientism is just what you get when you apply reason to the world without superstition. He calls these "subtraction narratives." His point is that these subtraction narratives tend to ignore all the positive ways secularism was constructed, and indeed that some of its core tenants grow out of Reformation and Enlightenment era theology quite explicitly.

We could also consider here the secular "religious" holidays of the French Revolution, or more successful attempts since to create secular "festivals," or to turn religious holidays into secular festivals (e.g. the transformation of American Thanksgiving into secular Thanksgiving/Black Friday, or Christmas into a festival primarily of decorations, gifts, consumption, and a more amorphous "Christmas spirit" of good cheer and benevolence.)

Here is a related passage from C.S. Lewis:

If we could ask the medieval scientist 'Why, then, do you talk as if [inanimate objects like rocks had desires]?' he might (for he was always a dialectician) retort with the counter-question, 'But do you intend your language about laws and obedience any more literally than I intend mine about kindly enclyning? Do you really believe that a falling stone is aware of a directive issued to it by some legislator and feels either a moral or a prudential obligation to conform?' We should then have to admit that both ways of expressing are metaphorical. The odd thing is that ours is the more anthropomorphic of the two. To talk as if inanimate bodies had a homing instinct is to bring them no nearer to us than the pigeons; to talk as if they could ' obey laws' is to treat them like men and even like citizens.

But though neither statement can be taken literally, it does not follow that it makes no difference which is used. On the imaginative and emotional level it makes a great difference whether, with the medievals, we project upon the universe our strivings and desires, or with the moderns, our police-system and our traffic regulations. The old language continually suggests a sort of continuity between merely physical events and our most spiritual aspirations.

The Discarded Image

But of course, this shift did not come about by "removing superstition" alone, as it is often presented (nor did the "new science" immediately result in any rapid advance in technological progress or living standards-Europe's "Great Divergence" from Asia"- for another few centuries). Sometimes you will hear it presented this way though way: "oh, people spoke of the inclinations of rocks before because Aristotle thought rocks fell because they wanted to," (which is, of course, false, he didn't) "but then modern science came and got rid of all that bad baggage and gave us a "clean" view."

Yet this isn't what happened. The idea of the entire universe "obeying laws" was originally created with divinely issued laws in mind. It was created because the Aristotelian idea of a word populated by (relatively) self-determining natures seemed to encroach on divine sovereignty, as did Patristic notions of man attaining freedom and deification through the perfection of the virtues, which returned to him his original divine nature (Christ the God-man being ultimately, the preexisting type of Adam, and not vice versa).

Given some other popular assumptions at the time, any freedom for creatures came at the expensive of freedom for God. Even "only doing what is good" was seen as a limit on divine freedom. Thus, goodness had to be the result of a "moral law" dictated by the inscrutable divine will, while the behavior of natural things had to be the product of a "natural law" likewise dictated. Things don't do what they do because of what they are, so much as everything happens as it does according to inscrutable fiat. Man's reason is too damaged by the Fall to fathom the causes of nature (and this assertion unfathomable of "brute facts" at the center of all things still finds a home in atheistic scientism). The resulting image of Providence is thus far more totalizing (and we might say totalitarian) than that of the Patristics, for instance.

This is key in that various flavors of scientism have both a mythos (i.e. "this view is what results from the triumph of reason and the discarding of superstition, e.g. the "New Athiests") but also a number of dogmas that go along with that vision. For instance, phusus, natures, being discarded in favor of "eternal natural laws" and initial conditions (a major philosophical extrapolation from mathematical physics, rather than "what the math tells us about being.").

But there are different forms of scientism. You have your Camus, Nietzsche, et. al. inspired "Overcomers," who can have a vested interest in smallism and the classical view of evolution as "blind mechanism," and the expulsion of all teleonomy as illusory, since this makes the world properly abusrd, while at the same time placing all moral and aesthetic judgement safely on the "subject" side of the dualist ledger (allowing man to be God within the confines of his own subjectivity), whereas others, e.g. Sam Harris, end pushing to ground almost everything in "neuroscience" (goodness and beauty, and potentially even truth being principles of neuroscience best explored via neuroimaging).

In either case the Problem of the One and the Many seems to haunt all the mythos. You see a constant floundering between a sort of bigism (there is just one thing, the universe, and everything traces back to the inscrutable brute fact of the Big Bang) and smallism (everything is made up of fundamental parts and is reducible to them).Sapolsky's Determined is an excellent example here, because in his efforts to disprove "free will" Sapolsky constantly flips back and forth between bigism and smallism, whenever one or the other helps his arguments (i.e. "you cannot be a [relatively] self-determining whole because your behavior relates to individual neurons (parts), but you also cannot be self-determining because all efficient causes can be traced back forever, to the brute fact of the Big Bang.") There is no via media available here because a framework of "laws and obedience" is very much baked into the mythos, as is the reduction of reason to mere ratio (dividing and composing in propositional knowledge), which pulls out the epistemic ground for any true wholes and seems to make nominalism inevitable.

They need to define their terms. There is a fairly controversial, obvious sense in which propositions exist. "Exist as 'abstract objects?'" Then what said is probably something like what is going on. They might even be agreement and just dealing with ambiguity and equivocation.

"Exist mind-independently" is also unhelpful if undefined, and the same goes for "objective." There is an obvious sense in which propositions cannot be mind-independent (we are speaking and thinking of them) and on the common dictionary usage of "objective" they would seem to exist "objectively," yet often "objective" is used to denote something like "noumenal."

So they might be in disagreement about a great many things. The problem with going off the SEP summary sentence ITT is that it does not define its terms. For instance, I would imagine that many Platonists (capital P) would deny that anything has the sort of "mind-independent" existence that some contemporary philosophers would take them to be arguing for. That is, this "mind-independence" would be a bad definition, since for anything to be anything at all it has to have some intelligible eidos, although surely they also do not mean "rocks disappear when no one is looking at them or thinking about them," either.

I think Plotinus is informative since he brings up this line of reasoning and uses it to reject truth as simple correspondence. If truth is the correspondence of phenomenal awareness to a sort of noumenal being, then one can never know truth because one can never "step outside of experience," in order to compare the two. But Plotinus (and I see him as following Plato here) simply rejects this notion of truth and substitutes what might be called an identity theory.

Forms, then, are the very ‘whatnesses’ of things that enable them to be anything at all. Without such identities or whatnesses, without forms, there is no truth, nothing is anything, and there is no reality...

Here, then, we have Plato’s answer to the age-old question, τι τὸ ὄν, “What is being?” Being, τὸ ὄν, that which is, is εἶδος, form, the looks in things that are there to be seen by intellect and in virtue of which anything has any identity, any intelligibility, and hence any reality at all. Henceforward, not only in Plato but throughout the philosophical tradition we are considering, οὐσία will mean not simply ‘reality’ in an unspecified sense, but, more precisely, reality qua that which is intelligible. Being, as what is given to thought, consists of ‘looks,’ that is, intelligible whatnesses, identities, ideas, that show up
in varying connections and contexts, and thus lend a share of intelligibility, and hence of reality, to the world around us...

But neither is being ‘mind-independent,’ as if it were prior to and could exist without, or in separation from, intellect. There is no thought without being, but neither is there any being without thought. In order to avoid subjectivism, it is necessary, as Plotinus says, “to think being prior to intellect” (V.9.8.11–12), but this is only because in our imperfect, discursive thinking they are “divided by us” (V.9.8.20–21), whereas in truth they are“one nature” (V.9.8.17). Neither thinking nor being is prior or posterior to the other, for, just in that thinking is the apprehension of being and being is what is apprehended by thought, they are ontologically simultaneous: “Each of them [i.e., each being] is intellect and being, and the all-together is all intellect and all being, intellect in thinking establishing being, and being in being thought giving to intellect thinking and existence … These are simultaneous [ἅμα] and exist together [συνυπάρχει] and do not abandon each other, but this one is two, at once [ὁμου] intellect and being, that which thinks and that which is thought, intellect as thinking and being as that which is thought” (V.1.4.26–34).

Eric Perl - Thinking Being

I find this to be almost the inversion of the modern supposition that we must be skeptical because we cannot "get outside thought." This is why mathematical knowledge, dianoia, occupies the highest portion on the Divided Line below the Forms themselves. Noesis (immediate intuition, apprehension, or mental 'seeing' of principles) is not "stepping outside thought to thoughtless reality" either.

Didn't I just tell you that what I am doing is expressing skepticism, and not making claims about what does and doesn't objectively exist?

Ok, that makes more sense. I had thought these were supposed to be good reasons for rejecting platonism, not simply not affirming it.

However, it does seem like you have made "objective knowledge" apply to essentially nothing. Mathematics, the natural sciences, world history, the rules of chess, presumably metaphysics as well, will not qualify. And it seems to me that even the notion of the existence of any reality "behind the veil of appearances" also falls victim to this lack of objectivity. It too might be something that only appears like a real distinction, but perhaps it isn't e.g. Shankara, there is only Brahma, even maya.



There is "logic" as formal systems of the sort you listed, but also logic as "good reasoning" more generally (rhetoric was long part of logic), "logic" as the "rules of thought," the "discourse of the soul," and "logic" as the logos of the world, its intelligibility and rationality. I would assume platonists often are looking to some of the broader conceptions instead of a narrow, formal one.

I don't think it makes any sense to say that they platonistically exist in New Foundations but don't platonistically exist in ZFC. We can only take the approach of mathematical fictionalism and say that they exist according to New Foundations but not according to ZFC.

You're probably right in many cases, but I have seen the systems themselves proposed as platonic objects. So both can be right because both are really just descriptions of a mathematical object. For instance, Tegmark's Mathematical Universe Hypothesis, which is fairly opaque on some of the more philosophical elements, takes a very broad view of mathematical objects.

Tegmark brings to mind another view, ontic structural realism. Things just are the math that fundamentally describes them. This seems to me to be, if not a type of platonism, then something quite close, and it seems not unpopular in the physics community (although certainly not a majority view or anything like that). The question: "which sorts of mathematical objects exist" is various answered as "all of them" or "just the computable ones" (with efforts to try to justify the latter position being, IMO, unconvincing).

So rather I am expressing skepticism towards those who would claim mathematics is 'objectively real', and also pointing out the contradiction in the term 'mathematical platonism'.

What contradiction? The only one I've seen is that "since math is a sui generis human creation that doesn't exist "objectively " then it doesn't exist objectively." Yet this is just assuming the conclusion. At best you've argued for a sort of nescience on this question, but skepticism and agnosticism are not the same thing as rejecting a thesis.

Note that I am not saying that science shows us what is real, rather it seems to heavily suggest the existence of an underlying reality because it is able to make models of how that reality works to a degree that is at least accurate enough for our human endeavors.

Ok, why can't this involve numbers, which are essential to modern science? Can we infer what biology and evolution tells us about how our sense organs work in some way corresponds to reality, but not that the math that underpins these finding does? Why is that?

The core of what I'm saying is that, as Plato argued, it is very difficult to even access the reality that underlies our world of sense experience, let alone make statements about this reality.

Your position seems far more similar to Locke, Hume, Kant, etc. To be sure, Plato acknowledges a distinction between reality and appearances, but he does not suppose that reality is some sort of noumenal "reality as divorced from all appearances." Indeed, his supposition is that threeness, circles, etc. are more real than the world of sensible appearances because they are more intelligible/necessary/what-they-are. This is, in an important sense, the exact opposite of supposing that reality is the world with all appearances (including intelligibility) somehow pumped out of it or abstracted away.

Sure, but he is firm that this is not truth properly speaking.

No, he is firm that dividing and composing is where truth is known as truth (for us). The paradigmatic knowledge is God's knowledge,which is not discursive. So while he does prioritize "truth as known in judgement" in several places (e.g., Q16 of ST, the Disputed Questions Q1 A3), this is as an inversion. In the Questions for instance, he inverts the entire order of things, putting the truth of things as respects their conformity to the divine intellect as secondary, and the truth of the intellect composing and dividing as primary, even though in the same text he has the former as the principle of the latter. (Here, he lists many ways "true is said.")

To be honest, I find his answer in the Questions here pretty thin. It relies on the idea that our intellect needs to make something "its own" so that it differs from the thing known and isn't simply identical with it. However, it seems obvious that this is at least somewhat true in sensation as well, since the sight of an apple is not the same thing as its being. But I have long been suspicious of the general scholastic tendency to suppose that only conscious judgement can be in error, never the senses, because this seems to be a rather artificial separation of how consciousness actually works, and conditions like agnosia seem to involve error at the pre-conscious level.

Anyhow, he has a better answer in ST; truth is primarily spoken of in terms of judgement (composing and dividing) because this is where we know truth as truth, and the knowledge of truth as truth is a perfection. I can live with that. Yet: 'Truth therefore may be in the senses, or in the intellect knowing "what a thing is," as in anything that is true; yet not as the thing known in the knower," (Q16 A2).

It seems to me that this is a perfection for us. There is not division in the Divine Intellect.

I think what Thomas is motivated by the fact that we generally speak of beliefs, statements, likenesses, etc. being true or false, not things. It's a good motivation, although I am not sure if the solution, particularly the earlier one, is right, unless the idea is that the order of judging and the order of being are inversions of each other.

The univocal nature of truth (i.e., the state of being true) is that of conformity to some actuality—truth hence has this meaning in all cases—this either as a process of conforming to the actuality, which requires duality between that which conforms and that which is conformed to, or else as a state of being fully conformed to the actuality, which implies a nondualistic format of truth wherein there is only the law of identity (A=A) to specify the truth concerned.

What do you think about cases where we can speak truthfully about potency or what is not? For instance:
"Joe Biden could have stayed in the 2024 election."
"I can learn Italian, but I currently do not."
"Joe Biden did not win the 2024 election."
"Dogs are not reptiles."

There is also the issue of authenticity, particularly as it is often applied to personal freedom. When we are not being "true to ourselves" or "being our true selves" the issue is precisely our actions (actuality) have failed to conform to something that is true, presumably of our nature, but which is as yet only potential.

While it’s interesting to me to note that truth in other languages can hold a somewhat different set of denotations and connotations (e.g., the Ancient Greek “alethes” meaning un-concealment or un-forgotten—to my knowledge hence not easily specifying something like “the arrow’s aim was true”), I so far do think that the English notion of truth does hold the univocal general meaning just specified: conformity to the actual, and this either as a) the process of remaining aligned to that which is actual or b) the state of being absolutely conformant and hence identical to that which is actual (such that (b) can be found to be a perfected form of (a)).

The English notion of truth is bound up in where Anglo-American philosophy has gone for the last 150+ years or so. So, for instance, despite philosophy having a long history different types of truth (e.g., logical vs ontological), the IEP article focuses entirely on more recent univocal theories.

I would agree that all truth has something to do with a certain sort of conformity or adequacy. There are not sui generis, equivocal sorts of truth. The same is true of goodness and beauty. The good might be "that which all things seek," and yet it is not always predicated univocally such that we can set up some sort of "moral calculus." Likewise for an "aesthetic calculus."

The truth of formalizations of truth is rightly called, and it is binary. I don't think it makes sense to call this a sui generis artificial truth though.

Anyhow, if one follows Aristotle's idea that "being is most primarily said of substance (things)" I can see a strong argument for it being things which are primarily "good," "beautiful," "true," and "free." Just as a dog can be blind and there is never "just blindness," we don't have "just truth."

Now thought, belief, or apprehension would seem to be activities of the intellect, and so if intellect most properly is true than the truth of these is parasitic on the truth of the intellect. And the truth of utterances or written statements would seem to be parasitic on thought (although there are complications here).

Truth is a difficult special case though because we don't generally speak of rocks or trees "being true," but rather thoughts, sentences, etc. about them being true. At the same time, the truth of what can be said about things is presumably prior to our speaking. I'll admit, I am not really sure how this might be resolved saved for the appeal to the Divine Intellect. But, even cutting out the divine intellect, it seems that there must be a distinction between "ontological truth" and "(epistemo)logical truth."

Aquinas explains what it would mean:

Exactly, the predication is analogous, not the term. There is not an analogy between two different Goods (plural).

But if "adequacy of thought to being" (truth) has no clear meaning, then we're up a creek without a paddle.

Is the idea here: "either something is predicated univocally 'we're up a creek without a paddle?'"

This seems problematic to me. Is "good" or "beauty" always predicated unviocally. If not, is ethics and aesthetics impossible?

And my contention is that our predication of truth cannot become analogical, for the reasons already set out above. And as I said, I don't think you will find any philosophers claiming that we should use "truth" analogically.

This seems like a hard contention to support for Thomas when he uses the oft cited example of analogy vis-a-vis health to explain truth throughout the Disputed Questions (and quotes Avicenna is support of this frequently).

There is one Truth, because there is one, simple Divine Intellect. Yet, "the truths which are in things are as many as the entities of things" and "the truths said of things in comparison to the human intellect is in a certain way accidental to them because [on the supposition that there were no men] things in their essences would still remain" (Disputed Questions, Q1, A3, R). Just as health is primarily in the healthy body, and secondarily in urine, Thomas speaks of truth being primarily in the Divine Intellect and then in a descending order of things. For example, with man's knowledge of natural things it is those things that are the measure of man's knowledge.

No it's not. Aquinas is explicitly talking about univocal predication. It does not follow that health is being predicated analogically just because health for the kangaroo and health for the daffodil are not circumstantially the same. If univocity meant such a thing then univocalists could not have common nouns at all. "...when anything is predicated of many things univocally, it is found in each of them according to its proper nature; as animal is found in each species of animal." The predicate 'health' is not species-specific, just as the predicate 'animal' is not specific to each species of animal.

Of course health can be predicated univocaly of all healthy organisms. However, health in each does not have the same measure. It's a One unequally realized in a Many. Just as beauty might be predicated of many beautiful things, but the beauty of Beethoven is not the beauty of a beautiful horse (this is an analogy of proper proportionality not attribution). Note that in the passage you are quoting Thomas is referencing univocal predication as respects the way which all truth is one (in the Divine intellect) as opposed to many (unequally realized in a multitude, in Avicenna as per prior and posterior).

But you are just speaking about truth as analogical without specifying any circumstance at all. If you think it is just certain predications that are analogical rather than the concept of truth itself, then you have to say which predications of truth are analogical and which are not.

That varies by the proper measure. The measure of a man is man, the measure of horse is horse. A sentence is not the proper measure of truth for everything. There is not one measure for all "created truth," except in the sense that all ultimately share an ultimate principle and cause.

Having the truth of sentences (their measure) be the same as the truth of anything and everything seems like the exact opposite of the idea in play. IMO, beliefs are not reducible to collections of sentences, but they can certainly be true or false, and seemingly more or less adequate. Models and imitations are not composed of sentences, but they can be more or less "true to life" or "true to form," etc.

Of course, 20th century philosophy of science, the "Received View" and its decedents, put great effort in trying to reduce scientific theories to sentences precisely because of a refusal to acknowledge that the truth of speech and writing (artifacts) are necessarily parasitic. One does not have truth without a knower in the same way one cannot have a fast movement with nothing moving.

And my contention is that our predication of truth cannot become analogical, for the reasons already set out above. And as I said, I don't think you will find any philosophers claiming that we should use "truth" analogically.

Aquinas, Avicenna, etc. say this explicitly. On your view, how is True a transcendental, yet always predicated univocally?

E.g., Q. 16 of ST

"For a house is said to be true that expresses the likeness of the form in the architect's mind; and words are said to be true so far as they are the signs of truth in the intellect." Urine and blood-work are healthy as signs, but then words are true as the intellect is true? I don't think so.

Is a house true to the architect's intent in a manner that is binary? No doubt, the sentence: "This house was built to your specifications" will be either true or false as a sentence, although obviously it can also admit of many qualifications. "Yes, the house is mostly how I planned it, but we had difficulty with the intricate skylights in the entry hall and had to simplify them." But the idea here is not that it is only sentences about the house that can be true or false.

Lies are another interesting case because some, in telling a lie (lack of conformity of words to mind) might actually end up telling the truth (conformity of words to reality). Misspeaking as well, since here the issue is sentence's truth as conformity to the intellect (which may or may not be adequately conformed to the "truth in things.")

E.g.,

What is a basic tension in Aristotle’s affirmations concerning the relation between being and the true, i.e. the tension between the assertion that each thing is related to truth in the same way as it is to being and the assertion that being-as-true (ens ut verum) is a kind of intramental being that falls outside the science of metaphysics, is part of a synthesizing program in Anselm’s treatise De veritate, where the propositional truth, ontological truth, and moral truth are all explained, in an integrative effort, under the aegis of the basic concept of ‘rightness’ (rectitudo). Anselm’s definition was important in early attempts in the medieval doctrines of the transcendentals to relate the true that is convertible with being with the truth of the proposition. Gradually, the definition of truth as the ‘conformity of the thing with the intellect’ (adaequatio rei et intellectus) rose to hegemony, which has the advantage of making explicit the constitutive relation with the intellect, but threatens to make transcendental truth depend upon actual cognition...

The fundamental dimension of transcendental truth as an openness of being in its intelligibility to cognition, which Aquinas had identified in De ver., is also clearly expressed in Duns Scotus’ reflection on truth in his commentary on the sixth book of the Metaphysics. After having declared that all truth related to the divine intellect is studied by metaphysics, he continues to distinguish three senses in which the human mind is related to truth, of which only the first is studied by metaphysics: namely when a thing is said to be true because it is able to manifest itself to an intellect capable of perceiving it, of which Scotus explicitly says that it is convertible with being. The other senses, according to which a thing is true because it is assimilated to or known by the human intellect, fall outside the scope of metaphysics and belong to logic.

By contrast, there is Wittgenstein's On Certainty, which has generally be read as arguing to deflationary (and been widely influential in this direction). There, truth just is part of a language game. But this comes out of the idea that propositions are the bearers of truth.

They're both tools for modeling an inferred underlying reality. But they themselves are human creations, accurate enough for our human purposes.

Yes, you seem to be asserting this as a premise and then arguing from there. But this is to assume as true the very thing you're setting out to prove, that platonism is false.

What's the argument for mathematics being a sui generis human creation unaffected by the reality of multitude or magnitude? What caused us to create it? If it's useful, why?



To say that these questions are unanswerable suggests nescience, not one answer re platonism being supported over the other.

Neither am I, as far as I am aware

You certainly seem to be. Your claim is that, for something to be properly "real" it must exist wholly outside appearances. How is this not defining reality in terms of the noumenal? For all those following Parmenides, Plato included, there is no reality as totally divorced from appearances and intelligibility. Thought and being are two sides of the same non-composite whole.

If someone were to create a gigantic effigy of a flying spaghetti monster, would that suddenly make the flying spaghetti monster real?

Do you think making a statue of a fictional character makes them real? I don't. Yet is chess fictional? Is world history fiction? Temperature? Dates?

Scientific theories and paradigms are human creations. Yet if these are thereby fictions, then your appeal to "inferring reality from science" would amount to "inferring what is real from fiction."

I don't know if I agree with your diagnosis that the opposition to Platonism arises from 'subject-object metaphysics'. I think it goes back to the decline of Aristotelian realism and the ascendancy of nominalism in late medieval Europe. From which comes the oxymoronic notion of mind-independence of the empirical domain, when whatever we know of the empirical domain is dependent on sensory perception and judgement (per Kant). Hence those objections in that passage I quoted, 'The idea of something existing “outside of space and time” makes empiricists nervous'. Anything real has to be 'out there somewhere' - otherwise it's 'in the mind'. That is the origin of subject-object metaphysics.

:up: :100:

Yes, the philosophy of Plato does not seem to be commensurate with modern subject-object dualism. It seems even less applicable to later Platonists, such as Plotinus, St. Augustine, or St. Bonaventure.

Nominalism seems to me to be the larger issue and I think it has generally been nominalism that has motivated to errection of subject-object dualism, rather than the other way around (although obviously the influence is bi-directional).

I think the equivocity attaches to the term 'good' rather than to the truth value, but even an assertion utilizing analogical equivocity must have a determinate and assertable form. If it doesn't then there is not any unitary thing being asserted.

Peter Redpath makes a pretty convincing argument that it is never our terms that are (properly) analogical for St. Thomas (obviously when we equivocate we do have ambiguous terms). It is rather the predication of the term that is analagous.

Consideration of analogy and univocity vis-à-vis predication should focus on how we relate definitions/predicates to subjects, as opposed to considering concepts and definitions themselves to somehow "be analogous.” That is, for St. Thomas, analogical predication is primarily about judgements and relations, and only secondarily about the terms that are being related.

For example, when we say “good” of God, we are involved in analogical predication, since the manner of God’s being cannot be directly compared to the being of creatures. However, this does not mean we should take the predicate “good” to be “analogical” here, as if the “goodness of God” is somehow a loosely related to what we generally intend by the term “good.” Indeed, if God is “Goodness itself,” (i.e. that by which all things are good— https://www.newadvent.org/summa/1006.htm) it is unclear what it would mean for "our concept of goodness" to be an “analogy” of true goodness. If the “good for man,” the fulfillment of our telos, lies in the contemplation and adoration of God, there is a sense in which God’s goodness must be the paradigmatic example of all goodness, even if we, as finite creatures, can never fully understand goodness as it is univocally predicated of God.

Mistaking the “analogy of predication,” (i.e., how a term applies to a subject) for an “analogy of concepts” (i.e. what a term means) seems to risk opening the door on a pernicious slide towards equivocity, since the predicates we are working become ambiguous themselves. One example of this might be found in Luther’s response to Erasmus’ critiques of his understanding of predestination, to which Luther replied:

”If it is difficult to believe in God’s mercy and goodness when He damns those who do not deserve it, we must recall that if God’s justice could be recognized as just by human comprehension, it would not be divine.”

The issue here is not, of course, the claim that we might be capable of misunderstanding God’s justice. This is true. Rather, it is the claim that God’s goodness is inaccessible to us; that it would not be divine goodness if we recognized it as "goodness". Yet it is easy to see how the move towards such a position might be enabled if we begin to think of the term "good" in "God is good," as being itself analogous. But the good car is "most choiceworthy" of cars, just as God is "most choiceworthy" without qualification.

So, my contention would be that truth doesn't need to become analogical, merely our predication of it. When we modify ambiguous statements, we are making it more obvious how the term relates to the subject, not making it clear which term we are "really" using. Analogy is about how things relate.

The question for the equivocity of truth is this: if the first statement is not meant to be true in a univocal sense, then is it possible for the respondent to disagree with it? To agree? To even understand what is being said?

Sure, we can understand it. We can also have questions about how "great" is related to "the day." Just as "Frodo is tall" can be true if tall relates to him having any height at all (to having an extended 3D body), but false in the sense that "Frodo is taller than average for the humanoid beings of Middle Earth." The question is how the propositions relates to the adequacy of thought (and language) to being, or language to thought.

Again, the reduction of all knowledge to discursive knowledge plays a role here to. Language is often ambiguous for the sake of brevity, but thought can be unclear too. This gets back to Aristotle's distinction:

-Asytheta: truth as the conformity of thought and speech to reality (whose opposite is falsity); and


-Adiareta, truth as the grasping of a whole, apprehension (whose opposite is simply ignorance).

It is worth noting that Aquinas sees truth in a largely discursive manner:

In a certain sense yes, it is in discursive knowledge that we have judgements whose opposite is falsity as opposed to ignorance. However, he often seems to follow the Neoplatonic camp in elevating the primacy of simple apprehension of wholes as wholes.

And this is in Aristotle too, knowledge of principles is what allows us to know the Many through a One. It's what makes science possible, since (in Aristotle's eternal universe) there can be an infinite number of causes but not an infinite number of unifying principles. I see this largely jiving with these sources I mentioned before:

In Ad Thalassium 60, St. Maximus the Confessor argues for the superiority of unified and direct experience, as opposed to discursive reasoning/knowing. Similarly, in Philosophiae Consolationis (4.6), Boethius argues that reason is to the intellect as time is to eternity, and what “circle” is to “center.” This is because it is “proper” for reason to be “diffused” (diffundi, i.e., scattered or spread) about many things, and then to gather from them a single cognition (i.e., unifying the “Many” into a “One”). Pseudo-Dionysius makes a similar point, (De Divinis Nominibus, 7.2) claiming that souls have rationality insofar as they “diffusedly encircle” (diffusiue circueunt) the truth of multiple existent things. Conversely, the intellect considers one simple truth and grasps the cognition of a whole multitude in it.

If science was just logic, and it had to deal with univocal predication, this unifying process would be frustrated.

In proof of which we must consider that when anything is predicated of many things univocally, it is found in each of them according to its proper nature; as animal is found in each species of animal.

Right, yet "health" for a kangaroo is analogically related to "health" for a daffodil. They do not share the same measure. The relation of the term to the predicate is the same though when we want to speak about the health of different organisms in some overarching sense. We do not have an ambiguous term when we say "it is good for all organisms to be healthy."

It is inferred that there exists our world of sense experience, and a reality underlies it. Science has gone a long way in confirming this, showing how our senses mislead us, and only show us the tip of the iceberg.

Ok, but you didn't answer how this "reality" can be inferred "by science," but numbers absolutely cannot be. It seems to me that the empirical sciences only ever deal with phenomena.

Further, can we do physics, cognitive science, or biology without mathematics? More importantly, you haven't given any answer for why or how ratios are useful if they don't *really* apply to or exist in your noumenon. If the noumenal isn't the sort of thing that can be accurately described by number and ratio (we have many things like this in the world of phenomena) then why is it "useful" to describe them that way anyhow? Shouldn't the usefulness of mathematics in science lead us to "infer" that it says something about reality?

It just seems strange to me to appeal to all the ways in which science shows our senses can be misled, when those same sciences often rely on mathematics to point out these illusions, but then to turn around and say that the math you used to discover the illusions (and so to infer their "reality") is itself illusory. And of course any corrections to perception made by "by empirical science" are also discovered through the senses, so if the senses and intellect "mislead us," they're also responsible for correcting this.

It seems that at best you're arguing for nescience: "we can never know if numbers are *really* in the noumena with total certainty." But your positions seems to require actually demonstrating that there is no good reason to infer that ratios/mathematics apply to "things-in-themselves." Having some avenue for skepticism is not enough, people can also doubt that there is any reality that is distinct from appearances (e.g. solipsism, subjective idealism, etc.), but clearly you don't think this is good grounds for accepting that reality is just appearances yourself.

(Note: both noumena [plural] and things-in-themselves imply plurality, number—this is why people who want to go along with Kant's distinction normally speak of simply "a noumenon.")

It is pretty much the central theme of Plato. It's not that reality is cleaved, but that we do not experience reality - only a reflection of it. That's the cave.

Plato makes a distinction between reality and appearances. He does not make a distinction between appearances as "subjectivity," and reality as the "objective/noumenal"—i.e., reality as "things-in-themselves" as set over and against appearances. This Kantian division makes no sense given Plato's philosophy of appearances and images as participation. Kant's view requires the presuppositions of modern representationalism, i.e., that "what we experience" are our own "mental representations of ideas" and that such representations are "what we know" instead of "how we know." The later Platonists allowed that "everything is received in the manner of the receiver," but not that things' appearances are disconnected from what they are (i.e "act follows on being" and "appearing" is an act of the subject of predication).

For instance, Plato's Good is absolute. The absolute is not reality as separated off from appearances. It must encompass all of reality and appearances to be truly absolutely. Thing's appearances are really how they appear. Likewise, the transcendent Good isn't absent from the very finitude it is supposed to transcend. This would make it less than truly transcedent.

It seems like a lot of people, when it comes to philosophy, think "objective" is a synonym for "noumenal." But this is certainly not how the term is employed by many philosophers, and this leads to all sorts of confusions, like the idea that an "objective" goodness or beauty is somehow one that is wholly absent and disconnected from experiences (Sam Harris has this misreading of the Platonic Good in The Moral Landscape for instance). In which case, no wonder such ideas seen farcical. On this misunderstanding they are incoherent, the objective Good must be, by definition, "good for precisely no one." But Platonic eidos (forms), as the term's usual connotations in ancient Greek suggest ("shape," "something seen") are not unrelated to, or absent from, appearances—a reality as set apart from appearance.

I think the word 'reality' is a misnomer here. Chess is something we made up. Would you accept it if people were arguing for the reality of the flying spaghetti monster?

Presumably, the latter is an intentional fiction created to critique religion. It is one thing to claim that Homer's Achilles is a "fictional character." It is another to claim that the Iliad doesn't "really exist" because Homer wrote it. Do airplanes also not exist because they are the invention of man? States? World history? Chess?

I think a view that commits us to claims like: "there are no objective facts about what constitutes a valid move in chess," or "the proposition 'Kasparov is a better chess player than the average preschooler' is one with no truth value because it refers to the "subjective" game of chess," has serious deficits. Does "the Declaration of Independence was signed in 1776" also become subjective because our calendar system is the creation of man? But then temperature would also have to be subjective because it involves both man-made scales and measurement from particular perspectives.

Yeah, why answer a difficult question when we can just engage in question begging? And if everyone just assumes the asserted conclusion is right, this will prevent any skepticism or charges arbitrariness!.

Usually the non-binary response will be an attempt to distinguish different parts of the day instead of collecting it into a single whole.

This works sometimes. I don't think it always does; that is, we cannot reduce thought down to "atomic propositions."

But even if we can, does this mean the higher level statement has no truth value at all?

Of course, there is also the issue of the adequacy of language to thought and experience and the true unity of composites described under one name.

But is this a matter of the univocity of truth or of the ambiguity of language? And is the LEM being rejected if the truth-value is not binary?

Both IMO. Language involve analagous predication because being involves analogy.

I don't see how LEM is directly at stake. LEM is defined in terms of negation and negation and affirmation are contradictories. If we say "it is dark outside" is true, then this entails that it is not "not dark" according to however "dark" is used in the first instance.

"I took a magnifying glass to every part of your vehicle and found a squeaky axle. Therefore I will not drive or trust it."

A fair characterization. But I think the view of truth as related primarily to isolated (often "atomic") propositions has a wide reach even outside of those who go all the way over into deflation. It affects a lot of analytic thought.

Okay, so how would you characterize the view you take exception to?

Here is one based on a class I had on the philosophy of AI:

Truth is something that applies to propositions (and only propositions). All propositions are either true or false. If this causes issues (which it seems it will), this is no problem. All propositions are decomposable into atomic propositions, which are true or false. Knowledge is just affirming more true atomic propositions as respects some subject and fewer false ones. Thus, knowledge can accurately be modeled as a "user" database of atomic propositions as compared to the set of all true atomic propositions.

"Artificial" seems to like the key word to apply here.

Alternatively, there are all the deflationary approaches, which often make some of the same assumptions, particularly that truth is primarily about propositions (or more broadly "how a community uses language.") There is the same issue here of missing the "adequacy of thought to being."

If I understand what you've written, you and I agree that we don't generally know the world as a bunch of propositions.

Exactly, and not all knowledge is discursive knowledge. It's a sad philosophy that has to look at the climax of Dante's Commedia in Canto XXXIII of the Paradisio, his appeals to the inadequacy of language and memory, and say "well he's just sputtering nonsense." And it's just as sad to have to say something like "we can appreciate the words but not its rational content," since the Comedy is one of the very best (IMO the best) instances of philosophy breathed into narrative form.

Plato says something similar in Letter VII. He sort of explains why he uses images, dialogues, and symbolism instead of trying to write something like a dissertation—because what he wants people to understand cannot be communicated that way.

This point of view is very congenial to yours, I would think, since Rödl is doubting whether "p" -- a proposition -- could possibly do the things, all by itself, that formalism says it can. A thinker is required.

Well, according to narrow views of formalism there is very little it can do. It's just the rules, and an AI can do "logic" as well (probably better) than any man. But of course people always end up equivocating on this extremely narrow definition because if that's all logic was it would be completely uninteresting. What we really care about when we read about developments in formal logic is why people think these developments are worthwhile.

Not quite. Think of it in terms of Frege's "force" as equivalent to (one sense of) "assertion". The question is then: How does the "content" (of the force/content distinction) make itself known independently? If "p" is different from "I think p", how exactly does p come to be present to us? This quote from Rödl captures the problem:

I've only read Rödel on Hegel. This is the sort of thing that might get resolved with the distinction between objective and subjective logic, but I don't know how much he runs with the Logics.

The first: Yes.

The second, no. My point is that it is not only or even primarily propositions that are true or false. We have beliefs that can be true or false. Presumably, even people who cannot speak have beliefs. We have theories that get falsified.. We have models that can be more or less true to what they model. Etc.

Propositions cannot be both true and false without qualification. However, we can have propositions that make statements about how true something is to some ideal. "This is a good car." Does this reduce to a binary? I don't think so. Is it simply not truth-apt? I don't think this works either, because a car that won't start is in an important sense not a good car. It isn't true to its purpose.

The same is true for "its dark outside." Darkness is contrary, but the adequacy of thought to being here is contradictory? No doubt it wouldn't make sense to say it is both dark and not-dark out without qualification.

And to say that something is not-black is to say that it is false that it is black. Something cannot be true and false, therefore the true and the false are contradictory:

Something cannot be true and false because nothing can both be and not be anything, in the same way, at the same time, without qualification.

But sentences can be true and false with qualification. Consider: "Ron Artest is good." Well, he was an NBA starter, so if you were talking basketball back in his prime, this is true, he was good. If you're talking other behavior? Well he jumped into the stands to attack a fan who threw a drink at him and attacked some random uninvolved person instead. This seems to qualify as "not good." When it comes to logic, our predicates should be univocal, and this sort of ambiguity should be ruled out.

But even for propositions like: "you had a good day," the truth of this is not reducible to a binary. Sometimes, if asked if we had a good day, we don't really know. Does this mean that there is no truth as to whether or not anyone ever has a good day? That the sentence is not truth-apt? I don't think so.

Okay, that's fair, but ontological truth/falsity as they exist primarily in the intellect. I guess I didn't realize that in the OP you were talking about true/false as states of the intellect. For example, you critique a thesis regarding propositions, and seem to in some way question the LEM:

Well, the problem that I think is most acute is ascribing truth and falsity primarily to propositions. Actually, it seems that in a lot of philosophy they are the only bearers of truth. That's what leads to, IMO, bad conceptualizations of knowledge.

Surely we agree that "p is false" contradicts "p is true."

:up:

Provided the terms are clear. But I suppose my point is that contradiction in this case is used as the lens through which truth as a whole is analyzed. This leads to concepts like "the one true canonical database of all true propositions" and when concepts like this are shown to be flawed, there is a crash into deflation. Truth ends up being either univocal, and contained in "the one true set of propositions," or else entirely relativized (with some appeals to "pragmatism" as a backstop).

I know that sounds absurd, but so much depends on how we construe "assertion," and the long thread on Kimhi a few months back revealed a lot of work to be done on this question.

:rofl: It does. Is the idea here that just thinking something is asserting it? Surely a woman can suspect her husband of cheating, and thereby hold a belief that is either true or false, without having to utter or write down that belief, right?

I have definitely felt stupid and laughed at myself for believing (false) things that I never expressed.

The monist wants to be able to say that there is no disjunction between truth and validity -- that there is something ill-formed or incoherent about "A thinks ~p", as opposed to "A doesn't think p".

Ah, I think I know a good one for this sort of thing. in Metaphysics, IX 10, Aristotle distinguishes between two kinds of knowledge/truth:


-Asytheta: truth as the conformity of thought and speech to reality (whose opposite is falsity); and


-Adiareta, truth as the grasping of a whole, apprehension (whose opposite is simply ignorance).

It might make sense to think about our knowledge of things as "passing back and forth between these two modes." For instance, because they are very complex topics, it took me a lot of reading and reflection to understand "Plotinus' conception of divine freedom" or "Hegel's dialectic." But now, having studied them, I can also consider them as unified wholes and understand or vet propositions that reference them without having to "unpack" all that I know about them. And it seems to me that the better one understands something the more one is able to consider it as an undivided whole (of course, the thing in question being more of a true unity matters too).

From my notes on similar ideas:

In Ad Thalassium 60, St. Maximus the Confessor argues for the superiority of unified and direct experience, as opposed to discursive reasoning/knowing. Similarly, in Philosophiae Consolationis (4.6), Boethius argues that reason is to the intellect as time is to eternity, and what “circle” is to “center.” This is because it is “proper” for reason to be “diffused” (diffundi, i.e., scattered or spread) about many things, and then to gather from them a single cognition (i.e., unifying the “Many” into a “One”). Pseudo-Dionysius makes a similar point, (De Divinis Nominibus, 7.2) claiming that souls have rationality insofar as they “diffusedly encircle” (diffusiue circueunt) the truth of multiple existent things. Conversely, the intellect considers one simple truth and grasps the cognition of a whole multitude in it.

So, to this question:

This is the problem from Parmenides that Kimhi begin T&B with, you may recall: How can we think that which is not?

Discursive knowledge involves combining, concatenating, estimating, etc. This is a "feebler" sort of knowledge. It is possible to combine things inappropriately, etc.

We can chalk this up to finitude. You can explain it in naturalistic terms too. For perception to occur, signals in the form of various types of energy in the environment must be transformed into electrochemical signals within/between neurons before becoming “present” in phenomenal awareness. This transformation of signals is not lossless. Organism’s sensory systems must be extremely selective about what information they take in from the environment. Taking in even a small fraction of the total entropy an organism is exposed to in the ambient environment would cause it to be overwhelmed by entropy.

To see why, consider the total number of molecules interacting with the surface of an organism at any given moment. Even leaving aside the difficulties in being able to develop sense organs sensitive enough to take in all this information, it is clear that sensitivity to the environment at this level of granularity would require a massive neurological apparatus just to encode the incoming data, let alone sift through it for relevance. Thus, which signals are allowed to pass from the environment into an organism's nervous system must be curated such that most information does not pass into the nervous system. Representationalists are correct that this facet of sensory systems introduces a great deal of bias into perception, just not about some of their other assumptions IMO.

Terrance Deacon has some good stuff on this and the semiotics he (and everyone else in biology) uses is derived from the Scholastic Doctrina Signorum: https://www.researchgate.net/publication/281155120_Steps_to_a_science_of_biosemiotics

Thinking cannot be dependent for its success on anything that is external to it.

Maybe I'm misreading it, but this seems implausible. My success at diagnosing a disease as a doctor depends on the quality of my diagnostic equipment, not just my own thought. My success at correctly reading of the letters on the chart at the optometrists depends on the curvature of my eye's lens, etc. These are all external to thought.

So yes, the distinction you're making between contraries and contradictories is extremely important. The essential unity of the thinker with the thought, the knower with the world, can only be shown by rejecting, as Kimhi does, the idea that a proposition can be true or false in the absence of some context of assertion.

Agreed, although I don't know if "context of assertion" is the right framing. Beliefs can be true or false without being needing to be "asserted."

Are we sure that thought and being exist in the sort of relationship that needs to be "conformed" or "adequated"?

Well, presumably we need to be able to explain false beliefs and false statements. There is adequacy in the sense of "believing the Sun rotates around the Earth" being, in important ways, inadequate.

Can we paint a plausible picture that is at bottom monistic?

Monistic in what sense?

But I don't see Thomas saying that the true and the false are not contradictories, nor do I see Aristotle saying that. Classically, true/false are contradictories:

What about the quote from the OP?

I answer that, True and false are opposed as contraries, and not, as some have said, as affirmation and negation [i.e. contradictory]. In proof of which it must be considered that negation neither asserts anything nor determines any subject, and can therefore be said of being as of not-being, for instance not-seeing or not-sitting. But privation asserts nothing, whereas it determines its subject, for it is "negation in a subject," as stated in Metaph. iv, 4: v. 27; for blindness is not said except of one whose nature it is to see. Contraries, however, both assert something and determine the subject, for blackness is a species of color. Falsity asserts something, for a thing is false, as the Philosopher says (Metaph. iv, 27), inasmuch as something is said or seems to be something that it is not, or not to be what it really is. For as truth implies an adequate apprehension of a thing, so falsity implies the contrary.

https://www.newadvent.org/summa/1017.htm#article4

opposite assertions cannot be true at the same time” (Metaph IV 6 1011b13–20)

Yes, something cannot be black and not-black, just as a sentence cannot be true and not-true. This is because being involves contradictory opposition, as does affirmation and negation. For instance, opposing universal and particular assertions would involve negations of each other (i.e. the square of opposition).

Obviously, the truth of a statement often depends on its context. "Peanuts are healthy" is true as respects most men, and false as respects the person with the peanut allergy. Truth and falsity are mutually exclusive in cases where the truth (or falsity) of a statement would both affirm and deny being without qualification (being and non-being are contradictory).

Thomas also says that univocal predication is proper to the discipline of logicians. If you're building a syllogism, then the truth or falsity of your premises vis-a-vis predication should involve contradiction. It would be problematic if they didn't.

I always assumed Thomas's point here was pointing back to Avicenna and ontological truth. There is also truth as adequacy of being to the divine intellect (truth most perfectly) addressed in the prior question (16).

Perhaps you need to define what you mean by "contrary."

Truth represents a perfect adequacy between the intellect and being. Falsity is the absence of this adequacy. If any inadequacy makes a belief or statement false, that seems to be quite problematic. For one, it would mean that all or almost all of the "laws" of the natural sciences are false, along with our scientific claims.

A theory or hypothesis might not perfectly conform to reality, but this doesn't make it completely inadequate either.

Pretty sure you can relate this to the Square of Opposition as well. For instance, "all elephants have big ears” cannot be true at the same time as “no elephants have big ears," but they can both be false. Whereas with "all elephants have big ears" and "some elephants do not have big ears" one must be true and the other false.

This distinction seems more Kantian than Platonic to me. I think "noumenal" might be a better tern here, i.e. "a thing that exists independently of human senses." At least, Plato himself would reject such a cleavage in reality, as well as existence without any edios (quiddity, intelligibility, form).

Claiming things are real runs into all sorts of prickly problems, though. Have you peeked beyond the veil and seen it was so?

Have you looked on both sides to see if the veil itself is real? I am not sure if you can have a "reality versus appearances" dichotomy if there is only appearances. If there are just appearances, then appearances are reality. But then how do we justify the claim that there is a reality that is completely isolated from appearances?

On the other hand, if we can "infer" the "'reality' behind the veil," then why can't we likewise infer that this reality includes numbers?

This is, BTW, Hegel's critique of Kant. Kant himself is dogmatic. He doesn't justify the assumption that perceptions are of something, that they are in some sense "caused" by noumena (although of course, "cause" itself is phenomenological and so suspect). He just presupposes it and goes from there (and look, he just happens to deduce Aristotle's categories, convenient!). The Logics are pretty much Hegel's attempt to start over without this assumption.

Math is a very useful way of describing relations and ratios between things.

But then wouldn't these objective/noumenal things need to be the sort of things that have ratios? If they don't have ratios, why is it useful to describe them so? If they do, then numbers (multitude and magnitude) seem to apply to the noumena.

Hmm.. I'm inclined to say that there are indeed no objective facts related to chess. Chess tells us nothing about this underlying reality.

But presumably it tells us something about the reality of chess. This is why I don't know about making "objective" and "noumenal" synonyms. For one, it seems likely to me that many people will find a use for the former while rejecting the assumptions that make the latter meaningful. Second, we wouldn't want to have to be committed to the idea that facts about chess, or the game itself, are illusory.

Sort of besides the point though.

I'm actually kind of curious what passages of Plato this refers to.

Platonism in many areas is lower case "p" platonism, which tends to be only ancillary related to Platonism. For instance, :

At least according to the SEP article here, (2) is platonism:

Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and non-mental.

This could apply to Plato in some sense, but you'd really need a lot of caveats. Plato's metaphysics works on the idea of "vertical" levels to reality. Forms are "more real" they aren't located in some sort of space out of spacetime. But at the same time, even for Plato and the ancient and medieval Platonists, the Forms aren't absent from the realm of appearances. The reason medieval talk of God can be so sensuous without giving offense is because they thought all good, even the good of what merely appears to be good, is still a participation in/possession of the Good.

So, the world of the senses and spacetime would be deeply related to the Forms, not isolated from them. However, I am not super familiar with platonism in contemporary philosophy of mathematics.

Just as electrons and planets exist independently of us, so do numbers and sets. And just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects’ perfectly objective properties, so are statements about numbers and sets. Mathematical truths are therefore discovered, not invented.

I know this isn't your definition, but I would suggest a modification to just:

"Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is not dependent on us and our language, thought, and practices."

"Independent" might suggest that the two don't interact, but it seems obvious that they must for platonism to be an interesting thesis. The whole second part is problematic in that it seems to assume that "statements" are also independent of us (and true or false independent of us), and I am not sure if all mathematical platonists would like to be committed to those implied premises. It seems to require being a platonist about "statements" in order to be a platonist about any mathematical objects. But, at least for me, "threeness exists without humans around" seems a lot more plausible than "sentences exist without humans around."

I am inclined to argue that maths do not 'exist' in any objective sense.

Math is a product of the human mind, and a very useful for modeling reality for human purposes. It's a way of describing ratios and relations between things. The actual objective nature of such relations seems inaccessible to humans though.

Well, my turn to ask for a definition: what does "objective" mean here? I've noticed it tends to get used in extremely diverse ways. I assume this is not "objective" in the same sense that news is said to be "more or less objective?"

As a follow-up, I would tend to think that the game of chess does not exist independently from the human mind. Chess depends on us; we created it. However, are the rules of chess thus not objective? Are there no objective facts about what constitutes a valid move in chess?

I suppose this gets at the need for a definition.

Isn't it easier then to accept that mathematics does not exist objectively, and is simply a very useful tool conceived by the human mind?

But isn't the follow up question: "why is it useful?" Not all of our inventions end up being useful. In virtue of what is mathematics so useful? Depending on our answer, the platonist might be able to appeal to Occam's razor too. A (relatively) straight-forward explanation for "why is math useful?" is "because mathematical objects are real and instantiated in the world."

This also helps to explain mathematics from a naturalist perspective vis-a-vis its causes. What caused us the create math? Being surrounded by mathematical objects. Why do we have the cognitive skills required to do math? Because math is all around the organism, making the ability to do mathematics adaptive.

1. Human beings exist entirely within spacetime.
2. If there exist any abstract mathematical objects, then they do not exist in spacetime. Therefore, it seems very plausible that:
3. If there exist any abstract mathematical objects, then human beings could not attain knowledge of them. Therefore,
4. If mathematical platonism is correct, then human beings could not attain mathematical knowledge.
5. Human beings have mathematical knowledge. Therefore,
6. Mathematical platonism is not correct.

I think the platonist response would be that premise 2 is false. Mathematical objects exist in spacetime. There is twoness everywhere there are two of something (e.g. in binary solar systems). Premise two seems to imply that any transcendent, Platonic form is absent from what it transcends. Yet this is not how Plato saw things. The Good, for instance, is involved in everything that ever even appears to be good. Plus, my understanding is that many mathematical platonists (lower case p) are immanent realists, along the lines of Aristotle. So, numbers exist precisely where they are instantiated (in space-time). A Hegelian theory would similarly still allow that numbers exist "in history."

I will just note that the path from the elimination of analogy vis-a-vis goodness and beauty to total equivocity (extreme relativism or nihilism) is quite similar. Philosophy first removes the option of analogy. It then discovers that a single univocal measure of goodness, truth, or beauty is seemingly impossible. Faced with this result, it has a "slide into multiplicity" and produces a multitude of isolated truths, goods, and beauties, with each varying by culture, individual, or even context.

"Philosophy as therapy," has always interested me. There is this neat New Yorker article on it. It would be interesting to me if anyone had ever tried to set up a retreat with this in mind.

https://www.newyorker.com/culture/annals-of-inquiry/when-philosophers-become-therapists

But then I've been reading about Patristic philosophy, particularly from Syria and Egypt, because this is probably one of the key eras where philosophy is practiced as a sort of therapy on a large scale.



The Philokalia is another great example here, although obviously not focused on the laity.

Superdeterminism isn't really an interpretation in quantum foundations, like Pilot-Wave or multiple worlds is. Some interpretations are sometimes said to be superdeterministic (e.g. retro-causality, Many Worlds, etc., depends on how you define things though) but the term more often refers to a "theory without a theory," i.e., explaining different sorts of experiments related to entanglement without positing any overarching interpretation of QM.

The benefit here, if you want to champion "common sense" views is that many theories that might fix your "non-conmmmon sense problems," also say some pretty wild things. And you don't want that if you're a champion of common sense, so you remove the part you want and reject the rest.

The difficulty here is that this is not really an explanation or interpretation, so much as a premise just being asserted because it is "more common sense." Of course, what is often meant by this "closer to the classical picture," and we should also question if a view that took so long to emerge is really common sense or not.