- No, you're to blame for trying to reframe the issue around bogeys of "authoritarianism" and "closed-mindedness." You're a joke.

That wasn't reframing. We were talking about why a monist might insist on a logic for all cases when it's not clear what that logic would be.

Good shit testing requires accurate close reading. This is how you come up with genuine counterexamples. — fdrake

I am considering making a new thread on a related topic, but I am wondering what you actually mean by "shit testing"? Originally I thought you meant something like, "Throwing all the shit you can think of at a wall and seeing if anything sticks. Submitting an idea to a shitstorm of objections and seeing if it is still standing in the end." Yet now as you refine the idea we seem to be getting further and further from that idea, even to the point that I am wondering whether "shit testing" is an appropriate name.

(I suppose you might have meant, "Testing an idea to see if it is shit," except that that is much too far away from the quibbling that I complained of.)

That wasn't reframing. We were talking about why a monist might insist on a logic for all cases when it's not clear what that logic would be. — frank

That's my issue with the monistic approach. There's only one correct way to think about it and no one seems to know what that is exactly.

It's faith.

May as well let him be. You know I enjoy the attention.

, I was responding honestly to questions asked.

So now the thread is about me? Nice.

There's only one correct way to think about it and no one seems to know what that is exactly. — Cheshire

Good summation.

(I suppose you might have meant, "Testing an idea to see if it is shit," except that that is much too far away from the quibbling that I complained of.) — Leontiskos

I meant it as two complementary aspects - treating a definition exactly at its word to see what it entails. Sometimes this will entail something that seems very pathological. Eg here's an example of a curve which is discontinuous but you could draw without lifting your pen off a piece of paper or instantaneously changing the angle you're drawing at. Shit testing allows you to distinguish concepts, in the case of that curve, it provides an example that distinguishes continuity from the intermediate value property, by finding a curve which is not continuous but has the intermediate value property.

Since counterexamples like that let you distinguish concepts engendered by formalisations, they also let you try to distinguish what concept a collection of definitions are trying to capture from what concept they actually capture.

Philosophy has analogues, like Gettier cases exemplify shit testing of the justified true belief theory of knowledge. The concept "a rock a being cannot lift" is an attempted counterexample to an unrestricted concept of omnipotence. Lord of the Rings might serve as a counterexample to a strictly coherentist view of truth, since it may satisfy the definition of a self consistent and expansive set of propositions which nevertheless is not the one we live in. There is no Walmart in Middle Earth.

What I was calling shit testing is the process of finding good counterexamples. And a good counterexample derives from a thorough understanding of a theory. It can sharpen your understanding of a theory by demarcating its content - like the great circle counterexample serves to distinguish Euclid's theory of circles from generic circles. Counterexamples of this form have a modus tollens impact on the equivalence of a target concept from concepts in terms of a theory targeted at that concept understood at face value in its stated terms.

I don't think the sphere cross section's circumference is a "good" counterexample like that, since the thing cutting the sphere to make a cross section definitely is a plane, some Euclid fan will be able to talk about "enclosing space" like the disk the cross section whose boundary is the great circle is is, or the fact the circle lays in a plane, but just an incline one. But the circles you make on the surface of a sphere alone are a good counter example in that sense, because there's no centre point and no enclosed space.

I switched counterexamples mid explanation because it became evident you weren't familiar with the difference in geometry between sphere surfaces and planes, in virtue of reading the great circle as the boundary of a cross section of the sphere. And also weren't comfortable playing around with weird subsets of the plane. Those latter examples were attempts to make similar flavour counterexamples without the... nuclear levels of maths... that help you distinguish the surface of a sphere from flat space.

The incline plane does let you see something important though, you might need to supplement Euclid's theory with something that tells you whether the object you're on is a plane. Which is similar to something from Russell's paper... "For all bivalent...", vs "For any geometry which can be reduced to a plane somehow without distortion...". The incline plane can be reduced to a flat plane without distortion, the surface of the sphere can't - so I chose the incline plane as another counterexample since it would have had the same endpoint. But you get at it through "repairs" rather than marking the "exterior" of the concept of Euclid's circles. Understanding from within rather than without.

Someone who was familiar with the weirdness of sphere surfaces, eg @Srap Tasmaner, will have seen the highlighted great circle, said something like "goddamnit, yeah", and understood that the intention of presenting the image in the context of your reference to Euclid was to reference only the circle on its surface, since they will have had the understanding that the surface of a sphere has nothing like a working concept of a "planar figure" applicable to it at all.

Someone who was familiar with that, eg Srap Tasmaner, will have seen the highlighted great circle, said something like "goddamnit, yeah", and understood that the intention of presenting the image in the context of your reference to Euclid was to reference only the circle on its surface, since they will have had the understanding that the surface of a sphere has nothing like a working concept of a "planar figure" in it at all. — fdrake

Ironically enough this is similar to one of Lakatos' quips in Proofs and Refutations. I can't remember the exact wording, but he pokes fun at mathematicians for the amount of assumed knowledge supposedly self contained and fully rigorous proofs they write have. Which is also unavoidable when building on top of theories.

will have had the understanding that the surface of a sphere has nothing like a working concept of a "planar figure" applicable to it at all. — fdrake

That isn't strictly speaking true, it's just that the generalisation of the concept of planar figure which applies to circles is so vast it doesn't resemble Euclid's one at all. You can associate planes with infinitely small regions of the sphere - the tangent plane just touching the sphere surface at a point. And your proofs about sphere properties can include vanishingly small planar figures so long as they're confined to the same vanishingly small region around a point.

Edit: or alternatively I guess you could think of shapes on a sphere's surface, but they have much different properties than those on the plane. Like triangle angles adding up to more than 180, the analogue of lines being great circles, and thus there's no parallel lines on the sphere surface.

This is simply using unclear terms. It's "P is true in L iff P is true in L." Whereas "P is true it and only if P," would simply be meaningless or ambiguous.

It's a sort of relativism. Perhaps not a pernicious sort in its original context, where the idea was to model correspondence, but the very paper we're discussing turns it into a cultural relativism of "communities."

Shapiro's eclectic pluralism says a logic is correct so long as it is useful for any "interesting" application. Trivial systems are interesting though. I assume the bar for "interesting" must be tightened up somewhat so it isn't the case that "correct logics," that is "logics that preserve-truth," are inclusive of those that show that anything expressible is true.

"P" is true IFF P is a formulation of redundancy among other things. It would be cool if @Nagase stopped by, for a number of reasons.

You're telling me I don't have to keep consulting my truth tables for statements like "P"? :rofl:

I don't think it's redundant in the context of trying to model correspondence though, since it's saying "the sentence P is true if what P claims is actually true." The claim and what makes the claim true are (often) distinct. But perhaps we should instead say something like: "S(P) iff P" However, it seems problematic for correspondence truth if logical nihilism is the case and there is no logical consequence relationship, such that P cannot entail S(P).

Of course, the history of philosophy is full of challenges to the correspondence formulation as well.

It doesn't model correspondence theory. For Tarski, it was a way of handling the truth predicate in formal languages. Maybe he would have wished he could resurrect correspondence, but he knew he hadn't.

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

I'm basing that on what Scott Soames and Susan Haack said about it. Tarski's truth predicate doesn't even mean truth in the common sense. It's more like satisfaction.

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. — Moliere

I'm not sure, but it leads me to this question: Frege's account of the indefinability if truth is a logical brick house. Why couldn't a pluralist say, "that's not helping me, I think it would be more interesting to create a logic that eliminates Frege's concerns."

AP would have gone in an entirely different track, possibly into a ditch. How does that work?

It doesn't model correspondence theory

That's how it's generally been interpreted and how it was originally presented, but yes, I agree, it need not be interpreted that way and often isn't.

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.

Well there I wholeheartedly agree. However, the thesis that there is no truth preserving logical consequence is necessarily going to be at odds with many conceptions of truth. What is coherence truth of nothing follows from anything else?

The difficulty here is that the strongest arguments for nihilism, or at least the most popular, implicitly deflate truth.

It's faith. — frank

Well, if we follow the evidence it suggest that self-reference isn't a reliable source of truth, in the sense the system breaks down per Russell and Godel. So, Popper's principle that we can know the truth about things, but not when in a technical sense has always seemed reasonable to me. It preserves truth and seems to model the evidence available.

Apparently the controversy stems from some comments from Popper. The fact that this is not the prevailing interpretation is reflected in two articles in the SEP about Tarski and his definition.

Notice that they don't use "correspondence" to describe his definition, but focus on logical consequences and satisfaction.

If you have university access you can read Susan Haack's article, which lays out explicitly how we know Tarski did not see himself as offering any definition for truth in natural languages. Just Google Haack on Tarski.

Well, if we follow the evidence it suggest that self-reference isn't a reliable source of truth, in the sense the system breaks down per Russell and Godel — Cheshire

I've always wondered if Russell's paradox is coming from the foundations of set theory: the contradiction of fencing in infinity. Maybe when I land on a deserted island all by myself I'll sit and figure it out. :razz:

The problem has always been the assumption of a foundation instead of lateral corroboration. It's like doing a puzzle, but taking all the pieces apart to put a new one in. We don't really confirm things against everything that's come before in a linear process.

If you have university access you can read Susan Haack's article, which lays out explicitly how we know Tarski did not see himself as offering any definition for truth in natural languages. Just Google Haack on Tarski.

:up:

Yeah, as I mentioned, I recall reading somewhere where he says truth in natural language was "meaningless," but I wasn't sure if this was a later position. So this would make sense to me.

So, STT is originally/intended to be deflationary I guess, which jives with how it is often used.

Yeah, as I mentioned, I recall reading somewhere where he says truth in natural language was "meaningless," — Count Timothy von Icarus

I don't think he meant meaningless, but definitely indefinable: too basic to define.

So, STT is originally/intended to be deflationary I guess, which jives with how it is often used. — Count Timothy von Icarus

In his paper he basically says that the concept of truth had disappeared from math. He felt like it could be brought back in some form, and he is ground zero for renewed interest in truth. It's just not correspondence, because that concept resists clarification sufficient for math and logic.

Deflation can be truth skepticism, which is what redundancy is. @Nagase explained once that some use the T-sentence rule without being skeptics, emphasizing that indefinable isn't the same as meaningless.

The problem has always been the assumption of a foundation instead of lateral corroboration. It's like doing a puzzle, but taking all the pieces apart to put a new one in. We don't really confirm things against everything that's come before in a linear process. — Cheshire

You're saying it's like a bubble universe?

No, I'm saying foundationalism/monistic systems lead to explosion. And relativistic truth implies constraint. Where is the correct position of the first puzzle piece? It's anywhere and nowhere. The last one is determined. I'll take the system that relies on the other pieces.

It's always true or false or maybe otherwise relative to some context. Thinking you can establish truth without a point on the map seems like the radical approach. So, nihilism is atheism. A label given to people for being correct.

That isn't strictly speaking true, it's just that the generalisation of the concept of planar figure which applies to circles is so vast it doesn't resemble Euclid's one at all. You can associate planes with infinitely small regions of the sphere - the tangent plane just touching the sphere surface at a point. And your proofs about sphere properties can include vanishingly small planar figures so long as they're confined to the same vanishingly small region around a point. — fdrake

We seem to think about mathematics very differently. You think that a point can be deleted; that a set of coplanar points might not lie on a plane, etc. Those strike me as the more crucial disagreements. Whether something can be "reduced to" a Euclidean plane or "contains" a Euclidean plane seems less crucial and more arbitrary.

At the heart of this thread seems to be the question of whether we can actually say that someone is wrong. In mathematics the point becomes protracted. For example, you might say that I am wrong about the great circle only if I am determined to bind myself to purely Euclidean constraints. Your notion of "correctly assertible" seems to be something like a subjective consistency condition, in the sense that it only examines whether someone is subjectively consistent with their own views and intentions. For example, given that someone says something contradictory, on this theory one can only say that they are wrong and disagree if there is good reason to believe that the person accepts the PNC. If there is no good reason to believe that the person accepts the PNC, then one cannot call them wrong or disagree. The logical monist, among others, will say that someone can be wrong for contradicting themselves even if they don't subjectively claim to accept the PNC.

As I have noted many times, whether the great circle is a circle seems to be a mere matter of names, or stipulated definitions. Not so with the PNC. We can't just change a name and resolve that conflict.

A paper that I often return to in this regard is Kevin Flannery's, "Anscombe and Aristotle on Corrupt Minds," although this paper is about practical reason, not speculative reason.

What I was calling shit testing is the process of finding good counterexamples. And a good counterexample derives from a thorough understanding of a theory. It can sharpen your understanding of a theory by demarcating its content - like the great circle counterexample serves to distinguish Euclid's theory of circles from generic circles. — fdrake

Okay, but I still don't understand why you are calling this "shit testing." Why does it have that name? It sounds like you want to give counterexamples that highlight subjective inconsistencies. Fine, but why is it called "shit testing?"

If you are just trying to give good counterexamples, then my critique of Cartesianism does not hold, but in that case I have no idea why it would be called "shit testing."


(The other possibility here is that someone's counterexample is more method than argument. For example the ancient Skeptics would argue with everyone who made a strong claim in order to try to demonstrate that strong claims cannot ultimately be made. That is apparently part of what is going on here, for the great circle has no direct bearing on square circles, but if one can generate a strong enough skepticism about circles then all claims about circles become mush, including claims about square circles.)

Well, logical nihilism is not the position that true and false are always relative, it's the position that nothing follows from anything else. It is certainly easier to argue for it if truth is relative, but it's the claim that truth cannot be inferred. You could presumably claim that there are absolute truths, just not that there is anyway to go from one truth to another.

In terms of a puzzle analogy, this seems more like claiming the pieces don't fit together, in which case it doesn't even seem like a puzzle any more.

Yes

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

So you use phrases like that in conversation?

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

Bollocks. It is absurd to claim that such a sentence pertains to, "everyday language use and reasoning," or that a child could understand it.

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

Well, 2+3+4+5 doesn't seem to be a noun, but okay.

The pronoun in "This sentence is false" points to itself, which is a statement. — Moliere

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

1. The clause "...is false" presupposes an assertion or claim.
2. "This sentence" is not an assertion or claim.
3. 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.

-

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.

---

Edit:

"This sentence is false" — Moliere

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.

It is as interesting to say, "2+2=4 is false." Have we thus proved Dialetheism? That 2+2=4 is both true and false? Of course not. :roll:
In both cases the only takeaway is that the speaker is confused.

We seem to think about mathematics very differently. You think that a point can be deleted; that a set of coplanar points might not lie on a plane, etc. Those strike me as the more crucial disagreements. — Leontiskos

I don't know what to tell you other than you learn that stuff in final year highschool or first year university maths. If you're not willing to take that you can do those things for granted I don't know if we're even talking about maths.

A set of coplanar points could have a plane drawn through them if you had the ability to form a set in that space which was a plane... and contained them. So they wouldn't even be coplanar if you couldn't draw the plane, no? Like how would coplanarity even work if you've just got three points {1,2,3}, {4,5,6} and {7,8,9} embedded in no space.

Maybe we're talking about Leontiskos-maths, a new system. How does this one work? :P

At the heart of this thread seems to be the question of whether we can actually say that someone is wrong. — Leontiskos

Of course you can. If someone tells you that modus ponens doesn't work in propositional logic, they're wrong.

our notion of "correctly assertible" seems to be something like a subjective consistency condition, in the sense that it only examines whether someone is subjectively consistent with their own views and intentions. — Leontiskos

More normative. It's not correct to assert that modus ponens fails in propositional logic because how propositional logic works has been established. And modus ponens works in it.

Okay, but I still don't understand why you are calling this "shit testing." Why does it have that name? It sounds like you want to give counterexamples that highlight subjective inconsistencies. Fine, but why is it called "shit testing?" — Leontiskos

I used it as a joke and then ran with it. And they aren't subjective inconsistencies, they're norms of comprehension, and intimately tied up with what it means to correctly understand those objects.

Counterexamples that I've been giving don't just refute stuff, they mark sites for theoretical innovation and clarification.

I don't know what to tell you other than you learn that stuff in final year highschool or first year university maths. If you're not willing to take that you can do those things for granted I don't know if we're even talking about maths.

Maybe we're talking about Leontiskos-maths, a new system. How does this one work? :P — fdrake

Shit-testing? I think you're just pulling shit out of your ass out of desperation at this point. You're a few inches away from Amadeus', "I'm right because I'm right, and you're wrong because I said so!" ...Which is ironic given that you meant to demonstrate that being right about math is not as easy as one supposes. Have you succeeded, then?

I've had plenty of university math. You strike me as someone who is so sunk in axiomatic stipulations that you can no longer tell left from right, and when you realize that you've left yourself no rational recourse, you resort to mockery in lieu of argument.

Of course you can. If someone tells you that modus ponens doesn't work in propositional logic, they're wrong. — fdrake

Maybe "propositional logic" is as slippery as "circle."

More normative. It's not correct to assert that modus ponens fails in propositional logic because how propositional logic works has been established. — fdrake

"Established"? A bit like, "verbatim"? All you mean is, "If you mean what I mean then you will conclude what I have concluded." You vacillate on the question of whether one should or does mean what you mean, and that's a pretty serious problem. It seems like you haven't thought about these issues as much as you thought you had.

they're norms of comprehension, and intimately tied up with what it means to correctly understand those objects. — fdrake

So are there rational norms or aren't there? What does it mean to "correctly understand a stipulated object"? One minute you're all about sublanguages and quantification requiring formal contexts, and the next minute you are strongly implying that there is some reason to reject some sublanguages and accept others. I suggest ironing that out.

Someone who was familiar with the weirdness of sphere surfaces, eg Srap Tasmaner, will have seen the highlighted great circle, said something like "goddamnit, yeah" — fdrake

The problem is that if you hold that mathematics has no unconditional or "unquantified" relevance, then you can't give a top-level mathematical critique. You say the point at the center of a circle can be "deleted" and I say it can't, but you presuppose that there is no way of adjudicating this question. You want to be right while also holding that there is no right or wrong in such things. Hence the bluster.