@fdrake, Have a quick look at What is Logical Monism? I suspect you would enjoy it, since it draws on the parallels with mathematics that you are using here.

So be honest. When you say, "This sentence is true/false," do you think you are saying something meaningful? Would you actually use that phrase, speak it aloud, and expect to have said something meaningful? — Leontiskos

Yes

Here I am using it, no? Its use-case is philosophical, rather than pragmatic, but I don't think that makes it meaningless.

Also I've changed over to the plain language version of the paradox to accommodate fears of formalism -- it's an example that arises from natural language use. What's so hard to comprehend about it?

To use 's division, this example is in (1). A child can understand the sentence.

How one answers the paradox is the interesting philosophical part, and also demonstrates the virtue of the analytic approach. The idea here is that we ought not poison the well because the implications of changing a logic are philosophically wide-reaching, at least with respect to some traditions of philosophy.

So it's not that metaphysics or knowledge are entirely ignored, but the hope is to find some implicating hint from an exposition of the conceptual map. The conceptual map doesn't represent battlelines as much as possible distinctions one can take up.

A sentence says something if it presents a comprehensible assertion. It says something if its claim is intelligible. — Leontiskos

Intelligible to whom?

Now when you say, "X is false," I can think of X's that fit the bill. I might ask what you mean by X, and you might say, "2+2=5." That's fine. "...is false" applies to claims or assertions. If there is no claim or assertion then there is no place for "...is false." For example, "Duck is false," "2+3+4+5 is false," "This sentence is false."

I don't think it's so incomprehensible. I think it's very simple. "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. Now if by "This is false" I indicated a duck perhaps I'd be using "...is false" in the place of "...is fake", but it wouldn't be the "...is false" which we use when talking about statements.

The pronoun in "This sentence is false" points to itself, which is a statement. And the statement utilizes a predicate normally reserved for statements, so there's no category error as you're implying. It's not nonsensical for this reason at least.

It may be nonsensical because it flies in the face of the principle of non-contradiction, or the principle of explosion. These are normal metrics for judging whether something is sensible or not -- the funny thing with this topic is that we can't rely upon those norms to decide the question since they are the things in question.

Do you agree that at least paraconsistent logic is significantly different enough from either Aristotelian or symbolic logic that one would count as a logical pluralist if they subscribed to the belief that both logics are valid or true in their own way or domains? That is the reason I brought up dialetheia and paraconsistent logic, after all: It seemed to be an obvious case of logical pluralism that is significant.

Not all paraconsistent logics accept dialetheism, but dialethiests are pretty much obligated to accept paraconsistent logic. — Banno

Cool, got it. Makes sense. One doesn't have to accept true contradictions to abandon the principle of explosion -- it could be that contradictions still always lead to falsity, but not explosion, or something like that.

I did enjoy it. It is also written in a very entertaining way. I would need to read it a few more times to follow the argument though.

@Leontiskos - 's linked paper here seems to interface with your position much more explicitly than Russell's paper. The argument is quite sequential and not modular so skim reading would be difficult, there is nothing particularly maths or logic technical in it, but the discussion regarding whether there is a privileged logic for metaphysics - and what that would even mean - are far closer to what I think you want this discussion to be. Also @Srap Tasmaner, assuming you're interested in pursuing the thread of argument regarding formalism, "the true rules" and metaphysics earlier. Also @Joshs, because the paper has a rare Rorty vibe while being very much from the mathematics and logic flavour analytic philosophy branch.

I've seen that paper before. I give it credit for at least addressing the issue of metaphysical truth, but it is a prime example of implicit question begging re the deflation of truth. "Truth just is something to do with formalism, and how can you pick between formalisms? According to which one is true? Well, you have to use a formalism to discuss truth, and different formalisms say different things."

The background assumption throughout, and what the arguments routinely rely upon, is that truth is simply formalism.

What is wrong with the standard answer? Even if ‘the Goldbach Disjunction is a logical truth’ is determinately and unambiguously true out of our mouths, it is not true out of another possible community’s mouth.6 They may use ‘logical truth’ to mean, say, intuitionistic validity. Goldbach’s Disjunction is not an intuitionistic validity. So, there are two relations: validity Us and validity Intuitionistic.

There is no dispute that both relations ‘exist’ if either does.7 The only dispute is about which of these we happen to pick out with ‘logical truth’ (or about what is packed into the concept of logical truth that we happen to employ). The monist and the pluralist, understood in the standard way, agree on the non-semantic world. (Indeed, one could make classical logic the One True Logic, in the standard sense, by indoctrinating children with the classical truth tables!)8

Of course, it is often of metaphysical and methodological import what a sentence is about. The fact that another possible community means ether by ‘dark matter’ hardly undercuts the interest of the debate over dark matter. But the logical case is not like this. It is more like the case of pure (rather than applied) geometry. Hyperbolic lines exist if Euclidean lines do, qua pure mathematical entities. So, all we would learn in deciding ‘’whether the…relations so defined agree…with the pre-theoretic notions’ would be something about ourselves. We would just learn which line-like things we happened to refer to with ‘line’... The only factual question at stake is what we happen to mean by ‘valid’. If there were a (meta)logical analog to the question of which geometry is true of physical spacetime, then the logical case might be like the dark matter case...

...But the choice of (meta)logic under which to close cannot itself be made on the basis of the physical facts. We need a metalogic to state them in the first place! For instance, do they include that either there are gravitons or that it is not the case that there are gravitons (or the denial of the 15 claim that there both are gravitons and are not gravitons)? It depends on whether the Law of the Excluded Middle (or Noncontradiction) is valid

But what's good for the goose is good for the gander. This is exactly the same charge leveled at pluralists by G&P. "Show pluralism is the case in your correct logics," or more strongly "show us it's the case in all of them. We think you'll find that quite impossible"

The response from Shapiro and others is, "well, the argument for pluralism is abductive." Fair enough (although G&P still point out that abduction involves deduction). But it's hard to think of a thing it is easier to make a strong abductive argument for then "things can be actually true, not just true as respects an arbitrary formalism." How do you choose between logics in this respect? The issue is epistemic, it cannot be handled by formal systems, at best they are an aid. And this is demonstrated that whenever the author wants to bring up a case of apparent conflict, they always resort to examples from formal systems, even when discussing the metaphysical view.

"The Goldbach Disjunction is a logical truth" and the like are simply ambiguous. They are claims about stipulated sign systems without reference to which system. I think the retreat into formalism covers up the obvious here. If bishops could move to the left in Pakistani chess, we could say the truth of "the bishop cannot change its color" is ambiguous and varies with context. Different systems, different logical truths. But the issue here is simply that the term "chess" is unclear.

This is not the case when we move to "all men are mortal," which isn't situated in a stipulated system. If we ask, "what does being mortal actually entail?" then "it depends," is hard to swallow as a good answer. So, the case the pluralism has to make in this respect is that there is no one intelligible pattern unifying the preservation of truth vis-a-vis this sort of (metaphysical) truth.

The study of form cannot tell us about things like "all men are mortal," but this doesn't mean that what constitutes a correct logic is unrelated to them since we care about "truth-preservation," not "truth-preservation relative to x formalism."

Thought you would enjoy it.

The Open Logic Project is a Wiki of sorts, designed to provide a free textbook on logic. It works thorough Naive set theory, propositional an predicate logic, model theory, computability, second-order logic, Lambda Calculus, many-valued logics, modal logic, intuitionistic logic and set theory.

At the end of the section on first-order logics is a short chapter named "Beyond First-order Logic". It ends with this admonition to creativity:

As you may have gathered by now, it is not hard to design a new logic. You
too can create your own a syntax, make up a deductive system, and fashion
a semantics to go with it. You might have to be a bit clever if you want the
derivation system to be complete for the semantics, and it might take some
effort to convince the world at large that your logic is truly interesting. But, in
return, you can enjoy hours of good, clean fun, exploring your logic’s mathe-
matical and computational properties.
Recent decades have witnessed a veritable explosion of formal logics. Fuzzy
logic is designed to model reasoning about vague properties. Probabilistic
logic is designed to model reasoning about uncertainty. Default logics and
nonmonotonic logics are designed to model defeasible forms of reasoning,
which is to say, “reasonable” inferences that can later be overturned in the face
of new information. There are epistemic logics, designed to model reasoning
about knowledge; causal logics, designed to model reasoning about causal re-
lationships; and even “deontic” logics, which are designed to model reason-
ing about moral and ethical obligations. Depending on whether the primary
motivation for introducing these systems is philosophical, mathematical, or
computational, you may find such creatures studies under the rubric of math-
ematical logic, philosophical logic, artificial intelligence, cognitive science, or
elsewhere.
The list goes on and on, and the possibilities seem endless. We may never
attain Leibniz’ dream of reducing all of human reason to calculation—but that
can’t stop us from trying.

The commendation to the student is to be creative. This is a methodological pluralism.

I've read that post twice and I'm still not sure what your criticism is.

I've seen that paper before. I give it credit for at least addressing the issue of metaphysical truth, but it is a prime example of implicit question begging re the deflation of truth. Truth just is something to do with formalism, and how can you pick between formalisms? According to which one is true? Well, you have to use a formalism to discuss truth, and different formalisms say different things. — Count Timothy von Icarus

Am I to read this as you saying truth is something to do with formalism, or as you saying that the flaw in the paper is that it considers truth only to be something to do with formalism?

Or do I just need more coffee?

I guess the obvious question is, if you know what truth is, apart from formal systems, then tell us. Otherwise, it seems to me that we could do far worse than Tarski's account of truth in terms of satisfaction.

And I am still not too sure what you mean by "deflation". Do you think Tarski's account is necessarily deflationary?

Yep. Kleene logic is explosive.

- That is closer to the foundational discussion between Srap and I, but still different. I think 's post is quite good.

There are two questions with this pluralism/monism debate: What the heck is the thesis supposed to be, and Who has the burden of proof in addressing it? The answers seem to be, respectively, "Who knows?" and "The other guy!" :lol:

By rephrasing it in terms of the puzzle of the Meno and the possibility of discursive knowledge I sought to avoid such swamps, and I did that before this thread was necrobumped. The problem with this thread is that Banno and G. Russell want to say something controversial and novel and are therefore always moving between their motte and their bailey. The first question is to ask what the thesis is supposed to be, and what 'logic' means for the person proposing a thesis.

The answers seem to be, respectively, "Who knows?" and "The other guy!" :lol: — Leontiskos

I have invented a logic in which there is no other guy and no one knows who they are.

- And here I was under the impression that Jamal invented TPF. :smile:

My hypothesis is that there's a deep seated drive in most people to insist on logical monism. I think it's related to unity of consciousness: one self, one world, one logic. I think pluralists are using the term differently.

On deflationary accounts, “all that can be significantly said about truth is exhausted by an account of the role of the expression ‘true’... in our [speech] or thought,” and we might add formal systems here. Thus, notions of truth are neither “metaphysically substantive nor explanatory.”

This is clearly going to be a problematic background assumption to have going into an analysis of a metaphysical case for a single entailment relation applicable to being.

I guess the obvious question is, if you know what truth is, apart from formal systems, then tell us. Otherwise, it seems to me that we could do far worse than Tarski's account of truth in terms of satisfaction.

Ah, but this is perhaps the cardinal sin of contemporary philosophy! "X is difficult to define or account for, let's eliminate it." We've seen this done with Goodness, Beauty, Truth, meaning, and finally, in eliminitivism, our own consciousnesses. What philosophy worth doing shall be left?

Not to mention, consider this same question on other finicky definitions, such as "life." We might very well run with some sort of formal definition for expediency on some issues, but it clearly won't do to for others. A bad definition can be worse than an ambiguous one.

Now I get, the metaphysical and scientific sections are just two parts of the article. It's too much to expect a deep dive into different theories. But just consider a very influential one, Aristotle. For Aristotle, "being" is said many ways, but it is said most primarily of substances. Mathematical entities aren't substances. They don't exist simplicitier, but with qualification. So obviously the arguments in those sections that use "exists" univocally throughout are problematic, particularly since this is hardly unique to Aristotle, but common, I would guess, to most thinkers.

It doesn't seem that different from looking at contradictory stories told about superheros, saying both "exist" and declaring an exception to LNC. This is missed if one supposes that we're talking about a blanket prohibition on "a and not-a" as opposed to a prohibition on something actually being and not-being, without qualification.

As a side note, while I know the example of different mathematical objects is intuitive, but I am not sure if a lot of these even require different entailment relations.

This goes back to the discussion with Tom:

To what extent does your disagreement on this involve, perhaps, one being a conservative and the other liberal? — Tom Storm

Monism, and authoritarianism, offer certainty.

Monism, and authoritarianism, offer certainty. — Banno

Which means it can't be defeated.

Which means it's methodological - it's about attitude. Closed or open.

~~

On deflationary accounts, “all that can be significantly said about truth is exhausted by an account of the role of the expression ‘true’... in our [speech] or thought,” and we might add formal systems here. Thus, notions of truth are neither “metaphysically substantive nor explanatory.” — Count Timothy von Icarus

So what's the problem? It's not as if deflationary accounts say that there are not truths.

In Model theory truth isn't eliminated, but given a firm grounding in satisfaction.

Issues of "being" are not ignored by formal logic, either, but explicated by quantification, predication and equivalence.

If I am candid, it seems to me that your fears are ill conceived and unfounded.

Which means it's methodological - it's about attitude. Closed or open. — Banno

The saying is "Be open minded, but not so open minded your brain rolls out."

I prefer "Keep your mind too open and it will fill up with garbage".

And thus the moralistic undercurrents driving this silliness have finally become fully explicit. It's hard to put so much effort into defending an undefined thesis without this sort of moralistic self-righteousness. But of course it was there all along.

"Keep your mind too open and it will fill up with garbage". — Banno

:grin:

The problem for logical monism is that if there is only one logic, then which one? — Banno

Generalized. Return to the basic principle things ought to make sense. How that is accomplished may vary.

:rofl:
So I'm to blame for and @Tom Storm's questions. Fine.

From the SEP article...

One option available to the monist is to interpret the claim that there is one and only one correct logic noncognitively. Clarke-Doane, after finding no satisfying factualist construal of monism, interprets the claim as expressing an attitude. Perhaps this strategy could be extended to the debate between monists and pluralists more broadly.

That's were I came across the Clarke-Doane article and the discussion of approaching the issue as one of attitude.

But you are right, that things would be a lot simpler if we were just to go back to Aristotle.

I prefer "If you can't tell the difference between the various garbages, or worthwhiles, then it's time to open your mind more" :D

Return to the basic principle things ought to make sense. How that is accomplished may vary. — Cheshire

Yep. And if there are more than one set of basic principles, then we have one form of pluralism.

And if a set of basic principles is found, then the challenge is set to see what happens if we change them, try different basic principles, or diagonalise in some way... to look at logic differently and undermine it to see what happens.

Put another way, how could we ever be sure that some set of basic principles is sufficient for all of logic?

The story at least since Russell's paradox and Gödel seems to indicate that this is not what happens.

The story at least since Russell's paradox and Gödel seems to indicate that this is not what happens. — Banno

Isn't it though? What did they both do but modify their systems. Russell decided you can't have self-referential sets and Godel concluded that no system really has a foundation. And both did it based on the generalized principle that things should make sense. I wasn't being dismissive, if you want a one stop shop for logic that's it. Things ought be sequitur when explained.

If that fits in catagory A or catagory B, I'm not asserting. So, if we need to translate it due the massive hurry philosophers are always in call it
For Every X is some Y
if you want to make it a party
For Every X is some Y or not some Y.

And if we can't agree on that, then what's the point of breaking it down further. All knowledge is likely probabilistic and referential and yet facts exist. Why? Some Y. Or not.

Not really pluralistic. Discovery of the undeniable rejection of monism would be one. If pluralism entails the monism of pluralism then logic has to be pluralistic and essentially monistic in that fact. The error is thinking they're two things.

First , I didn't say formal logic ignores being I said the arguments in the paper use "exist" univocally in a way that makes them facile.

Second, there seems to be a pretty strong abductive argument for "there are many cases where truth does not depend on how we choose speak."

One of the benefits of STT is that is based on notions of correspondsnce truth, and it is certainly often used it with the idea in mind that there is a "real truth." However, stripped down to mere form and taken alone as the final word on the issue it is relativistic. IIRC, Tarski claims truth is "meaningless" outside formalism. If we accept this, not as a useful tool, but as a claim about truth tout court, what exactly makes STT a better theory of truth than any other? Can it be truly better? True relative to what, itself? If we say its more useful, we might ask "is it truly more useful? Truly more useful relative to what? Why not any other theory that might justify itself?

If I am candid, it seems to me that your fears are ill conceived and unfounded

Well, that makes sense if you read the post as "I don't think logic has existential quantifiers."

If we accept this, not as a useful tool, but as a claim about truth tout court, what exactly makes STT a better theory of truth than any other? Can it be truly better? True relative to what, itself? — Count Timothy von Icarus

True relative to something else some one could assert. It's an approximation with an arrow toward truth.

~~

what exactly makes STT a better theory of truth than any other? — Count Timothy von Icarus

Well, it's right. "P" is true iff P is about as direct as you can get.