Mathematical Platonism requires a different, spiritual, mechanism that has not been observed or experienced — Dfpolis

Is that really so? The IEP article I've referred to on the Indispensability Argument for Mathematics says:

Some philosophers, called rationalists, claim that we have a special, non-sensory capacity for understanding mathematical truths, a rational insight arising from pure thought. But, the rationalist’s claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.

Another essay says

Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something [i.e. number] existing “outside of space and time” makes empiricists nervous.

I interpreted these objections as simply a reference to rational thought itself. How do we know the proofs of mathematics? Through pure reason, I was always taught. Why it can't be explained in other terms, is because it the source of explanation, not something itself in need of further explanation, so in that sense, not able to be reduced. I think that's what drives many of the objections - the faculty of reason transcends empiricist explanatory paradigms. As the first passage says, it's challenge to physicalism.

I agree that the depiction of Platonism as holding there is a kind of 'ethereal realm' of abstract objects - the 'Platonic heaven' - is a dubious concept, and that the Aristotelian view is more realistic. But I still believe that Aristotle insists on the reality of universals - that they're more than simply mental constructions or names. As James Franklin says:

Aristotelians agree with Platonists that the mathematical grasp of necessities is mysterious. What is necessary is true in all possible worlds, but how can perception see into other possible worlds? The scholastics, the Aristotelian Catholic philosophers of the Middle Ages, were so impressed with the mind’s grasp of necessary truths as to conclude that the intellect was immaterial and immortal. If today’s naturalists do not wish to agree with that, there is a challenge for them. ‘Don’t tell me, show me’: build an artificial intelligence system that imitates genuine mathematical insight. There seem to be no promising plans on the drawing board.

Plato's view that there are actual numbers in nature, which is what I was talking about, is naive for the reasons I gave. — Dfpolis

I don't know if that is Plato's view. From everything I read, the basic tenet of mathematical Platonism is that numbers are real independently of any mind. They have a reality which is analogous to, but different from, material objects.

[Platonism is] the view that mathematics describes a non-sensual reality, which exists independently both of the acts and [of] the dispositions of the human mind and is only perceived, and probably perceived very incompletely, by the human mind. — Godel

From here

since the moon had been measured, it cannot suddenly jump into a nonexistent state. It's not a solution to the moon's wave function, or at least not one with a probability of zero to more digits than you can imagine. That's what I mean by the moon still being there when nobody looks at it. The moon has been measured and cannot be unmeasured. — noAxioms

I think there's a deeper underlying issue. Despite your professed scepticism about scientific realism, I think your philosophical framework is still committed to a form of realism. This is an opportunity to explore the implications of that.

It is often said by way of objection to philosophical idealism, that idealism must mean that things go into or pass out of existence depending on whether they're being observed. After all that appears to be the implication of Berkeley's 'esse est percipe' - 'to be is to be perceived'.

But I don't think this is what philosophical idealism means - not, at least, as I understand it. This has to do with the nature of the objects of perception. Realism posits that the existence of those objects is independent of our perception or experience. They exist just so - in the case of the moon for billions of years. So it is preposterous to claim that they could cease to exist simply because nobody is looking at them. Yet this is what idealism seems to claim.

And I think this was the point of Einstein's rhetorical question. Realism expects that all such objects are really existent, independently of any mind or anyone's perception. That is, after all, the very definition of realism. This is the gist of Einstein's well-known declaration that he 'cannot seriously believe in [the quantum theory] because it cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance.'

But an alternative is to acknowledge that the existence of sensable objects is contingent and not absolute. This not to assert that objects exist in any absolute sense, on the one hand, but neither is it to claim that they cease to exist when they're not observed, on the other. It is to acknowledge that judgement concerning the reality of objects is a function of human sensory perception and reason, and that it is therefore not absolute. From the human point of view, all such objects exist - you'd better believe it! - but their existence is contingent and not absolute.

So this attitude does call realism into question but without falling into a caricature of idealism that it is easily taken to imply. I think it teaches us to respect that science is a human undertaking and that it's not a revelation of what is truly the case independently of any observer.

Or, put another way, that physics alone cannot constitute the totality of our experience.

Kant erased us from the picture — Antony Nickles

how so?

Basically you're asking, How is it that all humans are homo sapiens yet with such a diversity of appearance?

I think I cried when I had my first religious/spiritual experience as an atheist that’s how strong and magnificent it was to my non-believing eyes. ... — invicta

I hear you.

What if the purely "mechanical" act of measurement produces a numerical result that goes automatically into a computer file and is never "observed" as it sits there and rots? — jgill

As I said - through inductive reasoning, we can expect that the measurement is taken, that the data exists on that system unobserved. But you won't empirically verify that inductive step without observing the result. And isn't this very much at the heart of the whole issue? The realist attitude is, well all these processes simply occur, whether we're observing or not. But if that were so, then we wouldn't even be having this discussion!

Just noticed the mechanic... :lol:

It's significant that empiricist discussions of the nature of number tend to question how it is that humans even have a faculty that knows mathematical facts, because such facts are not, by definiton, empirical (discussed in e.g. The Indispensability Argument in Philosophy of Math)

Yet, to find the numbers, we have to measure nature, not intuit them mystically, as Plato believed — Dfpolis

You're not even allowing for pure mathematics. Also for the role that mathematics has had in disclosing things about nature that we could never, ever deduce through observation alone. And I humbly suggest that it is your depiction of Platonism that is 'naive'.

First, I need to comment again on the translation of 'being' by 'substance' in Aristotle, which Joe Sachs criticizes here. Sachs says in reference to this mis-translation 'It is no wonder that the Metaphysics ceased to have any influence on living thinking: its heart had been cut out of it by its friends'.

So imagine if the passage you quoted above put 'being' in the place of 'substance'. It is not entirely accurate, but I think it conveys something which has been lost in the usual discussion of 'substance':

But the universal too seems to some people to be most of all a cause, and the universal most of all a starting-point. So let us turn to that too. For it seems impossible for any of the things said [of something] universally to be substance [a] being. For first the substance being of each thing is special to it, in that it does not belong to anything else. A universal, by contrast, is something common, since that thing is said to be a universal which naturally belongs to many things. Of which, then, will it be the substance being? For it is either the substance being of none or of all. And it cannot be the substance being of all. — Metaphysics, 1038b9, translated by CDC Reeve

I think the discussion of substance tends to slant the discussion, because it's natural to reify substance as something objectively existent (or more likely non-existent) and that this is at the basis of the difference between the Platonic and Aristotelian doctrine of forms.

I believe that Plato's doctrine of ideas requires an understanding that the 'ideas' or 'forms' are real in a different sense to the reality of phenomena. Betrand Russell says that universals don't exist in the sense that horses, men, tables and chairs do, but that they're nevertheless real - they 'subsist'.

Suppose, for example, that we are thinking of whiteness. Then in one sense it may be said that whiteness is 'in our mind'. ... In the strict sense, it is not whiteness that is in our mind, but the act of thinking of whiteness. The connected ambiguity in the word 'idea', which we noted at the same time, also causes confusion here. In one sense of this word, namely the sense in which it denotes the object of an act of thought, whiteness is an 'idea'. Hence, if the ambiguity is not guarded against, we may come to think that whiteness is an 'idea' in the other sense, i.e. an act of thought; and thus we come to think that whiteness is mental. But in so thinking, we rob it of its essential quality of universality. One man's act of thought is necessarily a different thing from another man's; one man's act of thought at one time is necessarily a different thing from the same man's act of thought at another time. Hence, if whiteness were the thought as opposed to its object, no two different men could think of it, and no one man could think of it twice. That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus universals are not thoughts, though when known they are the objects of thoughts. — Betrand Russell

I've bolded the significant point, which I think resolves many of these issues. So the 'idea of a man' is just that - but it doesn't exist, not in some 'ethereal realm' or 'Platonic heaven' - not that Plato himself is clear about that, but it became manifest in later (ancient and medieval) philosophy. I think the key idea is that of the intelligible object - something which is real, but only perceptible by reason, not by the senses. The idea or form is what is manifested in the physical form of man. Hence the simile in this post.

And that - realism regarding universals - is what was lost from the Western tradition with the ascendancy of nominalism over scholastic realism. That's why there can't be any conception that universals exist in a different sense to particulars - because that is an aspect of the conceptual space that is no longer available to us (cf. dfpolis 'post-Cartesian conceptual space')

Anyway, carry on.

//I should add that it's much easier to concieve of an idea of a form as 'the being of all' than it is as 'the substance of all' i.e. the individual is an instantiation of a singular idea. Every man exemplifies 'the idea of man'. I don't see how this presents great conceptual difficulties.

Not 'mind' in the sense of 'conscious mind'. It is purely cellular and organic in nature, but it still can be conceptualised in terms of interpretation of signs, hence, biosemiosis. (Don't want to introduce that as a subject of discussion however, just footnote.)

a riverbed wouldn't store information of the passage of water, but then its physical state, which seems identical to the total information that can be taken from it, is somehow different? — Count Timothy von Icarus

Tree rings contain evidence of forest fires, ice-cores atmospheric records. I'm not disputing that. But I'm saying that the mere existence of those data don't constitute information about anything until they're interpreted. The contrast to living organisms is that in them, information is dynamically interpreted by cellular processes moment by moment, it's intrinsic to any organic process.

Having information rest solely in the minds of observers seems at risk of becoming subjective idealism. The information has to correspond to and emerge from external state differences or else how can we discuss incorrect interpretations of any signal? — Count Timothy von Icarus

I think you're referring to a rather simplistic conception of idealism, of the variety that Samuel Johnson attempted to refute by kicking the stone. I favour a form of objective idealism. It's not that 'the world exists in my mind', but that what we understand as reality entails an ineliminable subjective aspect, without which nothing would make any sense. And we supply that. The mind is continually interpreting and integrating information about the world so as to make it intelligible - and not only intelligible, but navigable - for us. That order is at once 'the order of perceptions' and 'the order of the world' - in very much a Kantian sense.

All due respect, I think the error you're making is that of metaphysical naturalism - the assumption that the world would exist, just as it seems to now, were no humans present within it. But even that apparently empty world is still organised around an implicit perspective. Take that away and you can't imagine anything whatever.

So, what kind of existence is mathematical existence? — Dfpolis

Mathematical platonism says that intelligibles such as number are real even if not existent, being the same for all who think. Mathematical ratios and relationships are deeply embedded in the fabric of the cosmos, hence the 'unreasonable efficacy of mathematics in the natural sciences'.

Thanks again for those passages. The point that I'm disputing is this:

. So a material object is a combination of form and matter, and that form is proper and unique to the particular object, complete with accidents. — Metaphysician Undercover

I don't think that each particular is an instance of a unique form (and as an aside I don't recall in anything I've read from Aristotle, which is not much, any reference to 'material objects' - rather the arguments are usually couched in terms of 'particulars', meaning, 'particular beings'.) But the salient point of the dispute is, is each individual an instance of a unique form? I say not, that the form 'man' is common to all men, that is why it is a universal.

The far side of the moon is still there when nobody looks at it since looking at it isn’t what makes it there — noAxioms

You do recall the anecdote that Einstein once exclaimed, when walking with one of his friends, 'surely the moon still exists when no-one is looking at it!' This was in relation to the very assumption you're making, and he said it because of the challenge that quantum mechanics poses to scientific realism. In fact it's what this whole debate is about. When it comes to the denizens of quantum physics - purportedly the most fundamental constituents of physical existence - Bohr said 'no elementary phenomenon is a phenomenon until it is observed'.

you can just call your local quantum mechanic. — Andrew M

Who could be anywhere :lol:

Computers certainly operate on information. — hypericin

Computers and libraries are human inventions. Whatever order they have originated from that.

The entire quantum subject would be better served if "observer" were eliminated everywhere and replaced by "measurement". — jgill

Can't have one without the other though. People often say, well measurement is any form of registration on any instrument, but we would never know that, save by checking. Long story short, science is an inextricably human undertaking, we can't perceive reality 'as it is in itself' as if were apart from our act of observing it. That's true all the time, but in quantum physics it becomes impossible to avoid.

namely, an intellect :lol:

I remember us recently discussing Adorno and Horkheimer's critique of the 'instrumentalisation of reason'. Pinker's notion of reason falls squarely into that definition. I've never bought Pinker's obvious scientism, but on the other hand, I don't think it's bad to have enthusiasts for the idea of progress. I actually believe in the ideal of progress, of trying to improve economic and social life through technology and planning. But then, Pinker isn't really representing all the Enlightenment values he claims as his own - only the aspects of it that are adopted by MBA courses and hawkish economic rationalists, as per this review. (Conflict of interest disclosure: Steve Pinker's The Blank Slate was the last Christmas gift I received from my dear departed mother, many years ago.)

As I previously quoted...


These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they. (On the Heavens Book 1, part 2) — Fooloso4

A simile comes to mind: imagine that 'the idea of the cat' is a silhouette in front of a light-source through which light is projected so as to create an image of the cat on a surface. But the surface on which the light is projected is irregular, so the image is always slightly different each time it is projected. In this simile, 'the silhoettte' is 'the form', but the actual impression is 'the particular' - due to the irregularities on the surface on which it is projected each image is slightly different, thereby making each one 'an individual'. The key point being, there is only one silhouette, but the resultant images are all different due to the irregularities - 'accidents' - of the surface on which it is being projected.

Valid simile, do you think?

There are two principal senses of "form" for Aristotle, hence primary and secondary substance. The one sense refers to human abstractions, conceptions, the formulae which we employ — Metaphysician Undercover

I'm going to stop arguing this point, you've been telling me this over and over for years, and I just don't think it stacks up. Over and out.

Hey I know, I've got immediate family in the US, son and family live in a really nice town in Wisconsin and I visit there regularly (last there in August). I never really seen any gun violence when I'm there, but then it's a pretty genteel part of the country.

That's more like it! I think the religious idea of 'the life eternal' is meaningful (although hardly anyone here will agree). In the popular imagination, it is often depicted as living forever in physical form, but I don't think it means that at all. In philiosophical spirituality, such as neoplatonism, it is more a matter of realising that your real nature is not separate from the same intelligence that animates the Universe itself. A similar intuition runs through Hindu and Buddhist literature, but in secular culture this tends to be scorned.

Check out a book that was very popular in the 1970's by a writer who has come back into fashion on Youtube. The book is The Supreme Identity, by Alan Watts. He had a big influence on me and many others back in the day. It turned out he was a pretty hardcore alchoholic, which was a let-down, but his brand of philosophical spirituality is very approachable still and he's an excellent prose stylist.

How does one try to protect one's self or family? — jgill

There are places where I would want to own a gun if I were to live there. New Guinea, for instance, is said to be a very dangerous place to live, with frequent home-invasions and assaults. But living in Sydney Australia, I've never felt the need. Gun ownership is very low, by US standards, and I've never seen a gun drawn or heard a single shot fired (outside a firing range during Cadet training in my teens.) So it's likely that the huge numbers of guns in circulation in the US and the extraordinary number of gunshot deaths, becomes, as I said, a vicious circle - fear of being shot drives the uptake of guns, which dramatically increases the risk of being shot. Classic vicious circle.

I deleted my comment. I will try and make a more serious point. Merely declaring that 'everything is meaningless in the light of eternity' is a kind of nihilistic attitude.It is true that when you consider the vastness of the universe and deep time, we humans seem insignificant. But on the other hand, we're the only beings we know of who are even aware of that immensity. That itself has significance. As has sometimes been said by evolutionary theorists, in h. sapiens the process of evolution becomes self-aware.

The philosopher Neitszche predicted an upsurge of nihilism in Western culture, due to the erosion of traditional religion and it's anchoring for morality. But, contrary to his prediction, religion has not, in fact, died, and I for one never accepted his proclamation of the 'death of God'. While it's true there is a crisis of meaning in Western culture, there doesn't have to be, and a sense of meaning can be recovered, if one seeks it.

Is there such a thing as uninterpreted information? Put another way, how does anything constitute information until its been interpreted? I mean, the genetic information transmitted by DNA is interpreted by ribosomes. But in the non-organic realm, what sense does it make to speak of information at all? Sure, we can ascertain vast amounts of data about the Universe, which then constitutes information, but does the Universe itself constitute 'information' in any meaningful sense?

Is this the case? Doesn't water eroding topsoil generate information about its passage in the form of riverbeds? — Count Timothy von Icarus

But that's informative to us. The difference with the information encoded in DNA is that it is morphogenetic, i.e. it causes things to happen, it transmits and stores information. THat is why some (although not all) biologists recognise an ontological distinction between life and non-life - living things are different in kind, not just in degree, to the elements of the periodic table.

Aren't our own minds the objects of direct perception? Arguably this is the only thing we observe directly, depending on how you define direct. Light, apples, cars, these are all filtered through the mind, Kant's old trancendental and all. — Count Timothy von Icarus

Very tricky distinctions, but I say that it's not. The mind is primarily the subject of experience, that which objects are perceptible to. We can't stand outside of the mind and make it an object in the same sense we can objectify perceptibles. We can obviously talk about our state of mind and mental events, but the question of what the mind is, that has these experiences, is a deep one. There's a theme in current phenomenology about this idea, along the lines of 'the mind knows but is not known', as it is always the subject or recipient, never amongst the objects of perception. It's a question with an ancient heritage, and of course, you're right in mentioning Kant.

Clearly existence (the uncreated void) — EnPassant

'The existent' and 'the uncreated' are different domains in classical metaphysics.

Lawrence Krauss published a book 10 years ago, A Universe from Nothing, which proposed to account for how fluctuations in quantum fields give rise to the Universe (hence the title!) It was subject to some pretty savage review, see here and here, which give some insight into the difficult metaphysics of these questions.

I'm certainly not claiming any kind of enlightenment on my part, but I'm not prepared to agree that the whole Platonic tradiition merely ends with questions that can never be answered.

'We', eh? ;-) There is in the later Platonic and neo-Platonic corpus a philosophy of illumination, much of it later incorporated into Christian mysticism. I don't think it is prudent to simply write that off, as if it has no value or never occured.

Biden's Chip Act has had a massive impact, Intel and TSMC are both building multi-billion dollar plants in the US (unlike DJT's much-touted refrigerator factory in Pennsylvania that transferred most of its operations to Mexico as soon as he walked out the door.) I've just read some fantastic books on the tech industry, Chip Wars, Chris Miller, and Silicon, by Federico Fagin (who desiged the first microprocessor.)

I fear for Taiwan, after what the PRC did to Hong Kong. Of course, we've stopped hearing about that now - wonder why that is? - but Taiwan is a proud and functioning democracy and a highly functional culture. It would be a travesty to see the communist jackboot on its neck (apart from being a possible cause of a global conflagration.) It's one of the scariest tensions in the world right now.

(Anyway I've drifted totally off-topic now so we better leave it for this thread, take it up elsewhere.)

It seems difficult to have information be mind independent but not computation. I won't comment on the status of such things in theoretical "mindless universes," but in the real universe meaning, at least at the level of reference to something external to the system, absolutely seems to exist sans observers, e.g. ribosomes are presumably not conscious but can read code that refers to something other than itself, and they in turn follow the algorithm laid out in the code to manufacturer a protein. — Count Timothy von Icarus

Interesting that the only place outside human activities and animal communications that something like transmission of information occurs is in living organisms and DNA, isn't it?

Humans are part of nature. Human minds presumably have natural causes and thoughts/subjective meaning are part of this natural world. — Count Timothy von Icarus

The mind is not something observable in nature. We can observe that other creatures are conscious and presume that they too have minds, but the mind is never a direct object of perception.

As for the interpretation of numbers and so on, humans inhabit a 'meaning world'. It doesn't comprise only objects, but also consists of a continuous process of interpretation, whereby we assign meaning to everything we encounter. Within that matrix, what is objective and what is subjective arise together - we don't see the world as if from no viewpoint, although we think it's easy to do so. But even the imagined panorama of an empty universe is organised around a point of view, without which there would be neither scale nor perspective.

Since form is the principle of intelligibility, each and every difference which is apprehended by a human being, as a difference, must be a difference of form. If it was not a difference of form, we would not perceive it as a difference. — Metaphysician Undercover

There is a reason the forms are also known as universals. If they were specific to each and every particular, the whole idea would crumble.

Assume X has the property 'existence'. In this respect we see X and existence as distinct entities. Now ask 'Does X exist? — EnPassant

That leaves aside a whole class such as numbers, conventions, principles, universals, and related. the question as to the sense in which number exists is an entire topic in philosophy. What about possibilities? There is a 'realm of possibility' - what might happen - and while none of its inhabitants exist, they are real possibilities (as distinct from things which could never happen). Similarly there are logical possibilities which might never exist, but which are real in some sense.

You're venturing into fundamental metaphysics, but I don't know if trying to re-create it from scratch will be a fruitful undertaking.

There are journal papers which differentiate being, reality and existence. Also an Oxford University external studies course of the same name.

Point taken :up:

Essentially my actions and life and all my accomplishments being reduced to nothing. — invicta

Be sure that’s not an excuse for not trying. It easily morphs into the nihilism which is an affliction of our age.

the word "phantasia" meant "the external appearance of something" and it originated from the verb "phaínō" (pronounced "faeno"), which mainly means "I show, I make appear", and which in passive voice becomes "phainomai" (pronounced "faenomae"), which mainly means "I appear (as something), I am visible*. — Alkis Piskas

Same root as 'phenomena' - very interesting. I had the idea that 'phantasia' came to mean 'mental image' in later philosophy.

Supernatural as a concept is intelligible. But declaring something supernatural seems, to repeat myself, presumptuous and foolish. — Art48

'Miracles are not against nature, but against what we know of nature' ~ Augustine.

A bundle of sticks that looks like this: VIII with no one to observe it is a bundle of sticks. It can't ever be more than that without some mind observing it and attaching additional signifiers. However, when the bundle of sticks is observed by someone who knows Roman Numerals, it's a bundle of sticks AND it picks up a new attribute courtesy of the mind observing it: it's a bundle of sticks and the roman numeral for 8. — RogueAI

Know exactly what you mean. I had a marathon thread here in the past about just this kind of thing. The broader situation is, modernity divides the Universe into subjective and objective. Then it says that the objective domain is entirely devoid of meaning, because meaning resides in the subject. Then it asks, why is it meaningless?

Sorry about that. Figure of speech connoting deadly warrior.