Yep - although the rigour is predominantly provided by mathematics rather than syllogism. And I sympathise with the conceit that science is essentially liberal.

I suppose I was thinking of conservatism as something more along the lines of 'there is one truth and it can be discovered by philosophy'. — Tom Storm

Ok - I'd be more comfortable calling that authoritarian, a word I nearly used in the place of "conservative" in what you quoted. The normatively of telling someone "This is how you ought think..." differs from the normatively of "If you think in that way, then this will be your conclusion..." That is, the logics here are systematic, not arbitrary - what "full-blown logical pluralism" might be remains unclear until Leon addresses the issue instead of my failings. If Aristotle showed long ago why attacks on PNC cannot work it should be a small thing to show why paraconsistent logic is flawed; yet instead it is an area of growth.

A lot to think about here. One would almost assume that nothing can be known if paraconsistent logic is sound. At the very least, it suggests that how we deal with the notion of contradiction has to be revised. I fear the potential for quantum woo emerging from the dying embers of classical logic...

Just as the apparent contradictions between classical physics and quantum physics might be about how reality manifests in different scales, perhaps logics may vary depending on the calibration of the problem they are applied to. Or something like that.

A lot to think about here. — Tom Storm

Yep, interesting stuff. In classical logic, A,~A ⊨ B (From A and not A you can derive whatever you want). This would cause all sorts of problems. Paraconsistent logics remove this problem, usually while maintaining the Law of Noncontradiction. One can get a handle on the idea by looking at many-valued logics.

Supose we allow three truth values - "true", "false" and "buggered if I know" - abbreviated to T, F, B. Then we set up truth tables with three values instead of two. With a bit of fiddling we can make it so that A ^ ~A (A and not-A) gives the truth value "buggered if I know". I'm cheating here, but the idea heads roughly in the right direction. A contradiction does not lead to just everything being true. If you want more, see here or Chapter Ten of Open Logic.

Point is, there are formally developed logics that are coherent, if inconsistent. So fears of Woo are dissipated...

Well, for some. Perhaps those feeling less conservative?

:up:

Oh, and there are paraconsistent logics that are being used in non-woo quantum mechanics.

It is a thing.

Why doesn't that surprise me? :wink:

:razz:

But what Russell is doing is a bit beyond all this - the next generation, if you will. She is considering:

• To be a law of logic, a principle must hold in complete generality.
• No principles hold in complete generality.
• There are no laws of logic.

And the approach is the antagonistic one of "You give me a law you think holds in complete generality, and I'll give you a counter-instance". The playfulness and creativity are appealing. Compare it to A nice derangement of epitaphs. The bit about undermining the law certainly will stick in some folk's craw.

She does not wish to conclude that there are no laws of logic, and so argues that a principle need not hold in complete generality. Instead, they hold in given logics.

(sorry - lots of edits.)

To be a law of logic, a principle must hold in complete generality.
No principles hold in complete generality.
There are no laws of logic. — Banno

Well, that's logical...

She does not wish to conclude that there are no laws of logic, and so argues that a principle need not hold in complete generality. Instead, they hold in given logics. — Banno

A likely concession! Well, it's pretty much off limits to me, I have no knowledge of logic or philosophy, so I'll need to leave it to the cognoscenti. Thanks for the clear explanations.

The framing in the OP seems to lean towards the idea that "logic" is "formal logic." Thus, we speak of "languages," "systems," and "games" and difficulties within or between formalisms as problems for "logic."

I would just chime in that many people who oppose logical nihilism (and many, but not all forms of pluralism), would rather say that material logic has priority over formal logic in some important respects. Formal logic is about "ways of speaking," but logic is not about "ways of speaking" tout court.

There is the "discourse of language" which is constrained by the "discourse of the mind." As Aristotle says in the Posterior Analytics, we might very well say "square circle," or "x both is and is not, in precisely the same way, without respect to time," but we cannot think it true. But there is also the "discourse of being," the matter of logical statements. These must have form to be intelligible, but their form-"whatness/quiddity"- is not necessarily going to be found solely in the stipulated signs developed for communicating that form (e.g., an embrace of tripartite Augustinian/Scholastic/Piercean semiotics will entail a sort of realism here, where objects are relevant to the sign relation and signs not arbitrary).

Anyhow, to the extent that logical nihilism will tend to imply that things have no causes, that there is no metaphysical truth, etc. I think it's open to the criticism that:
A. This seems demonstrably false on all the evidence of sense experience, the natural sciences, etc.;
B. No one actually has the courage of their convictions on this matter and really acts as if causes and truth are "just games," and;
C. This makes the world inherently unintelligible and philosophy pointless.

Plus, to the extent that someone still tries to justify logic on "pragmatic" grounds it seems to be the case that any "pragmatic" standards bottom out in arbitrariness, there being no truth about what is truly a better standard or what truly ranks higher on any given standard. Hence appeals to the "usefulness of certain games," are unsupportable.

There is the "discourse of language" which is constrained by the "discourse of the mind — Count Timothy von Icarus

What are your thoughts on Russell's paradox? Is it like Witt thought, from a transcendental logic? Or what?

I haven't given Russell's paradox two much thought, at least as it respects logic as a whole. I think Wittgenstein gets something right in his early work re the necessary conditions for intelligibility and meaningful speech about the world. Whereas I take his later work to be useful in terms of rejecting a narrow view of truth and language that had become prominent in analytic philosophy in the early 20th century. Unfortunately, Wittgenstein never undertook a study of earlier philosophy, and so we don't get to see how he might have engaged with other views of truth and intelligibility, which is a shame because it could have been quite interesting.

IMO, early analytic philosophy has unfortunately become a sort of popular strawman for continental philosophy and pro-deflation analytics.

Some might say that if you have strong feelings about logical monism, you would probably have some way of dealing with paradoxes. Would you agree?

Perhaps, with the caveat that how one approaches paradoxes depends on how one views logic in the first place. If we follow the peripatetic axiom that "nothing is in the intellect that was not first in the senses," my question is "where are the paradoxes in the senses or out in the world?" I have never experienced anything both be and not be without qualification, only stipulated sign systems that declare that "if something is true it is false," and stuff of that sort.

Griffiths and Paseau's isomorphic invariance accounts of "true logics" seems like a step in the right direction, but still seems likely to founder on the equivalence of logic with formalisms.

Deflationists are often quick to point out that they are just talking about "games" and "ways of speaking," lest they step on the toes of the dominant naturalist paradigm and common sense, but they seem to invariably want to start making philosophical/scientific claims based on the study of completely abstracted formalism eventually. It's all just talk of "systems" until it isn't, e.g. "truth cannot be relational because in classical logic it only takes one argument (adicity)."

↪Cheshire Yep - although the rigour is predominantly provided by mathematics rather than syllogism. And I sympathise with the conceit that science is essentially liberal. — Banno

Specifically, it's provided by Statistical mathematics which reaches for an approximation to the truth. Which is probably why it's reliable, unlike syllogism which fails to account for unknown error. Which points to my earlier misadventures of pointing out that knowing A; entails the possibilty of being wrong about A and asserting it is true. The problem isn't in the system of logic but the flux of the evidence.

'What is, is' only works if you're correct about what it is initially.

Specifically, it's provided by Statistical mathematics which reaches for an approximation to the truth. Which is probably why it's reliable, unlike syllogism which fails to account for unknown error. Which points to my earlier misadventures of pointing out that knowing A; entails the possibilty of being wrong about A and asserting it is true. The problem isn't in the system of logic but the flux of the evidence.

'What is, is' only works if you're correct about what it is initially. — Cheshire

A thought came to mind about Kant's (still useful) way of breaking up the world. Logic is a way of recognizing rules. This is how information is parsed out. Scientific principles regard distilling correlations to a point of being able to distill rules (of the empirical). The two logics are different- one has to do with language pattern, and one has to do with empirical patterns. However, they are both intertwined, as the rules of logic seem embedded in language, something that comes prior to the empirical correlation-distillation that takes place in the cultural practice of scientific research.

A thought came to mind about Kant's (still useful) way of breaking up the world. Logic is a way of recognizing rules. This is how information is parsed out. Scientific principles regard distilling correlations to a point of being able to distill rules. The two logics are different- one has to do with language pattern, and one has to do with empirical patterns. However, they are both intertwined, as the rules of logic seem embedded in language, something that comes prior to the empirical correlation-distillation that takes place in the cultural practice of scientific research. — schopenhauer1

The framing in the OP seems to lean towards the idea that "logic" is "formal logic." Thus, we speak of "languages," "systems," and "games" and difficulties within or between formalisms as problems for "logic." — Count Timothy von Icarus

I agree with both statements in acknowledging the difference between logic as a transmission protocol and logic as it happens about the mind. Saying our rules for making statements are imperfect doesn't establish that the world can't make sense.

The framing in the OP seems to lean towards the idea that "logic" is "formal logic." Thus, we speak of "languages," "systems," and "games" and difficulties within or between formalisms as problems for "logic." — Count Timothy von Icarus

Formal logic is about "ways of speaking," but logic is not about "ways of speaking" tout court. — Count Timothy von Icarus

Yes, very good. In my opinion this all gets a little tricky because what is at stake is a ratio, not a concept. For instance, to use a formal logical system is not thereby to commit oneself to the view that logic is formal logic. Lots of people who used and even created formal systems recognized that their formal system is not identical to logic itself.

Anyhow, to the extent that logical nihilism will tend to imply that things have no causes, that there is no metaphysical truth, etc. I think it's open to the criticism that:
A. This seems demonstrably false on all the evidence of sense experience, the natural sciences, etc.;
B. No one actually has the courage of their convictions on this matter and really acts as if causes and truth are "just games," and;
C. This makes the world inherently unintelligible and philosophy pointless. — Count Timothy von Icarus

Very good. :up:

Plus, to the extent that someone still tries to justify logic on "pragmatic" grounds it seems to be the case that any "pragmatic" standards bottom out in arbitrariness, there being no truth about what is truly a better standard or what truly ranks higher on any given standard. Hence appeals to the "usefulness of certain games," are unsupportable. — Count Timothy von Icarus

Agreed. :up:

(I am tagging @Srap Tasmaner given that we were talking about similar issues elsewhere.)

If we follow the peripatetic axiom that "nothing is in the intellect that was not first in the senses," my question is "where are the paradoxes in the senses or out in the world?" — Count Timothy von Icarus

A paradox is not the type of thing that has a location.

I have never experienced anything both be and not be without qualification, only stipulated sign systems that declare that "if something is true it is false," and stuff of that sort. — Count Timothy von Icarus

Not having experienced it so far doesn't rule it out, though.

Not having experienced it so far doesn't rule it out, though. — frank

Right, and it is very important that we keep our eyes peeled for square circles. They are probably lurking just around the corner.

I was looking for a 'it can't happen because it's illogical.'

Care to step up to the plate?

Right, and it is very important that we keep our eyes peeled for square circles. They are probably lurking just around the corner. — Leontiskos

I was looking for a 'it can't happen because it's illogical.'

Care to step up to the plate? — frank

Frank, how would a square circle look? That is how would you know something was a square circle?

Frank, how would a square circle look? That is how would you know something was a square circle? — Janus

Perfectly round with four corners.

Something that appears perfectly round could not appear to have four corners.

Granted it seems intuitively accurate, but what logic prevents it? You could cut a square out on the back of a circle. And argue which side defines the object.

...material logic... — Count Timothy von Icarus

A new term to me - no mentions in SEP or in IEP. Not just no article, but no use of the phrase. so I googled it. A couple of blogs, none of them very clear, and with a few obvious errors. Merriam-Webster gives "logic that is valid within a certain universe of discourse or field of application because of certain peculiar properties of that universe or field —contrasted with formal logic". I gather it means informal logic or possibly applied logic.

So I could find no justification for your claim that "many people who oppose logical nihilism (and many, but not all forms of pluralism), would rather say that material logic has priority over formal logic in some important respects.". Many people do not talk of "material logic".

Logical nihilism is not the view that things have no causes. It is the view that there are no laws of logic. But also, despite the title, it is not the conclusion being argued for in the Russell article. The article that this thread concerns, and which neither you nor Leon have so far addressed. It is also not concerned with any form of pragmatism.

Logic has moved on a bit since Aristotle.

Granted it seems intuitively accurate, but what logic prevents it? You could cut a square out on the back of a circle. And argue which side defines the object. — Cheshire

A circle is a drawing or something imagined. it doesnt have a "back" since it is a representation of a two dimensional object. So it's not clear what you are proposing.

A thought came to mind about Kant's (still useful) way of breaking up the world. Logic is a way of recognizing rules. This is how information is parsed out. Scientific principles regard distilling correlations to a point of being able to distill rules (of the empirical). The two logics are different- one has to do with language pattern, and one has to do with empirical patterns. However, they are both intertwined, as the rules of logic seem embedded in language, something that comes prior to the empirical correlation-distillation that takes place in the cultural practice of scientific research.

Well, in terms of priority, it would seem that perception is prior to speech, both in evolutionary terms and in the development of the individual. But then we would do well to remember Aristotle's dictum that "what is best known to us," are the concrete particulars (the "Many") whereas what is "best known in itself" are the generating principles/principles of unity (the "One"). Prima facie, it seems that the intelligibility of being must be prior to knowledge in the order of being/becoming, while the reverse is true in the order of becoming.

A paradox is not the type of thing that has a location.

Indeed, although the paradoxes I find most interesting are paradoxes that might be said to have many instantiations, e.g. the sorties paradox, the ship of Theseus, the problem of the many. The issue here seems to lie in predication, and so it's more obvious that there has to be a metaphysical side to the investigation. Now, this is also true of Russell's paradox, since we're talking about proper predication of group membership, but I feel the issue tends to get muddled due to the degree of abstraction involved and the difficulty when it is simply assumed that, because groups can be arbitrarily stipulated, group membership is properly thought of as arbitrary. The issue at stake that the genus and species of the logician are not those of the philosopher and scientist, the latter deal with generating principles "at work" in a multitude in the world, the former with merely the possible forms of predication.

You see a similar split in the application of information theory to the sciences. What is the proper distribution to use in determining the information content of a message? This is an issue that cannot be solved by looking at the formalism is isolation.



Thanks. I should probably add that it's obvious that tackling formalism alone can be very useful. The idea that there is "nothing but formalism" is the problem. I think you can trace these problems back pretty far, to the confusion mentioned above above about the species and genus proper to the philosopher/scientist versus the logician. In the late-medieval period, these two got combined and species and genus were turned into logical constructs of a sort, which in turn fostered all sorts of arguments for a thorough-going nominalism. But if you take nominalism far enough, then of course logic is going to reduce to formalism. Frege's idea of an "empty subject," where predication has nothing to do with what is being predicated of is a step in this direction.



"Material logic," is not an esoteric term, it was part of all logic curricula for over two thousand years. The form/matter distinction is where we get the term "formal logic" from. It's a going concern for some 20th century philosophers who are less convinced about the reduction of logic to form (e.g Peirce and through him Deeley.) The term is less in vouge now, probably because of the hylomorphic distinction it implies, but obviously the relation between human discourse, the discourse of the soul, and this discourse of being is still something people talk about all the time.

Of course "logic has advanced since Aristotle," nothing I said suggested otherwise. However, I wouldn't take it as a badge of honor to be entirely ignorant of the basics of logic prior to the 20th century on account of this fact.

As for the other comments, I was just pointing out the assumptions that seemed implicit in the opening post. Logical nihilism and a deflationism vis-á-vis truth and a denial of causes certainly seem to go together as a package deal much of the time. I've don't think I've ever seen logical nihilism not paired with deflation; who would be a counter example here?

Well, in terms of priority, it would seem that perception is prior to speech, both in evolutionary terms and in the development of the individual. But then we would do well to remember Aristotle's dictum that "what is best known to us," are the concrete particulars (the "Many") whereas what is "best known in itself" are the generating principles/principles of unity (the "One"). Prima facie, it seems that the intelligibility of being must be prior to knowledge in the order of being/becoming, while the reverse is true in the order of becoming. — Count Timothy von Icarus

Sure, I didn't say that perception/basic experiential sensation isn't prior to language. Rather, I am simply saying that language seems to have a logic and so do the "empirical rules" that one can distill from repeated testing/correlation-distillation. These are different but related. Prior to the scientific/empirical rules, language, and its adjacent abilities (conceptual-thinking, capacity for inference, etc.) seem to need to be in place. Both need to be explained for a proper metaphysics, and in some theories (like information theories), they aren't so separated as part of the same type of thing going on.

:up:

I want disagreeing BTW, just chiming in.

I want disagreeing BTW, just chiming in. — Count Timothy von Icarus

Cool. :smile: :up: