, Perhaps you might enjoy Logic and Consciousness. A bit about thought and logic, and some considerations on Frege and Penrose.

It's not a long read.

Tell me what you think fo the notion of "overloading" logic with expectations.

Tell me what you think fo the notion of "overloading" logic with expectations. — Banno

It starts with the present King of France and why it's false that he's wise. How do we evaluate a proposition whose subject doesn't refer? Meinong attempts to help by inventing the idea of possible objects, which subsist instead of exist. The present King of France is such an object, and so the subject does have a reference. I actually like this view, but it was objectionable to Russell, who felt like this theory would cause the universe would become overcrowded, but also because this theory leads to misconceptions about what people actually think and intend to say.

Russell decided that it must be that this proposition is compound. When you start a sentence with The present King of France, you're asserting of the universe that it contains this object. And next, you're asserting of this object that it's wise. So now that we've broken the P down into q and r, we have a way to explain why P is false: because one of its parts is false. Everybody loved Russell for coming up with this way of looking at it.

@Banno
So one of the strawmen I think Peregrin is lighting ablaze is the idea that someone somewhere thought logic is the end-all to what goes on in the human psyche. No. It wasn't supposed to be that. I'd like to introduce Peregrin to analytical philosophy: the land of temperance and little tiny answers to little tiny questions.

Coming back after being away for a few days… I think @Count Timothy von Icarus has successfully highlighted the fundamental problems in this thread and in Banno’s polemical approach. That aside, there are a few posts that deserve a response:

I disagree that that is what is going on. — fdrake

Whether or not it is what is going on, it is what is at stake, and that’s the point. Your construals avoid the problem of intent, and intent is the crucial aspect (e.g. when you talk about “verbatim” or “taking someone ‘exactly’ at their word”).

When someone stipulates a definition, they are committed to that definition insofar as it relates to the intended concept. — fdrake

I agree, but I really don’t think your approach in the discussion of square circles manifested anything like an attempt at close reading or an investigation of intended concepts. It was more an exercise in interpreting utterances as they suited your purpose (of arguing for square circles). Granted, it is no wonder that a polemical and insubstantial thread continued in polemics and lack of substance. You and I were just following Banno's lead in this, and it is why Banno should not be allowed to set the pace.

Which could equally mean "mind", "minds", "people"... — fdrake

And that was quite intentional on my part. When dealing with people prone to misrepresentation it is best to give a starting point which either makes them think or ask a question. If they do neither one then they show themselves to be uninterested in philosophical discussion. It is in no way surprising that Banno managed to do neither, and after dealing with this for long enough I’ve just put him on ignore. Indeed, my earlier definitions were more specific, and the later ones became more general in proportion to my realization that the instigators were not willing to look outside their paradigm.

-

Yes. I thought it went without saying. Some things people think of are more appropriate than others in some contexts, and strictly better by some metrics. Some fiction is more valuable than others. If a thingy works better than another thingy on every relevant facet, the first thingy is better than the second thingy.

How would you judge that for a given context? Well I suppose you'd look for examples, see what pans out, provide definitions of things to see if they capture the relevant phenomena... Maybe you'd refine your criteria for what counts as a good thing in a given context based on the what you've seen and what's been created, too. — fdrake

I’m still not seeing a straight answer. Why? Because you claim to be talking about metaphysics but then you qualify everything by words like “context,” “value,” and notions of artifice. Earlier when I asked if there is better and worse “fan-fiction” you again cleaved to the metaphor and gave examples of literal fan fiction.

I still have the impression that you think of this is as an Objectively Correct vs Subjective-Relativist sense, and I don't want to accept the Subjective-Relativist role in the discussion since the proofs and refutations inspired epistemology of mathematics isn't relativist in the slightest, because its emphasis is on communities of people agreeing on what follows from what by following coordinating norms and demarcating those norms' contexts of application. Minimally then, it's intersubjective, and communities create knowledge about collectively understood subject matters. — fdrake

So then do you think intersubjective agreement is metaphysics? Is that the goal? To try to garner agreement? The democratization of science?

I’m perplexed at how impossibly difficult it is for folks on this forum to think about metaphysics and to escape modern immanentism. Truth has been so thoroughly deflated that folks around here can’t even recognize the notion of truth when it shows up at the party. “Communities of people agreeing on what follows,” is a very common substitute, but also a very bad substitute! When peer review and intersubjective consensus shifts from a helpful aid to truth, to truth itself, something very problematic and bizarre has occurred. What began as, “A number of instruments agree, therefore they are probably telling us the truth,” shifted to, “A number of instruments agree, and we’ll just define that as truth qua truth.” This is substituting truth with agreement; metaphysics with intersubjectivity. This is a significant misstep. Einstein’s physics is not superior to Newton’s physics because more people agree with Einstein. It is superior because it has more purchase on what is actually occurring in reality; because it is truer. Agreement is an epistemic criterion, not a metaphysical criterion.

The modern world is merely anthropocentric. We have made everything about ourselves, our desires, and our values, so that this is all that even exists. To talk about something beyond that is not allowed. Science, metaphysics, and truth are barred at the gate, even to the point that we cannot say what a woman is.

But the strengthened liar's sentence persuaded me that there is at least an interesting formal concern. — Moliere

That's an interesting background explanation for why the "Liar's paradox" tempts you, but what I am hearing is that you are interested in playing a game that has nothing to do with reality. You have not answered the objections, and I don't see that Marx and Hegel have much at all to do with this issue. When you talk about "truth" and "falsity" you are not talking about truth and falsity; you are equivocating. We could play an arbitrary game and call the Liar's paradox "false," but we cannot call it false, and I have explained why.

I think this is all symptomatic of the decadence of contemporary philosophy, which is more a matter of novelties and entertaining oneself than actual philosophical engagement. On this point, there was a recent article about the filmmaker Terrence Malick and his encounter with droll contemporary philosophy, "Malick the Philosopher." This form of philosophy will be made to reckon with its own vacuity.

An afterthought -- in a way the pluralist is actually more anti-nihilist than the monist. The monist has to hold that contradictory statements cannot be logically comprehended which is, in a way, a baby nihilism: Here is the field of inquiry where no logical rules hold. — Moliere

Something like that. I would say that the so-called "monist" accepts that people can be wrong about things, and that that is probably at the pragmatic core of this thread. Truly, there is a mystery about how error can occur. But this was never a real thread. The people behind it were never interested in giving real arguments for their position, or even attempting to distinguish "monism" from "pluralism."

Edit: I realize this was curt, but I don't see the conversation going anywhere and so I am just setting out my view. I take it that Epictetus is much more interesting, substantial, and philosophical than the "Liar's paradox."

Banno’s polemical approach — Leontiskos

:blush:

That's an interesting background explanation for why the "Liar's paradox" tempts you, but what I am hearing is that you are interested in playing a game that has nothing to do with reality. . — Leontiskos

Reality is what's interesting here -- what I don't want to do is define reality within my logic, though. And I don't think that logic needs to restrict itself to objects since reality is not composed of objects and objects only -- it also contains sentences.

You have not answered the objections, and I don't see that Marx and Hegel have much at all to do with this issue

As I see it right now the objection is we don't agree on what a pluralist logic would even mean. I've asked you if you'd accept a defense of dialetheism, the belief that there are true contradictions, as a basis for making the inferences that there is more than one logic.

Unless you answer that question it becomes rather hard to answer your objections since we don't have an agreed upon notion of pluralism. I've already laid out, with the liar's sentence, why I accept dialetheism. Marx and Hegel are philosophers which, like the liar's, utilizes contradiction in their reasoning. My thinking here is to ask if you'd accept that as a basis for dialetheism.

So what do you say?

Reality is what's interesting here -- what I don't want to do is define reality within my logic, though. And I don't think that logic needs to restrict itself to objects since reality is not composed of objects and objects only -- it also contains sentences. — Moliere

Well you can't say what it means, you can't say what a sentence is, you can't say why it would count as a sentence, you can't say how it would ever have any purchase on reality, and you don't seem to think it would ever be utterable in real life. That's a pretty problematic place to be. Again, it looks to me that you are playing a game that has nothing to do with reality.

As I see it right now the objection is — Moliere

The objection was given <here>. You tried to answer it by redefining "false" as "fake," and I think we both agreed that that answer failed. That's where things stand, as you never made another attempt.

I've asked you if you'd accept a defense of dialetheism, the belief that there are true contradictions, as a basis for making the inferences that there is more than one logic. — Moliere

Sure: if dialetheism is true, then strong logical pluralism is true.

Marx and Hegel are philosophers which, like the liar's, utilizes contradiction in their reasoning. — Moliere

No, they don't. This is equivocation. Neither one has anything like the standing contradictions of dialetheism. Tensions which go on to get resolved are nothing like the stable contradictions of dialetheism.

The objection was given <here>. You tried to answer it by redefining "false" as "fake," and I think we both agreed that that answer failed. That's where things stand, as you never made another attempt. — Leontiskos

What I said was

"Duck is false" and "2+3+4+5 is false" don't work because "Duck" and "2+3+4+5" are not assertions at all, but nouns. — Moliere

It's the object that's different which changes the meaning of "...is false", which is why these examples don't work. Since the liar's sentence is a sentence the usual meaning of "...is false" works just fine.

I didn't redefine the predicates but pointed out how your counter-example didn't stick.

Sure: if dialetheism is true, then strong logical pluralism is true. — Leontiskos

Cool. Then it seems that an argument for dialetheism is very much on topic then, and the liar's sentence is what I'm proposing as a dialetheia

No, they don't. This is equivocation. Neither one has anything like the standing contradictions of dialetheism. Tensions which go on to get resolved are nothing like the stable contradictions of dialetheism. — Leontiskos

I disagree. The moment of sublation in either Hegel or Marx is not a singular moment which is separable from their negations, but is rather the composition of negations and the negation of that composition. Without recognizing the unity of the opposites -- contradiction -- sublation wouldn't be recognizable as a distinct moment in the logical process.

Now that may very well be the case in fact, but conceptually speaking it seems you at least have to accept contradictions which are operable in some fashion in the logics of each philosopher -- not two opposing things that happen to yield a third thing, but rather the two opposing things very opposition is connected to this third thing in a relationship of inference, where the contradiction is part of the inference, and is not a reductio.

Well you can't say what it means — Leontiskos

I set out the meaning of the liar's here:

I'd say that just from a plain language sense "This sentence is false" is clear to a point that it can't be clarified further. "This sentence" is a pronoun being used to refer to the entire phrase which the pronoun is a part of. "... is false" is the sort of predicate we apply to statements.

"...is false" is the predicate which yields the value "true" for sentences which are false in a truth-functional sense — Moliere

Isn't a tautology as much a contradiction as anything? (p or ~p) We always take as true but really it's only going to be 1 p. We aren't describing two possible things. A thing can't really be otherwise or not.

It's about the number of correct logics (i.e. logics that ensure true conclusions follow from true premises). In general, it's a position about applied logic, which is why monists and pluralists often justify their demarcation of correct logic(s) in terms of natural language, scientific discourse, etc. Nihlism would, by contrast, say there are no correct logics (and also no incorrect ones). This is not to say that reasoning is entirely arbitrary, presumably there are some standards for what constitutes appropriate reasoning. But there is no logical consequence relationship that is appropriate or correct for any particular topic. So, for instance, the intuitionist and his rival in mathematics are both wrong in that neither are "right."

You could think of this as similar to how there are very many geometries, and unfathomably many possible ones. One can identify what "follows" from their axioms according to whatever logical consequence relationship one cares to use, but this doesn't necessitate that the geometry of the physical world is infinitely variable or that it lacks any "correct" geometries. We tend to think that there would be just one geometry for physics (at least physicists normally do), or that, if there were many, there would be morphisms between them. The claims of the monist in particular are roughly analagous to the claims of the physicist re geometry. For instance, when Gisin recommends intuitionist mathematics for quantum mechanics, he does not mean to suggest that this is merely interesting or useful, but that it in some way better conforms to physics itself in ens reale, not just ens rationis.

Normally it gets framed in terms of the entailment relationship. This avoids unhelpful "counterexamples," like competing geometries that use some different axioms, but nonetheless have the same underlying entailment relationship. These are unhelpful because the question isn't about "what specifically is true/can be known to be true given different axioms" but rather "how does one move from true premises to true conclusions." This is why monists might also allow for multiple logics that are "correct," the "correct logic" being more a "weakest true logic."

So, is a fine example of the basic intuition at work in rejecting some logics for some contexts (pluralism) or holding to one logic as truth-preserving (monism) vis-á-vis natural language, a metaphysical notion of truth, etc.

And 's "a thing can't really be otherwise or not," would be a similar sort of reasoning. Dialetheism is normally argued for in the context of paradoxes related to self-reference (as has been the case in this thread). I think critics would argue that these are no more mysterious than our ability to say things that aren't true (which perhaps IS mysterious). At any rate, the "actual" true contradictions that get thrown out, in the SEP article for example, etc. tend to be far less convincing. For example, "you are either in a room or out, but when you are moving out of a room, at one point you will be in, out, both, or neither."

I don't think Hegel is really a good example here because the Absolute is the whole process of its coming into being, in which contradiction is resolved, and contradictions contain their own resolution. It's examples of contradiction, being's collapse into nothing, etc. are very much unlike the standard examples meant to define dialetheism.

I think for Hegel a thing contains its opposition. So for redness, non-redness is part of what it is. Everything you think about is like that. You think in oppositions. But dialetheism would be a mystical state of mind?

Correct, although not everything in the Logic follows the formula of "thing" → "negation" → "negation of negation," some get a good deal more complex.

I think Pinkard is right that Hegel is in some sense very Aristotlean (even if I think Pinkard generally deflates Hegel for modern tastes). Hegel wants to track down the necessity in everything, the intelligibility of concepts. In his book on Hegel, Robert Wallace uses "red" as an example. We don't just have "red" implying "~red," but rather red implies the entire category of color and the things that can be colored (primarily light; nothing is red in total darkness).

Hegel describes the determinateness of quality as involving both “reality” and “negation.” These are the successors, within determinate being, of being and nothing (WL 5: 118/GW 21:98–99,29–35/111). What Hegel seems to have specifically in mind, in connection with “negation,” is that qualities are organized in what we might call a conceptual space, such that being one particular quality is not being the other qualities that are conceptually related to it. Being the quality, “red,” for example, is not just being a conceptually indeterminate “something or other,” knowable only by direct inspection; rather, it is being something that belongs in the conceptual space of color, and thus it is not being the color,“blue,”the color,“yellow,”and soon. In this way, the identity of the quality, “red,” essentially involves reference to what that quality is not:It essentially involves “negation.”6 Hegel sometimes refers to this dependence of quality on other qualities as “alteration” (WL 5:127/GW 21:106,8–9/118;EL§92,A), but it’s important to remember that in this initial context of quality as such, there is nothing analogous to time(or space) in which literal alteration could take place, so the term should be understood as referring to a relationship of logical dependency rather than to one of temporal sequence or transformation, as such.

Under the heading of “reality,”in contrast to“negation,”Hegel seems to want to capture a thought shared by philosophers such as John Duns Scotus, F. H. Jacobi, and C. S. Peirce, who stress an irreducible brute “this-ness,” or haecceitas, distinct from any relatedness or subsumption, as essential to reality. It seems to them that what a particular determinate being or quality is should just be a fact about it, rather than being a fact about how it relates to innumerable other determinate beings or qualities.7 Hegel’s introduction of “negation” alongside of “reality” makes it clear that “reality” (as something like “this-ness”) is not without problems, but that doesn’t cause him to abandon it. Working its problems out will, in effect, be the motor of the Logic as a whole.

If Hegel were asked: Why should we be concerned about this “reality” of determinate being? Why couldn’t we just accept the notion that all qualities are interdependent, defined by their relations to other qualities, “all the way down,” with no remainder (and that all of them are thereby equally “real” or equally “unreal”)?– his answer would be that if something could be what it is by virtue of itself, rather than solely by virtue of its relations to other things, it would clearly be more real, when taken by itself, than something that depends on its relations to other things to make it what it is. This is not to say that the thing that depends on other things is, in any sense, illusory– the “reality” that we’re talking about here is not contrasted with illusion, but with depending on others to determine what one is. Something that makes itself what it is has greater self-sufficiency than something that doesn’t do this, and this self-sufficiency is likely to be among the things that we think of when we think of “reality.” If it is among the things we think of, this could be because we’re aware that “reality”– like the word that Hegel uses, which is real, “realitat”– is derived from the Latin res, or “thing,” so that it contrasts not only with illusion but with anything that is less independent or self-sufficient than a thing.

Robert Wallace - Hegel's Philosophy of Reality, Freedom, and God

You can see the strong Aristotelian bent in the last paragraph. But Hegel, living in a time where atomism is ascendant, cannot leave things as "unpacked" as Aristotle does with his vaguer concepts that cover more ground. However, maybe Big Heg should have listened to Slick A's advice in the Ethics re "don't demand that your explanations be more exact than your subject matter allows."

I agree with Wallace. I think the same idea is in Phaedo as the Cyclical Argument.

Me too. However, I also think the sense of "contradiction" here is quite far from that invoked by religiously motivated dialetheism or those motivated largely by problems of self-reference. It's quite different. But to 's point, I am not sure how much this carries over to Marx. I have read a lot of Marxists but not much Marx, so I am not really in a position to have a strong opinion on that front.

At any rate, Hegel affirms LNC in its usual contexts, but I think it's fair to call him a monist if anyone is. The role he has for logic is deeply ontological.

However, I also think the sense of "contradiction" here is quite far from that invoked by religiously motivated dialetheism or those motivated largely by problems of self-reference — Count Timothy von Icarus

The situation Hegel is pointing out isn't paradoxical, if that's what you mean.

I have read a lot of Marxists but not much Marx, so I am not really in a position to have a strong opinion on that front. — Count Timothy von Icarus

The secondary source I read said that Marx didn't use dialectics much, but I'd be interested to see a case where he did.

At any rate, Hegel affirms LNC in its usual contexts, but I think it's fair to call him a monist if anyone is. The role he has for logic is deeply ontological. — Count Timothy von Icarus

Sounds about right.

It's about the number of correct logics (i.e. logics that ensure true conclusions follow from true premises). In general, it's a position about applied logic, which is why monists and pluralists often justify their demarcation of correct logic(s) in terms of natural language, scientific discourse, etc. Nihlism would, by contrast, say there are no correct logics (and also no incorrect ones). This is not to say that reasoning is entirely arbitrary, presumably there are some standards for what constitutes appropriate reasoning. But there is no logical consequence relationship that is appropriate or correct for any particular topic. So, for instance, the intuitionist and his rival in mathematics are both wrong in that neither are "right." — Count Timothy von Icarus

I'm not sure I'd go as far as to say "correct" in describing a logic. What would it possibly mean for a logic to be correct in a non-question begging way? "Correct" seems to already presume some standards of coherency, and I'd say validity is a species of coherency.

That is, we'd be presuming some logic in setting out the correct logic. Now if there were only one logic that would at least be consistent, but then we get to the part on begging the question -- which, I think, is why the puzzle is interesting: Either answer can be made self-consistent (monism or pluralism), but in what sense can the two camps speak to one another?

You could think of this as similar to how there are very many geometries, and unfathomably many possible ones. One can identify what "follows" from their axioms according to whatever logical consequence relationship one cares to use, but this doesn't necessitate that the geometry of the physical world is infinitely variable or that it lacks any "correct" geometries. We tend to think that there would be just one geometry for physics (at least physicists normally do), or that, if there were many, there would be morphisms between them. The claims of the monist in particular are roughly analagous to the claims of the physicist re geometry. For instance, when Gisin recommends intuitionist mathematics for quantum mechanics, he does not mean to suggest that this is merely interesting or useful, but that it in some way better conforms to physics itself in ens reale, not just ens rationis.

[/quote]

Can you fill out this analogy?

Geometry:Physics :: Logic:D

What takes the place of "D" here? I understand the relation between geometry and physics, but also by the time we're talking geometry and physics it seems a logic, an epistemology, an ontology are already in play for the purposes of producing knowledge -- Also I'm not sure that the analogy serves the monist very well because geometers do geometry outside of the bounds of physics, and so we'd presume the same would hold for the logicians?

Normally it gets framed in terms of the entailment relationship. This avoids unhelpful "counterexamples," like competing geometries that use some different axioms, but nonetheless have the same underlying entailment relationship. These are unhelpful because the question isn't about "what specifically is true/can be known to be true given different axioms" but rather "how does one move from true premises to true conclusions." This is why monists might also allow for multiple logics that are "correct," the "correct logic" being more a "weakest true logic." — Count Timothy von Icarus

I'm not sure the entailment relationship ends up being any more stable than the LNC or the principle of explosion. Pick your hinge and flip it!

When you say

These are unhelpful because the question isn't about "what specifically is true/can be known to be true given different axioms" but rather "how does one move from true premises to true conclusions."

There's a quibble I feel that may indicate some miscommunication (or not, we'll see).

The question for logic, IMO, is not "How does one move from true premises to true conclusions?" -- I'd say that's a question for epistemology more broadly -- but rather logic is the study of validity. The big difference here from even introductory logic books is that the truth of the premises aren't relevant, which I'm sure you know already -- the moon being made of green cheese and all that.

So we don't care if the premises are true or not. We only care that if they are true, due to the form of inferences, that the conclusion must be true.

Do you see a difference between the questions?

I'd say your question asks for evidence or rationation, whereas the study of validity will depend upon how we define our logic.\

I don't think Hegel is really a good example here because the Absolute is the whole process of its coming into being, in which contradiction is resolved, and contradictions contain their own resolution. It's examples of contradiction, being's collapse into nothing, etc. are very much unlike the standard examples meant to define dialetheism. — Count Timothy von Icarus

Just to be clear, and I have not been so sorry, I'm not presenting Hegel as a dialetheist, but rather as a philosopher that uses contradiction in his reasoning -- since the conclusion to a contradiction is not "Meaningless" or "simply false" it strikes me as different from the older assumption of the LNC.

Also, you've mentioned it but, what makes Hegel an interesting case is his simultaneous acceptance and modification to the LNC. He accepts the LNC in its own context (i.e. outside of time), but when time gets involved he introduces a new inference -- sublation -- to manage the contradictions of becoming.

This isn't to say that he's a pluralist, either. I agree that if Hegel were anything that "monist" makes sense. It's only to say that in order for us to make sense of Hegel we have to be able to evaluate contradictions without rejecting them out of hand, and so at least the logic which makes sense of Hegel must reject the LNC.

The thread has wandered around quite a bit. It might be worth returning to my opening post and the philosophical curiosities around it.

Perhaps the core issue is whether there are logical laws that hold in every case. Given boundless human creativity, it is at least conceivable that whatever one posits as a logical law, a counterexample can be constructed. Russell gives examples of counter instances for identity, And elimination, excluded middle, and modus ponens. Whether these are thought successful or not, to rule out the construction of such counter instances is claiming that there is a one true logic that permits such a ruling. Exactly how and if such a logical monism might stand is one of the themes of this thread.

The opposite view would be that there are no rules that hold in any case. On this account logical reasoning has no compulsion, being little more than a rhetorical device. Exactly how and if such logical nihilism might stand is one of the themes of this thread.

Contradicting both these is the view that while no laws that apply in every case, there may well be laws that apply in some cases. On this account there might be a logic applicable to particular case or situations, but not in all cases or situations.

Russell proceeds by considering examples of mooted laws of logic and offering counter instances. You can get an idea of these by reading the paper or watching the video mentioned on Page One. The discussion concerns formal logic, and presumes some familiarity with that terminology and method. Those seriously considering the issues of the paper, video and of this thread should have at least some background in formal logic.

The logic talks at a meta level, so it talks about sentences, represented by greek letters such as φ and ψ, phi and psi, which are part of a language Γ, together with the usual connectives logical connectives. In addition she uses the Turnstile, ⊨. This represents the logical truth of sentences, so that "⊨φ" can be read as "Phi is true", and "Γ⊨φ" can be read as "Phi is true in Gamma". The topic presumes an understanding of the idea of truth as satisfaction, and there is some mention of possible worlds. These are things that folk who presume to philosophical discussion ought at least have some clear grasp.

The argument presented is a defence of the use of logic in the face of the strength of logical nihilism. If you have an interest in the topic, please take some time to look at the video or read the article. Some who have commented here have done so without that due diligence, for reasons of their own, and so entirely miss what is going on.

I'm not sure I'd go as far as to say "correct" in describing a logic.

Just to be clear, this isn't my term, but the term employed through much of the literature on this topic, including the papers discussed earlier in this thread.

However, I suppose the response would be: Are there not inference rules that allow us to move from true premises to true conclusions, such that if our premises are true our conclusion will be as well? If so, then it seems there are "correct" logics. Unless we want to say that all inference rules lead to true conclusions, making the distinction meaningless (this seems hard to defend), or that no inference rules lead us from true premises to true conclusions (this also seems hard to defend, for how would one show that such an argument makes legitimate inferences?)



I'm not sure how this would be question begging. Logic deals with valid inference, how we get from true premises to true conclusions—truth preservation. Presumably, it doesn't define truth itself, so the criteria for determining which inference rules (if any) preserve truth in which contexts (if any) is external.

The question for logic, IMO, is not "How does one move from true premises to true conclusions?" -- I'd say that's a question for epistemology more broadly -- but rather logic is the study of validity. The big difference here from even introductory logic books is that the truth of the premises aren't relevant, which I'm sure you know already -- the moon being made of green cheese and all that.

So we don't care if the premises are true or not. We only care that if they are true, due to the form of inferences, that the conclusion must be true.

How would you define validity?

"A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid," is the textbook answer from IEP. The textbooks I've used give the same definition.

Stanford's open introduction to logic puts it thus: "Valid: an argument is valid if and only if it is necessary that if all of the premises are true, then the conclusion is true; if all the premises are true, then the conclusion must be true; it is impossible that all the premises are true and the conclusion is false."

I am aware that some scholars have tried to redefine validity in normative terms, e.g. that it is "what we should or shouldn't accept." The Clarke-Doane paper Banno shared is from this camp. However, I have never seen such a view presented that does not assume a deflationary account of truth, that "truth " as most people think of it, does not exist.

Well, that's a fine argument to have. But it gets to the point I tried to make to Banno and fdrake that one cannot retreat into formalism and ignore discussions of truth on this topic. If it would be question begging to assume that logic is about truth-preservation then it would be equally question begging to say that truth depends on / is defined by normative or formal contexts. If the latter is accepted, then of course nihilism is true (or rather true relative to some contexts and false relative to others, depending on our normative games.)

Now the arguments for deflation are abductive (what would it even mean to "prove" such a thesis?) But like I said before, it's hard to think of things it's easier to make a strong abductive argument for than: "in many cases what is true does not depend entirely on how we choose to speak or which formal system we use. It is true that if you dip your hand in boiling water you will be burned in a sense that transcends social practice or formalism." And if we take logic to be wholly normative, e.g. "you ought not stick your hand in boiling water if you don't want to be burned," it seems that we will still have the question "why ought we not do this?" The answer: "because it is true that boiling water causes burns," seems like the most plausible one, but then we are back to truth.

So we don't care if the premises are true or not. We only care that if they are true, due to the form of inferences, that the conclusion must be true.

Yes, this is soundness versus validity. However, this distinction need not (and normally isn't) taken to imply that logic isn't about truth-preservation. The debate is about the rules of truth preservation, not about the truth of any particular premises in an argument.

I'm not sure the entailment relationship ends up being any more stable than the LNC or the principle of explosion. Pick your hinge and flip it!

Well, that's at least normally how it has been defined and it's been defined that way because the mainstream view of logic is that it is (largely) the study of validity, with validity being about truth preservation—i.e., how one goes from true premises to necessarily true conclusions. Obviously if we redefine validity this might make less sense.

But I think there is maybe a misunderstanding here because if you remove LNC you are changing the logical consequence relationship. What follows from what (the logical consequence or entailment relationship) depends on LNC, LEM, relevance conditions for implication, etc. The nihilist claims this relationship is empty, nothing follows from anything else (in any correct sense, i.e. ensuring truth preservation).

How would you define validity?

"A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid," is the textbook answer from IEP. The textbooks I've used give the same definition.

Stanford's open introduction to logic puts it thus: "Valid: an argument is valid if and only if it is necessary that if all of the premises are true, then the conclusion is true; if all the premises are true, then the conclusion must be true; it is impossible that all the premises are true and the conclusion is false." — Count Timothy von Icarus

These work just fine by me which indicates we're just talking past one another.


What say you to 's proposal? Does it seem to sidestep something important, in your view?

The reason I've been delving into historical examples, and I have hope I haven't gone too far afield @Banno, was to tie some of the above into the argument for pluralism: if we accept contradiction into our reasoning, and we also reject contradiction in some of our reasoning then we are pluralists.

Moving to that because of the incredulity of dialetheia, which is where originally I staked my flag in defense of pluralism.

Sorry if it was too off topic though.

if we accept contradiction into our reasoning, — Moliere

What would be an example of that?

You are welcome to go in such directions, of course. It's just not my cup of tea, too far removed from the original theme of this thread to hold much interest for me. Frankly, I think such stuff too ill-defined to be done well. That doesn't stop me occasionally indulging, of course.

If the liar's sentence is true then the liar's sentence is false.
If the liar's sentence is false then the liar's sentence is true.
The law of excluded middle states there can be no other values for a sentence than true or false.
Therefore the liar's sentence must be true and false, or not-true and not-false.

Though this doesn't get over the hurdle of relevance, which I think has what's mostly been at stake in various responses here -- the liar's sentence isn't useful in some context outside of philosophy and so it seems like a toy which ought to be viewed as such, whereas the knowledge we actually use in the real world is girded by a firm bivalency we not only can stand atop but have not choice but to do so or be in error.

I wasn't able to follow this.

Frankly, I think such stuff too ill-defined to be done well. — Banno

Now that's when we're doing philosophy! :D

But perhaps not well.

Oh, certainly. Fair enough.

Though not to be rude I'm still looking for good points of response @Count Timothy von Icarus, but rather in bits to see if we can stall the sprawl a bit.

Well, that's a fine argument to have. But it gets to the point I tried to make to Banno and fdrake that one cannot retreat into formalism and ignore discussions of truth on this topic. If it would be question begging to assume that logic is about truth-preservation then it would be equally question begging to say that truth depends on / is defined by normative or formal contexts. If the latter is accepted, then of course nihilism is true (or rather true relative to some contexts and false relative to others, depending on our normative games.) — Count Timothy von Icarus

One thing I'm guessing is that arguments for any logic, due to the generality of the topic, will by their very nature always beg the question -- otherwise the logic wouldn't be consistent with itself! And that's a terrible place for a candidate logic to be.

The point from there would simply be to demonstrate more than one logic -- one which results in a "F", where the other results in a "T" or there's perhaps another value other than "F" or "T". The trick is in being able to evaluate the logic without the logic. How can it be done? I think that's the puzzle, in a nutshell.

I don't see how to make sense of that quote in the light of the notion of satisfaction, which does define truth in many formal logics.

What do you think the term "correct logic" means in Russell's papers, G&P, Clarke-Doane's paper, etc.? I know you don't like the term, but you refused to elaborate on what you think means.

If "correctness" was simply satisfaction there wouldn't be any debate.