I, for one, do not trust math.

We may be immortal for all that. (EDIT: And it looks like a cool book that I'd enjoy reading)

M'kay. Then my example would not convince you of dialetheism, and at this point in the debate I'd ask -- if dialetheism were somehow justified would that then justify logical pluralism?

Can you think of any examples of a sentence wherein both A and not-A are true in the same sense or context? For example I could be said to be both old or tall and not old or tall but not in the same senses or contexts. — Janus

The liar's sentence.

"This sentence is false" is the liar's sentence.

This doesn't fit your "for example", though, because it's not about a person, but a sentence.

Since the sentence can be said in any context, and it's basically about words and how we describe them, we can place them within the sense of logic.

The sense of logic can be informal or formal, and insofar as we understand one another well enough it need not be specified.

Though I'm wondering if I've just lost you at this point?

My point was that within any valid logical argument of whatever stripe there must be consistency between the premises and the conclusion. If a premise contradicts another premise or the conclusion then the argument cannot be valid. That sort of thing. — Janus

Your choice of words here has me wondering if I can or not.

But I can give a straightforward answer to your question which may be aside from the point.

Can you explain how dialetheism rules out the LNC? — Janus

Quoting the SEP here:

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true. If falsity is assumed to be the truth of negation, a dialetheia is a sentence which is both true and false.

I've been advancing the argument that the LEM holds -- because there is nothing in between truth and falseness so we cannot choose some in-between or other -- but the liar's sentence is best treated as a dialetheia.

If one accepts that then the LNC cannot hold because the LNC says "A & ¬A" is false. Since ¬A and A, as a dialetheia, are both true and false, together, the LNC is rejected.

However I do remember someone asking whether there were any logical laws that applied to all forms of logic. How about validity and consistency? Or which is basically the same as far as I can tell—the law of non-contradiction? — Janus

I'm a defender of dialetheism, thus far.

Which rules out the LNC.

Hence, the notion of pluralism -- at least so far no one has said that the logics which include the LNC are the same as the logics which exclude the LNC.

Heh. I wouldn't go that far at least. I think @Leontiskos and @Count Timothy von Icarus would want us to come up with a notion of logical monism which is interesting enough for their concerns.

Thus far I've gathered that they both would like to relate to knowledge generation? I think?

This is what motived by earlier response about why the problem is interesting with respect to knowledge generation.

O.

In that case, clearly stipulate-able.

This does not belong in the lounge. This is a paradox that rest on a tricky difference between conditionals in language and conditionals in logic. — hypericin

I wouldn't restrict the lounge like that.

Off topic, but I think the various "wonderings" which are lounge-appropriate can lead to cool and interesting philosophical insights.

It's the creative space where as long as you're not a jerk go ahead -- random ideas, almost connected philosophical thoughts, conversational starting bits -- go for it!

So the philosophy bits do belong here -- I'd say especially because new philosophical thoughts often come from shooting the shit.

Yes, which maybe should make you question if you have any clue what the debate is about. — Count Timothy von Icarus

This comment makes me question if I know what the debate is about.

What's the debate about?

One thing unmentioned that I really like is the "A Very Short Introduction" series of books, as well as the "Introducing" series for similar reasons: They are easy to read and you get a fairly good all-around picture on the subject from someone whose taught it, but in comic book form. What's not to like?! :D

They write them on a number of philosophical, and sometimes other, subjects so I'll just post a link to one of each so you know what to look for if you're interested.

Introducing Descartes
Logic: A Very Short Introduction

:up:

That's a bit beyond me. How does it fail?

What if in place of Kant’s Transcendental categories we substituted normative social practices? Doesn’t that stay true to Kant’s insight concerning the inseparable role of subjectivity in the construction of meaning while avoiding a solipsistic idealism? Don’t we need to think in terms of normative social practices in order to make sense of science? — Joshs

That’s what pragmatist-hermeneutical and poststructural models of practice are for. For Hegel and Marx the dialectic totalizes historical becoming. In these latter models cultural becoming is contextually situated and non-totalizable. — Joshs

Yours has been the hardest to respond to for me. Hence my tardiness.

If we substitute normative social practices for Kant's Transcendental categories, what does that look like? In a very literal sense, which I don't think you mean but this is why I'm asking for clarification, I could substitute a model of practice for quality, quantity, relation, and modality -- substitution seems to need some relation of sameness, if not strict equality, and I'm not sure how practices would work within Kant's categorical frame.

I'd reach more for the ethics, but it becomes even more confusing there lol. So I'm reaching for what's making sense to me right now to respond in kind.

It is normativity all the way down.

How does this claim escape the charge of totalizing?

Hegel's contradiction is pretty far from most paraconsistent logics, given the unity and "development" of opposites. — Count Timothy von Icarus

I agree. I came to the same conclusion, and was disappointed. "Further research needed" :D

I enjoy the phenomenology, but only got 1/2 through the logic and couldn't say I understand it. I could tell it was not time to climb that mountain.

If you're interested though, formalization attempts have run through category theory and Lawvere is the big name here.

https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://philarchive.org/archive/CORMAA-3v1&ved=2ahUKEwjrxdPIz6CJAxURlIkEHUmyEkcQFnoECCEQAQ&usg=AOvVaw3XxnDtBEih45jE5c2zfW2d

Nlab has some stuff on this too.

I have read many commentaries on the Logic at the point. Houlgate and Wallace are my favorites (Wallace isn't quite a commentary, but he does focus on the Logic), but Taylor was useful too. Despite this and now years of effort, I find the essence chapter largely impenetrable lol. — Count Timothy von Icarus

Thank you! Next time I feel like trying the Kilimanjaro of philosophy I'll be referencing these ahead of time to prepare.

Like probably everyone on TPF, I have read about paraconsistent logic as I read about animals in a far off land, but I have never worked with it or made use of it. — Leontiskos

My brush with dialethiesm, and thereby paraconsistent logic, came from my studies of the liar's paradox. So for me it's the result of reading arguments about the liar's and thinking dialetheism provided the most satisfactory answer. And actually this might be related since I read you here:

Are you asking me whether I think that accepting both paraconsistent and explosive logic results in the robust kind of logical pluralism? My guess is that I would answer 'no.' Paraconsistency does not entail Dialetheism. And paraconsistent logic is often used informally in everyday life (if that counts). — Leontiskos

First to answer the question, yes that's what I'm after: attempting to define what would count as a robust kind of logical pluralism. Here it seems you indicate that, supposing a defense of dialetheism holds, logical pluralism would count? Rather than paraconsistent logic, just the notion of true contradictions would at least ask for a different kind of logic, even if not paraconsistent, and so we'd be justified in saying there is at least two kinds of logic: the ones which reject contradictions, and the ones which utilize them in some way.

Also I don't mean to say I'm an expert by any means. Just an interested reader who thinks about these things.

I also haven't seen anyone in this thread who favors logical pluralism embrace Dialetheism - other than yourself, of course. They seem to be mostly Augustinians, "Lord, give me logical pluralism, but not yet!"

I also have ulterior reasons for taking dialetheism seriously, namely Marx and Hegel. Marx's notion of contradiction I have a good feel for (but because it's more extensional it's easier to untangle Marx's notion of contradiction from the logical one by dividing wholes into parts that differ), but Hegel's continues to mystify me.

And then one day I came across Priest in reading through the Liar's sentence and as odd as it is on its face it kind of slowly grew on me. I'm not sure of extensions of the dialetheism beyond the liar's, though Priest lists several (also including some Eastern philosophy too), but I think I like dialetheism as a solution the to the liar's paradox because it's a queer conclusion that comes from the plainest understanding of the liar's: no fancy logic is really needed. I can understand thinking the liar's is incoherent -- once upon a time I thought that because it's hard to imagine an empirical use for it-- but since this concerns logic alone, and may provide some inroads to other interests I have, I find it worthwhile in trying to comprehend and use. (Also, I think it could be a promising theory to develop in fleshing out the absurd, which is where I began originally -- taking the absurd as a metaphysics seems to indicate that logic cannot contain reality, especially the absurd parts -- logic's whole thing is making sense!)

The other response to the liar's I held was that the liar's sentence is simply false. It's telling you exactly what it is on its face. there is no evaluation necessary.

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

Now I sit and wonder what it takes the to contain explosion, if anything rational could be proposed in empirical (rather than conceptual) cases.

To address your concern about knowledge and logic's relation to it: I think this exercise demonstrates that we can't contain the world with logic, but rather we invent the logic to fit the world. It works because we've seen this or that enough times and so we follow the habits which reward us and call it truth*.

What's interesting about this line of thinking is that it's not denying even a metaphysical truth. But rather is showing how knowledge is produced: Guess and check. There is no method that guarantees knowledge. You just have to work things out the best you can.

So it's not entirely a dry academic consideration, to me. I see lots of interesting inroads with these ideas to other things I'm interested in, and the creative nature of it all gets along with what I think knowledge generation takes: making up new things and seeing if they work.

EDIT: 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. The pluralist says "Well, so far, perhaps... but what if we...."

*EDIT2: That looks dangerously close to a pragmatic theory of truth. It's off topic but I'm not a pragmatist, in spite of these sayings which would easily cohere with pragmatist theories of truth.

Almost like I read philosophy to figure things out that I still wonder about ;)

And so it is up to monists to show what it is that all logical systems have in common. I don't see that it can be done. — Banno

It could be thought of as a regulative principle -- here we have multiple logics, but we would like them to cohere: the monist would then be more of a project than a position, the attempt to build a logic which contains all logics. (one could presumably derive the LNC from this meta-logic, for instance -- but it's just an idea)

Do you see why I feel that I am wasting my time? — Leontiskos

I believe that I do, and I'm happy that you continue to respond in spite of the frustration.

Gonna call it for tonight and rethink stuff, though obviously not in your favor :D

I'd appreciate you answering my question about whether or not paraconsistent logic would count as a plural logic insofar that we accept both paraconsistent logic and classical logic.

Perhaps that's a nice example of the methodological difference between pluralism and monism. I don't actually think this is quite right, but at the least it shows a difference in approach. — Banno

Interesting. I like this approach of defining the difference as a matter of method.

The liar is clear, in the way you have argued. Rejecting it as a "nonsense" is a failing of nerve, rather than an act of rationality. There are three ways of dealing with it that I think worth considering. Tarski would say that it is a mistake to assign truth values to sentences within the same language, but permissible between languages, so the problem with the liar is that it tries to say something about the falsity of a sentence within it's own language. Kripke would say that we can assign truth values within one language, but that we shouldn't assign them to every sentence, the liar being an example of a sentence to which we cannot assign a truth value. Revision theories would have us say "this sentence is true" is true on the first iteration, false and the second, true on the third... and so on. — Banno

I notice a distinct lack of dialetheism in your approach ;)

The way I understand Tarski's attempt to deal with it is the distinction between meta- and object- language. I think that's the neatest way to deal with it, but upon reading Priest I've reconsidered.

I'm not sure I understand the difference between Tarski and Kripke, though. By your sentences they look the same to me, so I'm missing something.

Revision theories sound like they can't make a decision. Not that I'd know anything about that ;D

Or if you like, why is it false, whatever "it" is supposed to be? How do we know that it is false? Is it because you said so? But you saying so does not make a thing false, so that's a dead end. Even Wittgenstein understood that a sentence cannot prove or show its own truth or falsity. — Leontiskos

Suppose that the liar's sentence is false. Then the liar's sentence is true because it says that it is false.

Suppose that the liar's sentence is true. Then the sentence is false because it says that it's false and we're saying it is true.

In either case you end up with the circuit of evaluation which yields both "...is true" and "...is false" regardless of its starting truth value.

Though I can see you're not having it.

Do you at least agree that paraconsistent logic is different enough to count as pluralism?

You haven't managed to address the argument. Let's set it out again:

The clause "...is false" presupposes an assertion or claim.
"This sentence" is not an assertion or claim.
Therefore, "This sentence is false," does not supply "...is false" with an assertion or claim.

Now here's what you have to do to address the argument. You have to argue against one of the premises or the inference. So pick one and have a go. — Leontiskos

I'll start with your first premise. "...is false" presupposes no such thing as an assertion or claim -- like I noted earlier "This duck is false" could mean "This duck is fake", right?

So it follows that the meaning of a clause depends upon the name and the predicate -- "...is false", outside of everyday, has no meaning.

Note too that, "This sentence is false," is different from, "This sentence is false is false," or more clearly, " 'This sentence is false' is false. " Be clear on what you are trying to say, if you really think you are saying something intelligible at all. Be clear about what you think is false.

I agree that "This sentence is false" differs from "This sentence is false is false" -- I think once we introduce substitution we're no longer in everyday reasoning, but it works at any level from what I can tell.

"This sentence is false" is all I need. It's a nefarious sentence. Or a purposefully chosen set that play with the notion of true and false and self-reference.

Also, even if we introduce subsitution the liar's works -- it's the extended liar's sentence. (the "strengthened" liar's sentence is what convinced me that it cannot be assigned some third value, as in many-valued logics)

Actually that's another example that I'm wondering about with respect to pluralism -- do logics with more than 2 values count as plural logics, or no?
***

Also I can just drop this point here. We're starting to getting into liar's paradox points and if it's something that doesn't really jive with you then there's no point in continuing here since the point isn't the liar's sentence but pluralism.

Nice.

I don't mean to speak for @Joshs, but I'd say that "living in the moment", which is possible, does not negate the triadic structure Josh mentions.

Maybe he would have wished he could resurrect correspondence, but he knew he hadn't. — frank

What makes you say that?

I kind of thought of Tarski's paper, that I still struggle with reading, was basically a correspondence theory of truth?

Either way, what I'm hoping to convey is that logical theories like Russell's are attempting to accommodate any metaphysics of truth -- else it would be begging the question on truth.

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

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.

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.

M'kay, cool.

I was looking for uses to get an idea of what you meant, and the one use-case I found looked like it fits with your idea of being a person -- not just the body, not just the mind, but the whole.

In order for a sentence to be true or false it must say something. That is what it means to be a sentence. "This sentence is false," does not say anything. It is not a sentence. It is no more coherent than, "This sentence is true," or, "This sentence is blue," or, "This sentence is that." — Leontiskos

If you think that answer is wrong then you'll have to tell us what the sentence means. — Leontiskos

What does it mean to "say something"?

I'll say more, though it's fair to ask what are the conditions you're after here -- what I have in mind is that English cannot refer to itself but must refer to objects. Is that so? Some sort of extensional theory of meaning?

Because 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, which seems to me to be pretty clear that this is the sort of background assumptions which are part of Russell's paper. (though what I'm advancing is different from Russell's, I'm in favor of her conclusion for logical pluralism)

But neither of these things rely upon truth-conditions or states-of-affairs.

And paraconsistent logic certainly seems to me to be a worthy candidate for being significantly different from bi-valent logic since it rejects the principle of explosion, and accepts dialethia.

Ran a search and found only one paragraph with the phrase. Is this the one you mean to reference?

We have become accustomed, through the influence of the Cartesian
tradition, to disengage from the object: the reflective attitude simultaneously purifies the common notions of body and soul by defining
the body as the sum of its parts with no interior, and the soul as a being
wholly present to itself without distance. These definitions make matters perfectly clear both within and outside ourselves: we have the
transparency of an object with no secret recesses, the transparency of a
subject which is nothing but what it thinks it is. The object is an object
through and through, and consciousness a consciousness through and
through. There are two senses, and two only, of the word ‘exist’: one
exists as a thing or else one exists as a consciousness. The experience of
our own body, on the other hand, reveals to us an ambiguous mode of
existing. If I try to think of it as a cluster of third person processes—
‘sight’, ‘motility’, ‘sexuality’—I observe that these ‘functions’ cannot
be interrelated, and related to the external world, by causal connections, they are all obscurely drawn together and mutually implied in a
unique drama. Therefore the body is not an object. For the same reason, my awareness of it is not a thought, that is to say, I cannot take it to
pieces and reform it to make a clear idea. Its unity is always implicit and
vague. It is always something other than what it is, always sexuality and
at the same time freedom, rooted in nature at the very moment when it
is transformed by cultural influences, never hermetically sealed and
never left behind. Whether it is a question of another’s body or my
own, I have no means of knowing the human body other than that of
living it, which means taking up on my own account the drama which
is being played out in it, and losing myself in it. I am my body, at least
wholly to the extent that I possess experience, and yet at the same time
my body is as it were a ‘natural’ subject, a provisional sketch of my total
being. Thus experience of one’s own body runs counter to the reflective procedure which detaches subject and object from each other, and
which gives us only the thought about the body, or the body as an idea,
and not the experience of the body or the body in reality. Descartes was
well aware of this, since a famous letter of his to Elizabeth draws the
distinction between the body as it is conceived through use in living
and the body as it is conceived by the understanding.40 But in Descartes
this peculiar knowledge of our body, which we enjoy from the mere
fact that we are a body, remains subordinated to our knowledge of it
through the medium of ideas, because, behind man as he in fact is,
stands God as the rational author of our de facto situation. On the basis of
this transcendent guarantee, Descartes can bllandly accept our irrational
condition: it is not we who are required to bear the responsibility for
reason and, once we have recognized it at the basis of things, it remains
for us only to act and think in the world.41 But if our union with the
body is substantial, how is it possible for us to experience in ourselves a
pure soul from which to accede to an absolute Spirit? Before asking this
question, let us look closely at what is implied in the rediscovery of our
own body. It is not merely one object among the rest which has the
peculiarity of resisting reflection and remaining, so to speak, stuck to
the subject. Obscurity spreads to the perceived world in its entirety. — MMP Phenomenology of Perception, end of chapter 6

It seems like the whole paragraph gets along with your notion to me. But I just ran a quick search out of curiosity.

That said, I get the distinction, and I think it's a useful one to some extent. Nevertheless, when logicians want to discuss truth, and validity as "truth preserving," one has to understand what is meant by "truth." One can declare one's logic "pure" and free from metaphysics, but honestly it seems that all this accomplishes is making one's presuppositions opaque and immune to scrutiny (and, relevant to this topic, does so in a way that I think is often question begging re logical nihilism). — Count Timothy von Icarus

I prefer to think of it as putting it to the side as something that can be discussed separately -- which isn't to say our choice of a logic is metaphysically innocent or anything. When you're trying to put it all together into some kind of coherent picture usually you can see how there are some natural implications of an idea; some ideas seem to "get along" better together than others.

My task here is to point out that the nihilism isn't absurd on the basis of anti-realism/realism, that nihilism is different from pluralism, that pluralism is a worthy contender whether we are realists or anti-realists, and that logical monism isn't obviously true.

I've read you as saying that logical nihilism leads to a lack of knowing -- that we would be unable to track what is relevant with respect to knowledge if there were no logical rules. I think the case of Humean skepticism is a good one to point to for demonstrating that knowledge need not have anything to do with our habits of inference -- we build knowledge around causation, but it could very well be that we find out we were mistaken in that knowledge.

Now, just because we were mistaken that does not then mean that things weren't real. It just means that our knowledge doesn't necessarily track what's real. So if we wash our hands before treating a bleeding wound to remove the humors from our hands since it causes diseases we will know something which is false, act on it, and in the process eliminate microorganisms which cause diseases.

The whole causal mechanism is a myth, but we manage because we are the ancestors of those who were lucky enough to reproduce in this environment (and they didn't know much either, so I'd guess -- though I don't know)

In fact we could look at induction as a survival strategy which violates the basics of logic all the time since it's an invalid inference. :D

Or, at least, I put those sorts of things under the heading "informal logic" which is the study of how people actually make inferences which includes a lot more on the "content" side (since that's how you demonstrate why such and so is a fallacy). It just seems that we'd be able to accommodate informal logic, or this kind of "content based" logic regardless of our position with respect to monism, pluralism, and nihilism in logic.

Just a helpful point of clarification, "classical logic," is confusingly the logic developed by Frege and co. relatively recently. There is no good catch-all term for logic before the late 19th century. People call it "Aristotlean," but then this tends to miss everything between Aristotle and 1850 or so. — Count Timothy von Icarus

Cool.

I mean logic prior to Frege. The square isn't found in Prior Analytics, but I would consider the likes of Frege, Peirce, and Cantor as part of the new logic which encompasses Aristotle's studies on validity, if not his entire project.

And why do we perceive it as regular? — Count Timothy von Icarus

I think that's a question for metaphysics rather than logic -- and which explanation one chooses will complement this or that metaphysic. These are different questions because we can reconcile various kinds of anti/realism with various kinds of monism/pluralism/nihilism in logic. This isn't to take a side on realism or anti-realism, but to demonstrate that the question of realism isn't the same as the question between logical monism, pluralism, or nihilism.

The nihilist account seems to get along with anti-realism, but it's possible to reconcile a realist metaphysic with a nihilist logic, and an anti-realist metaphysic with a monist logic. If that's the case I conclude that they are different questions and logicians need not answer the metaphysical question in exploring monism, pluralism, and nihilism.

Even on a realist account, though, I'd say we frequently find patterns that are not real -- we find regularities because we like them so much that we find one's that are false as well as true. This is what we mean by delusions and hallucinations and such.


Which is really just to convert the question of ontology -- what is it that we know about? -- to epistemology -- how do you know the true from the false?

I'm also not sure what "being" is supposed to be if it isn't what is given to thought. — Count Timothy von Icarus

It's a concept in metaphysics whose meaning cannot be articulated, but only approached. If I take a page from Sartre Being is transphenomenal. If I take a page from Heidegger, then the question of the meaning of being is itself an unarticulated assumption of all philosophy prior which relies upon the notion of presence.

Is non-being somehow not-known? If I am looking for someone in a bar because we said we'd meet and I do not see them then isn't this an account of absence-in-presence?

Either way I'd say that the question of being is not a question of validity -- another demonstration from logic.

If the moon is made of green cheese then Alfred is the president
The moon is made of green cheese
Therefore Alfred is the president

The actual truth-value of these sentences isn't in question when talking about logic. It's the form between the sentences under the assumption that if the premises are true that the conclusion follows. But since the moon is not made of green cheese the question of being -- what is -- differs from the question of validity, and logic is this study of validity.

They are supposed to be objections to Aristotle, so yes, of course they do. You might as well have objected to Mr. Rogers by telling us that you prefer people who put on shoes. Mr. Rogers puts on shoes in every episode. — Leontiskos

I don't exactly object to classical logic, though -- I'm saying it has limitations, not that it's wrong in every case.

To clarify -- the wiki on syllogism has a clear rendering of what I mean by classical logic:

There are infinitely many possible syllogisms, but only 256 logically distinct types and only 24 valid types (enumerated below). A syllogism takes the form (note: M – Middle, S – subject, P – predicate.):

Major premise: All M are P.
Minor premise: All S are M.
Conclusion/Consequent: All S are P.
The premises and conclusion of a syllogism can be any of four types, which are labeled by letters[14] as follows. ... — wikipedia

etc. etc.

Notice how these can be rendered in predicate logic in that article. These things aren't at odds, exactly. It's only that they are different.

And so it goes with non-classical logics. These aren't opposed, per se -- they rely upon a different set of assumptions and look for the patterns of validity after that.

Now in a given philosophy we'll want a particular logic, or particular logics for particular ends, but the logician need not adhere to one philosophy. Why would they? What would the point be, given that here the logicians are doing their thing without Aristotle's assumptions?

As has been pointed out numerous times, this is just gibberish. What do you mean by (1)? — Leontiskos

It's the name for a sentence.

A name denotes an individual.

The individual is an English sentence.

The sentence is "This sentence is false"

(1) is a shorthand to make it clear what "This sentence" denotes.

In a logical sense there's no reason to exclude this individual if we want our theories of logic to be entirely general -- to apply to all individuals. Denoting a sentence is surely not violating logical possibility -- it's the nefarious choice of self-reference with the "... is false" predicate which breaks the logical ambition and creates a paradox that calls for an answer.

One answer, which you've provided, is that the sentence means nothing.

It's not the only one though.

I am not sure if you can have an "epistemic endeavour," that is unrelated to being though. What is our knowledge of in this case? Non-being? — Count Timothy von Icarus

I'll quote Gillian Russell here from the opening of her One True Logic?:

Logic is the study of validity and validity is a property of arguments. For
my purposes here it will be sufficient to think of arguments as pairs of sets and
conclusions: the first members of the pair is the set of the argument’s premises
and the second member is its conclusion. An argument is valid just in case
it is truth-preserving, that is, if and only if, whenever all the members of the
premise-set are true, so the conclusion is true as well.

The domain of logic, then, might be thought of as a great collection of
arguments, divided into two exclusive and exhaustive subcollections, the valid
and the invalid, the good and the bad, and the task of the logician as that of
dividing one from t’other. — Gillian Russell

Suppose we had a formal system that answered all our questions about physics, or maybe some area of it like fluid dynamics. How could it have "no relation" to being? At the very least, it would have a relation to our experiences, which are surely part of being. — Count Timothy von Icarus

Humean skepticism comes to mind -- it could be that our logical discourse is constrained by our mental habits rather than by being. So it goes with causation: We cannot help but to draw causal inferences by our habits of thought, but the inference we draw is unjustified (insofar that we accept Hume's notion of causation, at least - but here I'm trying to point out how an anti-realism is possible, so that's enough).

I'm more tempted to say that if we have no more questions about physics this says more about our lack of curiosity than it does about our knowledge of being.

I want to do leap year physics. You get a nice three year break. — Count Timothy von Icarus

Here's the bit where reality kicks in: You can do leap year physics. But you won't be paid for it.

What you'll be paid for is tracking patterns which people like to track, which usually involves manipulating the world in some way which we perceive as regular. It's this social bit that stops the infinite possibilities, though that's not exactly a pure rational reason or a philosophical gatekeeper.

A good example of how re-thinking how we phrase the apparent paradox can provide new insight. We have "This sentence is false". It seems we must assign either "true" or "false" to the Liar – with all sorts of amusing consequences.

Here is a branch on this tree. We might decide that instead of only "true" or "false" we could assign some third value to the Liar - "neither true nor false" or "buggered if I know" or some such. And we can develop paraconsitent logic.

Here's another branch. We might recognise that the Liar is about itself, and notice that this is also true of similar paradoxes - Russell's, in particular. We can avoid these sentences by introducing ways of avoiding having sentences talk about themselves. This leads to set theory, for Russell's paradox, and to Kripke's theory of truth, for the Liar.

Again, we change the way we talk about the paradox, and the results are interesting.

And again, rejecting an apparent rule leads to innovation. — Banno

Right!

And far from rejecting classical logic it seems to me to give clarity to its underlying intuitions. These extensions of logic aren't so much an Undermining of All Thought, but in the critical tradition which explores terra incognita.

Super cool stuff.

But these are so far from counterexamples to Aristotle that they are all things he explicitly takes up. — Leontiskos

Do they need to be counterexamples to Aristotle?

I don't think so. I think that I'd simply have to want to utilize some other logic -- and there are some good reasons for putting Aristotle aside in these cases. First and foremost because we're not strictly utilizing Aristotle's logic here. The Logical nihilist or pluralist or monist isn't putting together All/Some statements into the classical forms -- The Background here has incorporated parts of Aristotle (classical logic is still taught!), but isn't appealing to Aristotle's commonsensical intuition about the logic of objects.

But I don't think statements behave exactly like objects do (and I am terribly allergic to commonsense -- it's not that I don't get it, but if the appeal is to commonsense then one need not study logic in the first place. There are far more lucrative and stable careers than academia)

Basically we don't need to explicitly refute Aristotle in how we do logic. We are free insofar that we create something interesting.

Every time I have seen someone try to defend a claim like this they fall apart very quickly. The "Liar's paradox" seems to me exceptionally silly as a putative case for a standing contradiction. For example, the pages of <this thread> where I was posting showed most everyone in agreement that there are deep problems with the idea that the "Liar's paradox" demonstrates some kind of standing contradiction. — Leontiskos

(1) is false. (1)

Read that as (1) being the name of the sentence so that the sentence references itself like we can do in plain English.

At face value it's clear to see that if 1 is false then it is true. And if it is true then it is false. If we combine this with the law of the excluded middle we must conclude that (1) is both true and false.



This is the notion of a dialethia. I went for a review before posting here and want to reference the SEP bit on paraconsistent logic in the liar's paradox article because just below it has an entry on dialetheism.

Priest (1984, 2006) has been one of the leading voices in advocating a paraconsistent approach to solving the Liar paradox. He has proposed a paraconsistent (and non-paracomplete) logic now known as LP (for Logic of Paradox), which retains LEM, but not EFQ.[10] It has the distinctive feature of allowing true contradictions. This is what Priest calls the dialetheic approach to truth.

He has some interesting examples, but this would take us very far astray.

It's more that here seems a reasonable approach to the liar's paradox that produces interesting and novel results in logic.

What if in place of Kant’s Transcendental categories we substituted normative social practices? Doesn’t that stay true to Kant’s insight concerning the inseparable role of subjectivity in the construction of meaning while avoiding a solipsistic idealism? Don’t we need to think in terms of normative social practices in order to make sense of science? — Joshs

That's a lot closer to home to my way of thinking -- and why I like Feyerabend's deconstruction of Popper as a kind of object lesson for all philosophies of science which try to encapsulate the whole within some system: what I'd call totalizing.

Though at that point we would be kind of in the realm of both Hegel and Marx -- the historical a priori looks a lot like those big theories of history to me. And that's getting close to a similar totalizing project, at least on its face.

Sure, if by "pure" we mean "ignoring the content and purpose of logic." But even nihilists and deflationists don't totally ignore content and the use case of logic. If you do this, you just have the study of completely arbitrary systems, and there are infinitely many such systems and no way to vet which are worth investigating. To say that some systems are "useful" is to already make an appeal to something outside the bare formalism of the systems themselves. "Pure logic" as you describe it could never get off the ground because it would be the study of an infinite multitude of systems with absolutely no grounds for organizing said study. — Count Timothy von Icarus

The difference I intend between pure (as such) logic and applied (transcendental) logic is that we can do logic without addressing questions of being, whereas the latter gets into the weeds of various philosophical questions (but simultaneously presupposes a logic to get there). Logic is an epistemic endeavor dealing with validity whereas the question of the relationship of logic to being is getting more into metaphysics rather than logic.

One might push back on Aristotle's categories sure, but science certainly uses categories. The exact categories are less important than the derived insights about the organization of the sciences. And the organization of the sciences follows Artistotle's prescription that delineations should be based on per se predication (intrinsic) as opposed to per accidens down to this day....

That said, if all categories are entirely arbitrary, the result of infinitely malleable social conventions, without relation to being, then what is the case against organizing a "socialist feminist biology" and a "biology for winter months," etc ?

They certainly wouldn't be useful, but that simply leads to the question "why aren't they useful?" I can't think of a simpler answer than that some predicates are accidental and thus poor ways to organize inquiry. — Count Timothy von Icarus

And to highlight why this is difference -- this line of questioning you're exploring here will be an interesting question whether we are logical monists, logical pluralists, or logical nihilists. Deciding the first question doesn't necessitate a relationship between logic, the mind, being, and knowledge. We could be logical monists on the basis that there is one true logic, but we don't know what that one true logic is yet -- inferred from the conflicting accounts of logical laws -- but retain the notion that there must be One Logic to Rule them All (or, that, in fact, one logic does rule them all, if you just incorporate this already implicit Lemma....)

And simultaneously hold that there is no relationship between logic and being -- i.e. that the One True Logic is the result of the structure of knowledge requiring this or that axiom, but could still be anti-realist projections which have no relationship to being.

The purpose and scope of logic is certainly being considered by logicians, it's just that these are different questions. (also -- I, for one, am all for a socialist feminist biology for the winter months :D )

I'd put it that the question which asks about the relationship between logic and being is no longer doing pure logic. The distinction I think of that makes sense of what you're saying is Kant's distinction between logic as such and transcendental logic: Logic as such deals with the forms of inference, whereas transcendental logic deals with the application of logic to our sensible intuition (which turn out to be the categories, much in the vein of Aristotle)

For my part I don't see much need for a transcendental logic because I don't think our sensible intuition conforms to the categories in the manner which Kant seems to believe -- in some sense what Kant does is define the absurd as outside of the scope of cognition, and yet the world remains absurd for all that: We can choose the categories we want to use in describing the world, and they change far more than what is desirable in a logical system.

As evidence of this I reference the difference between Kant's categories and the most general scientific theories -- I don't see any need for a group of categories to make sense of science. I don't think the structure of the mind or the minds relationship to being is the site of knowledge, but of comfort.
 
Basically I see the appeal of Aristotle and common sense as a mistaken appeal -- it makes sense of the world, but need not hold for all empirical cases: There are times when a person is in contradiction with themself, or an organism has a contradictory cancer, or a social organism is composed of two opposite poles (hence Hegel's use of contradiction in attempting to understand a social body or mind).

And I, for one, take up the liar's paradox as a good example of an undeniable dialetheia: A true contradiction.

Especially because the liar's sentence gives justification to P2 in the original argument: No principle holds in complete generality.

I agree.

Being wrong, and realizing it, is like removing a splinter which also gives me a new perspective.

At one point I thought it a pain but I've come to see how being wrong is the better joy than being right.

pretty sure the cracked pots are an exponential function such that if you allow 3 or 4 it's containable, but 6 or 7 might make all the non-crackpots become pots that can be cracked.

F(x) = x^C where "C" is the cardinality of the set of "pots"

That's a super cool video.

More research must be done, but if the idea survives the test of criticism it seems to support punctuated equilibrium.

Right.

So there exist some modern cynics, or some rough equivalent there -- all social backgrounds include people who want drugs or are mentally ill because social backgrounds, or philosophies, don't select for those things.