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

Making an argument for impossible things it seems. I maintain that a square circle ought to be perfectly round and have four corners regardless of how it appears. And if one was found then it would meet that criteria. Logically it can't exist by definition, but neither can a single point that's a wave and here we are.

"Material logic," is not an esoteric term — Count Timothy von Icarus

Well, the little evidence I could find says otherwise. Here's an Ngram of interest.



The point is moot, since it is so off-topic.

And yes, the topic here is logic. Not Aristotle.

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. — Count Timothy von Icarus

And not deflationary theories of truth nor a denial of causation, neither of which have any relevance to the arguments offered here. And nothing about square circles, either.

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 — Count Timothy von Icarus

Do you think the possibilities for this universe are limited by what strikes us as conceivable?

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. — Count Timothy von Icarus

:grin:

The idea that there is "nothing but formalism" is the problem. — Count Timothy von Icarus

Yes, but as I said earlier, I don't see much support for it generally or on TPF. Most people who think about this for more than 15 seconds realize that "nothing but formalism" is a complete dead end. Frank wants his square circles and Banno wants his logical pluralism. I would need to see other voices taking up such bizarre positions before I would be interested in engaging, and I don't see any. The same cannot really be said for things like nominalism or logical pragmatism, which have a wider base of support.

Logically it can't exist by definition, but neither can a single point that's a wave and here we are. — Cheshire

I think the problem there is that we are trying to understand micro quantum phenomena using macro concepts. So is a quantum particle anything like a particle of sand, or a quantum wave anything like macro wave phenomena? It seems to be not a true paradox and in part at least a terminological issue.

I think the problem there is that are trying to understand micro quantum phenomena using macro concepts. So is a quantum particle anything like a particle of sand, or a quantum wave anything like macro wave phenomena? It seems to be not a true paradox and in part at least a terminological issue. — Janus

It's been reconciled as a particle floating on a wave as well. But, that gets into 3d space. Anyway, seems like I lost the beat. I probably need to read a bit. Banno brought charts to a word fight.

:up:

Banno brought charts to a word fight. — Cheshire

:wink: Yep. Unfair advantage.

Think on i. $\sqrt -1$ isn't a thing except it is. What would we get if we just assumed a perfectly round square circle with four corners? What would be the implications? Could we construct a geometry that was interesting, if somewhat divergent? When we assumed the three angles of a triangle add to more than 180 degrees we were able to develop a geometry to navigate the globe.

What would we get if we just assumed a perfectly round square circle with four corners? — Banno

The properties that define circles make shapes that appear as squares in taxicab space. But the geometry jettisons our concept of roundness, unfortunately.

Here's a Proofs and Refutations - the source of Lakatos' concept of lemma incorporation - inspired investigation into square circles.

It's the corners that screw you up in trying to come up with such a square circle object, I think. For something to be a corner, two lines must meet at a right angle. Two lines meeting at a right angle doesn't produce a differentiable function (along the shape the lines meet in) regardless of how you rotate the shape or embed it in another one's surface, so you've got to choose between jagged edge to allow corners, and roundness.

You use the above, and the taxicab thing in my previous post (quoted below), to stipulate the following:

The properties that define circles make shapes that appear as squares in taxicab space. But the geometry jettisons our concept of roundness, unfortunately. — fdrake

I could guess the principle: every circle with corners is not round. Specifying

1) A circle is shape resulting from constant distance around a point.
2) A corner is a meeting of two lines at a right angle.
3) A round shape is smooth along its curve.

And hope to prove that there's no such shape. But I could've misspecified the underlying concepts. I imagine there's something odd about "corner" and "smooth", because "corner" relies upon "right angle", and "right angle" depends upon "angle", which depends upon the concept of an inner product, and the privileged connection between inner product and metric is something we get from usual Euclidean space. Moreover, "smooth" could also be generalised to reference a different metric.

So perhaps there is some space that has a metric related to an inner product in which there are round circles with corners, but I've not thought of such a counterexample myself.

Me going through the maths there isn't an attempt to side with over @Banno, because being able to explore the conceptual content of the allegedly logically impossible should tell you that logical impossibility isn't all it's cracked up to be. You do have to ask "which logic and system?", and "what concept am I not formalising right?" or "what concept is making the weird shit I'm imagining weird?".

The historical fact that "formal logic" is not called such because it is being set over and against "informal logic," but rather because the term refers to the study of the form of arguments as abstracted from their contents (matter) seems pretty relevant to understanding what formal logic actually is. If you think the difference is "formal versus informal" it seems easier to make the mistake of thinking that the study of form is simply all there is to logic (or that there is no debate to be had on this issue.)

This is the second time you've pulled out charts in this ridiculous way. The first was when you were telling others that "Russell had widely been seen as dispensing with causes in the sciences." Professional philosophers widely disagree with this sentiment, even partisans of Russsell. That time I shared multiple literature reviews by Neo-Russellians who themselves admit that Russell's premise that scientists don't speak of causes is false as of the 70s, false today, and likely false when Russell made the claim (although Russell bought himself some wiggle room by making an ambiguous appeal to an undefined set of "advanced sciences.") You produced a word count chart as a counter to well cited reviews in the field... Asking GPT would probably be more profitable, and I have a pretty low opinion of that as well.


You might consider that perhaps your interlocutors have some level of expertise on what they speak and that word searches are neither good arguments nor good ways of informing yourself about philosophy.

I assure you, I am not trying to trick you here. This is simply a fact, and in arguing against it I assure you that you look every bit as silly as the folks who disagree with you on the basics of classical logic and refuse to change their minds on it. Material logic is about as relevant to the history of logic as "eidos" or "form" in metaphysics. Perhaps those also fare poorly on word searches, but they are hardly esoteric.

I am not surprised that people fail to use the term, since the distinction is more apt to be phrased in terms of "form and content" today because "matter" had gained new connotations from physics. Yet clearly the subject area comes up all the time. Scientists regularly mention "the logic of thermodynamics," the "logic of natural selection," etc., and this is clearly not looking at form divorced from content.

How could this not be relevant to logical nihilism? If the form is abstracted from its contents, that's obviously going to be a much different basis for logic than if it's "form all the way down."

Anything goes" is a recipe for conservatism, since if anything goes then the way things are is as viable as the way they might be, and there is no sound reason for change. — Banno

“Anything goes” is also the common strawman argument against a logical pluralism that is taken disparagingly to imply a ‘relativism’ or or ‘nihilism’, a view that those accused of relativism never actually hold, according to Rorty.

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. — Count Timothy von Icarus

What is true is true in relation to a normed pattern. Perception, as pattern recognition, is conceptually based. This means that expectations guide recognition of perceprual objects. It also means that in assimilating the world to our expectations we at the same time modify those expectations to accomodate to the novel aspects of what we perceive. Put differently, in a certain sense what we perceive both is and is not what we anticipated. This not the same as saying that it is both true and false, since the sense of meaning of a conceptual pattern is being qualitatively adjusted in perceiving something. Thus the thing we continually recognize continues to be true differently. With regard to formal logic, if we think of a logic as producing a rule, then in following a rule we operate the same as we do in perceiving. The criteria of rule-following no more guarantees a criterion for correctly following it than our previous experience with a perceived object tells us how to recognize it correctly now.

Is it that formal logic outlines how one statement follows from another, and material logic looks at the limits of thought and language?

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.

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

Yep

I'd put it that the question which asks about the relationship between logic and being is no longer doing pure logic

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.

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.

This is why we have chemistry as the study of all chemicals, regardless of time, place, etc. and biology as the study of all living things as opposed to, say: "the study of life on the island of Jamaica on Tuesdays," and "the study of chemical reactions inside the bodies of cats or inside quartz crystals, occuring between the hours of 6:00am and 11:00pm," as distinct fields of inquiry. Certain sorts of predication (certain categories) are not useful for dividing the sciences or organizing investigations of phenomena (but note that all are equally empirical).

Of course, there have been challenges to this. The Nazis had "Jewish physics" versus "Aryan physics." The Soviets had "capitalist genetics" and "socialist genetics," for a time. There are occasionally appeals to feminist forms of various sciences. But I think the concept that the ethnicity, race, sex, etc. of the scientist, or the place and time of the investigation, is (generally) accidental to the thing studied and thus not a good way to organize the sciences remains an extremely strong one.

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.

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. — Count Timothy von Icarus

I agree with this. Roughly what I'm thinking is that consciousness evolves and that this involves both changes in environmental conditions and native mental flexibility. So, for instance, if the people who inhabit a two-dimensional world evolve into beings who can experience three dimensions, it will be partly because the environment makes it so they need to, but long before the general population changes, there will be those who have been expressing flexibility, even though it may have seemed pointless to those around them. These will be people who denied that their traditional logic limited them or the world.

Therefore it's ok to do pointless investigations. It's always been part of what we are, since at least 60,000 years.

We don't tend to talk about form and matter the same way today, so I would just thinking of it as the study of "content" in the "form versus content" distinction.(The term "subject matter," comes from this same distinction. The matter is the information in a subject or discipline, as opposed to the subject's formal definition, which defines which matter falls underneath it).

This could obviously include a discussion of psychology and the "laws of thought," and, depending on one's epistemic commitments, maybe it ends there. However, for most realists/naturalists it will also extend to things in the world (e.g. the real leaf we predicate "green" of).

For example, we can say "red" or "angry" of the number "4," in ways that are entirely correct vis-á-vis form. Yet obviously such talk is nonsensical because if one considers the content of: "the number four is angry and red," it is clear that the subject is not of the sort that it can possibly possess these predicates (obviously, this implies we are speaking of the number, not some drawing of 4 in a children's book, which might indeed be angry and red).

This distinction gets trickier when we get into analogous predication, which formal logic tends to ignore because it has proven difficult to formalize. Nonetheless, we cannot totally ignore it, because we use it in natural language and the sciences constantly.

For instance, economic recessions are an empirical phenomena that are studied by the sciences. But when we predicate "double dip" of recessions we obviously don't do so in the same way that we would say a road has a "double dip." Likewise, branching processes in population genetics don't "branch out" the way tree branches and veins do, although the use here is not totally equivocal either. It seems to me that analagous predication has to involve material logic to the extent that the content defines the sort of analogy we are speaking of.

As much as I dislike GPT, it does a fine job on the basics here.

Material logic is a branch of logic that focuses on the content and meaning of propositions and arguments, rather than just their form or structure. Unlike formal logic, which deals with the correctness of the reasoning process based on the form of the argument (independent of the content), material logic is concerned with the truth and validity of the subject matter itself.

In material logic, the emphasis is on:

Substance of the terms: It examines whether the terms used in a proposition accurately reflect the reality or essence of the concepts being discussed.

Truth of propositions: It deals with whether the statements made in the arguments are true or false based on the subject matter.

Validity of reasoning: While formal logic assesses validity based on the form, material logic looks at whether the reasoning process is valid when considering the actual subject of the argument.

In essence, material logic is more concerned with the actual content and how it corresponds to reality, whereas formal logic deals with abstract structures and patterns of reasoning

For example, we can say "red" or "angry" of the number "4," in ways that are entirely correct vis-á-vis form. Yet obviously such talk is nonsensical because if one considers the content of: "the number four is angry and red," it is clear that the subject is not of the sort that it can possibly possess these predicates (obviously, this implies we are speaking of the number, not some drawing of 4 in a children's book, which might indeed be angry and red). — Count Timothy von Icarus

I think this is about competent language use. Russell's paradox isn't about language use. It's not nonsensical.

In essence, material logic is more concerned with the actual content and how it corresponds to reality, whereas formal logic deals with abstract structures and patterns of reasoning

I asked you before: are you saying that if X is paradoxical, it can't exist? I guess I'm wondering if this is a question you don't want to address for some reason?

Anyhow, Kant's distinction is an interesting one, but it's guided by his metaphysics and epistemology. If we want to speak of why the mind is the way it is in terms of evolution, neuroscience, physics, etc., we are already leaving Kant behind.

For some, this is a bridge to far. Personally, I think the natural sciences, the study of phenomena, tell us about things other than phenomenal awareness (e.g. "the sun is made up largely of hydrogen gas," is not just about our phenomenal awareness, but expressing something true about the sun). And if this is true, then we can speak of the relationship between logic and being as opposed to just logic and experience or the necessary prerequisites of experience.

I think this is about competent language use. Russell's paradox isn't about language use. It's not nonsensical.

Sure, that was just an example on the relevance of content to meaningful predication. But Russell's paradox is about stipulated sign systems, "languages," no?

I guess I'm just not sure what you're asking? Of course paradoxes exist, Russell's paradox is one of them. You can observe it. But it exists in a stipulated sign system. Ditto for the Liar's Paradox. I mean, consider the common instantiated version of Russell's paradox. In this version the solution is simple, it simply is not true that "every man in the village either shaves himself or (exclusive or) is shaved by the barber." Either the barber doesn't shave or he is shaved by both (or maybe someone else shaves him). The paradox does not imply actual occasions of things that both do and do not do something in an unqualified way (although I will grant that the possibility of error and falsity itself are mysterious in a way).

What would be an example of a paradox in nature? To be sure, we call all sorts of natural phenomena "paradoxes," e.g. the Fermi paradox, the level of plankton in the Arctic given the amount of sun it gets, etc., but these seem like they could be resolved completely unparadoxically if we just knew more.

The only thing I can think of would be a case where something both is and is-not in an unqualified way, and no I don't think such a thing can exist (...and not exist :rofl: )

Sure, that was just an example on the relevance of content to meaningful predication. But Russell's paradox is about stipulated sign systems, "languages," no? — Count Timothy von Icarus

Tarski is stipulated sign systems. Set theory is fairly intuitive. Even the foundations, which obviously directly defy Aristotle, are fairly easy to embrace, especially after you've studied calculus. I guess you could target set theory's foundations in favor of finitism. Is that what you're thinking?

What would be an example of a paradox in nature? — Count Timothy von Icarus

I don't know. My consciousness might have to evolve some before I can see it. My question, though, is do you think the possibilities of our universe are limited by what appears inconceivable to us?

I think this is about competent language use. Russell's paradox isn't about language use. It's not nonsensical.

Actually, I will correct what I said above, is this just about competent language use? Does the fact that it doesn't make sense to speak about something "moving greenly," "economic recessions being pink," or "plants being prime," only have to do with the rules of competent language use and not with what those things actually are?

To be sure, the proximate issue might be competent language use, but is language itself arbitrary or a brute fact such that it isn't the way it is due to other causes? It seems to me that it is improper to speak of recessions being pink because they aren't the sort of thing that has color.

Does the fact that it doesn't make sense to speak about something "moving greenly," "economic recessions being pink," or "plants being prime," only have to do with the rules of competent language use and not with what those things actually are? — Count Timothy von Icarus

Good question.

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 — Moliere

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?

Good question.

Well, that's partly what material logic is concerned with. Semiotics, through Aquinas, John Poinsot, C.S. Perice, and John Deeley is one particularly developed area that has a lot of overlap with this question (Sausser-inspired and post-modern semiotics largely considers the question unanswerable/meaningless and so ignores it though).

My question, though, is do you think the possibilities of our universe are limited by what appears inconceivable to us?

To us? No. What is inconceivable to one man might be properly conceivable to another. I don't think toddlers can fathom many things adults can for instance. But can something exist that is inconceivable and unintelligible in an unqualified sense? I am not sure what that would mean. Something lacking not only in any possible explanation, but in any quiddity/whatness? Something that both is and is not in an unqualified sense?

Eric Perl raises the related question of: "what is meant by 'being' if 'being' is not to refer to what is apprehended by or 'given' to thought?" I think it's a good one.

Ironically, the positing of unintelligible noumena seems to have had the strange historical effect of resurrecting Protagoras' old doctrine that "man is the measure of all (meaningful/intelligible) things." I disagree with this; man is rather the proper measure of men, horse of horses, etc.

I've gathered that you're just not going to answer that question. That's cool. :up:

Semiotics, through Aquinas, John Poinsot, C.S. Perice, and John Deeley is one particularly developed area that has a lot of overlap with this question (Sausser-inspired and post-modern semiotics largely considers the question unanswerable/meaningless and so ignores it though). — Count Timothy von Icarus

You seem to summon the philosophy of apokrisis. The all-encompassing "information" of the language-species AND the universe versus the context-dependent post-modernists.

Edit: I see we've engaged with this briefly before: https://thephilosophyforum.com/discussion/comment/825333

https://thephilosophyforum.com/discussion/14334/adventures-in-metaphysics-2-information-vs-stories/p1

An overlap in interest maybe. His version is idiosyncratic though.