Tell me what you think fo the notion of "overloading" logic with expectations. — Banno
I disagree that that is what is going on. — fdrake
When someone stipulates a definition, they are committed to that definition insofar as it relates to the intended concept. — fdrake
Which could equally mean "mind", "minds", "people"... — fdrake
Yes. I thought it went without saying. Some things people think of are more appropriate than others in some contexts, and strictly better by some metrics. Some fiction is more valuable than others. If a thingy works better than another thingy on every relevant facet, the first thingy is better than the second thingy.
How would you judge that for a given context? Well I suppose you'd look for examples, see what pans out, provide definitions of things to see if they capture the relevant phenomena... Maybe you'd refine your criteria for what counts as a good thing in a given context based on the what you've seen and what's been created, too. — fdrake
I still have the impression that you think of this is as an Objectively Correct vs Subjective-Relativist sense, and I don't want to accept the Subjective-Relativist role in the discussion since the proofs and refutations inspired epistemology of mathematics isn't relativist in the slightest, because its emphasis is on communities of people agreeing on what follows from what by following coordinating norms and demarcating those norms' contexts of application. Minimally then, it's intersubjective, and communities create knowledge about collectively understood subject matters. — fdrake
But the strengthened liar's sentence persuaded me that there is at least an interesting formal concern. — Moliere
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. — Moliere
That's an interesting background explanation for why the "Liar's paradox" tempts you, but what I am hearing is that you are interested in playing a game that has nothing to do with reality. . — Leontiskos
You have not answered the objections, and I don't see that Marx and Hegel have much at all to do with this issue
Reality is what's interesting here -- what I don't want to do is define reality within my logic, though. And I don't think that logic needs to restrict itself to objects since reality is not composed of objects and objects only -- it also contains sentences. — Moliere
As I see it right now the objection is — Moliere
I've asked you if you'd accept a defense of dialetheism, the belief that there are true contradictions, as a basis for making the inferences that there is more than one logic. — Moliere
Marx and Hegel are philosophers which, like the liar's, utilizes contradiction in their reasoning. — Moliere
The objection was given <here>. You tried to answer it by redefining "false" as "fake," and I think we both agreed that that answer failed. That's where things stand, as you never made another attempt. — Leontiskos
"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
Sure: if dialetheism is true, then strong logical pluralism is true. — Leontiskos
No, they don't. This is equivocation. Neither one has anything like the standing contradictions of dialetheism. Tensions which go on to get resolved are nothing like the stable contradictions of dialetheism. — Leontiskos
Well you can't say what it means — Leontiskos
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 — Moliere
Hegel describes the determinateness of quality as involving both “reality” and “negation.” These are the successors, within determinate being, of being and nothing (WL 5: 118/GW 21:98–99,29–35/111). What Hegel seems to have specifically in mind, in connection with “negation,” is that qualities are organized in what we might call a conceptual space, such that being one particular quality is not being the other qualities that are conceptually related to it. Being the quality, “red,” for example, is not just being a conceptually indeterminate “something or other,” knowable only by direct inspection; rather, it is being something that belongs in the conceptual space of color, and thus it is not being the color,“blue,”the color,“yellow,”and soon. In this way, the identity of the quality, “red,” essentially involves reference to what that quality is not:It essentially involves “negation.”6 Hegel sometimes refers to this dependence of quality on other qualities as “alteration” (WL 5:127/GW 21:106,8–9/118;EL§92,A), but it’s important to remember that in this initial context of quality as such, there is nothing analogous to time(or space) in which literal alteration could take place, so the term should be understood as referring to a relationship of logical dependency rather than to one of temporal sequence or transformation, as such.
Under the heading of “reality,”in contrast to“negation,”Hegel seems to want to capture a thought shared by philosophers such as John Duns Scotus, F. H. Jacobi, and C. S. Peirce, who stress an irreducible brute “this-ness,” or haecceitas, distinct from any relatedness or subsumption, as essential to reality. It seems to them that what a particular determinate being or quality is should just be a fact about it, rather than being a fact about how it relates to innumerable other determinate beings or qualities.7 Hegel’s introduction of “negation” alongside of “reality” makes it clear that “reality” (as something like “this-ness”) is not without problems, but that doesn’t cause him to abandon it. Working its problems out will, in effect, be the motor of the Logic as a whole.
If Hegel were asked: Why should we be concerned about this “reality” of determinate being? Why couldn’t we just accept the notion that all qualities are interdependent, defined by their relations to other qualities, “all the way down,” with no remainder (and that all of them are thereby equally “real” or equally “unreal”)?– his answer would be that if something could be what it is by virtue of itself, rather than solely by virtue of its relations to other things, it would clearly be more real, when taken by itself, than something that depends on its relations to other things to make it what it is. This is not to say that the thing that depends on other things is, in any sense, illusory– the “reality” that we’re talking about here is not contrasted with illusion, but with depending on others to determine what one is. Something that makes itself what it is has greater self-sufficiency than something that doesn’t do this, and this self-sufficiency is likely to be among the things that we think of when we think of “reality.” If it is among the things we think of, this could be because we’re aware that “reality”– like the word that Hegel uses, which is real, “realitat”– is derived from the Latin res, or “thing,” so that it contrasts not only with illusion but with anything that is less independent or self-sufficient than a thing.
Robert Wallace - Hegel's Philosophy of Reality, Freedom, and God
However, I also think the sense of "contradiction" here is quite far from that invoked by religiously motivated dialetheism or those motivated largely by problems of self-reference — Count Timothy von Icarus
I have read a lot of Marxists but not much Marx, so I am not really in a position to have a strong opinion on that front. — Count Timothy von Icarus
At any rate, Hegel affirms LNC in its usual contexts, but I think it's fair to call him a monist if anyone is. The role he has for logic is deeply ontological. — Count Timothy von Icarus
It's about the number of correct logics (i.e. logics that ensure true conclusions follow from true premises). In general, it's a position about applied logic, which is why monists and pluralists often justify their demarcation of correct logic(s) in terms of natural language, scientific discourse, etc. Nihlism would, by contrast, say there are no correct logics (and also no incorrect ones). This is not to say that reasoning is entirely arbitrary, presumably there are some standards for what constitutes appropriate reasoning. But there is no logical consequence relationship that is appropriate or correct for any particular topic. So, for instance, the intuitionist and his rival in mathematics are both wrong in that neither are "right." — Count Timothy von Icarus
[/quote]You could think of this as similar to how there are very many geometries, and unfathomably many possible ones. One can identify what "follows" from their axioms according to whatever logical consequence relationship one cares to use, but this doesn't necessitate that the geometry of the physical world is infinitely variable or that it lacks any "correct" geometries. We tend to think that there would be just one geometry for physics (at least physicists normally do), or that, if there were many, there would be morphisms between them. The claims of the monist in particular are roughly analagous to the claims of the physicist re geometry. For instance, when Gisin recommends intuitionist mathematics for quantum mechanics, he does not mean to suggest that this is merely interesting or useful, but that it in some way better conforms to physics itself in ens reale, not just ens rationis.
Normally it gets framed in terms of the entailment relationship. This avoids unhelpful "counterexamples," like competing geometries that use some different axioms, but nonetheless have the same underlying entailment relationship. These are unhelpful because the question isn't about "what specifically is true/can be known to be true given different axioms" but rather "how does one move from true premises to true conclusions." This is why monists might also allow for multiple logics that are "correct," the "correct logic" being more a "weakest true logic." — Count Timothy von Icarus
These are unhelpful because the question isn't about "what specifically is true/can be known to be true given different axioms" but rather "how does one move from true premises to true conclusions."
I don't think Hegel is really a good example here because the Absolute is the whole process of its coming into being, in which contradiction is resolved, and contradictions contain their own resolution. It's examples of contradiction, being's collapse into nothing, etc. are very much unlike the standard examples meant to define dialetheism. — Count Timothy von Icarus
I'm not sure I'd go as far as to say "correct" in describing a logic.
The question for logic, IMO, is not "How does one move from true premises to true conclusions?" -- I'd say that's a question for epistemology more broadly -- but rather logic is the study of validity. The big difference here from even introductory logic books is that the truth of the premises aren't relevant, which I'm sure you know already -- the moon being made of green cheese and all that.
So we don't care if the premises are true or not. We only care that if they are true, due to the form of inferences, that the conclusion must be true.
So we don't care if the premises are true or not. We only care that if they are true, due to the form of inferences, that the conclusion must be true.
I'm not sure the entailment relationship ends up being any more stable than the LNC or the principle of explosion. Pick your hinge and flip it!
How would you define validity?
"A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid," is the textbook answer from IEP. The textbooks I've used give the same definition.
Stanford's open introduction to logic puts it thus: "Valid: an argument is valid if and only if it is necessary that if all of the premises are true, then the conclusion is true; if all the premises are true, then the conclusion must be true; it is impossible that all the premises are true and the conclusion is false." — Count Timothy von Icarus
Well, that's a fine argument to have. But it gets to the point I tried to make to Banno and fdrake that one cannot retreat into formalism and ignore discussions of truth on this topic. If it would be question begging to assume that logic is about truth-preservation then it would be equally question begging to say that truth depends on / is defined by normative or formal contexts. If the latter is accepted, then of course nihilism is true (or rather true relative to some contexts and false relative to others, depending on our normative games.) — Count Timothy von Icarus
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