Gonna call it for tonight and rethink stuff, though obviously not in your favor :D — Moliere
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. — Moliere
Edit: And why can't a quibbler say that R^3 and even R^2 spaces are not Euclidean? What's to stop him? When is a disagreement more than a quibble? — Leontiskos
But the deeper issue is that I don't see you driving anywhere. I don't particularly care whether the great circle is a Euclidean circle. If you have some property in your mind, some definition of "great circle" which excludes Euclidean circles, then your definition of a great circle excludes Euclidean circles. Who cares? Where is this getting us? — Leontiskos
Edit: And why can't a quibbler say that R^3 and even R^2 spaces are not Euclidean? What's to stop him? When is a disagreement more than a quibble? — Leontiskos
"If the center was deleted—per impossibile—then there would only be an Aristotelian Circle." — Leontiskos
But the deeper issue is that I don't see you driving anywhere. I don't particularly care whether the great circle is a Euclidean circle. If you have some property in your mind, some definition of "great circle" which excludes Euclidean circles, then your definition of a great circle excludes Euclidean circles. Who cares? Where is this getting us? — Leontiskos
There will be Euclid circles in that space which are not Aristotle circles too, I believe. — fdrake
I believe "A closed curve of constant positive curvature" is the one the differential geometry man from above would've said — fdrake
We could say that a circle is a [closed] figure whose roundness is perfectly consistent.* There is no part of it which is more or less round than any other. — Leontiskos
The discussion about capturing the intended concept is relevant here. The interplay between coming up with formal criteria to count as a circle and ensuring that the criteria created count the right things as the circle. That will tell us what a circle is - or in my terms, what's correctly assertible of circles (simpliciter).
That's the kind of quibble we've been having, right? Which of these definitions captures the intended object of a circle... And honestly none of the ones we've talked about work generically. I believe "A closed curve of constant positive curvature" is the one the differential geometry man from above would've said, but that doesn't let you tell "placements" of the circle apart - which might be a feature rather than a bug. — fdrake
It might not be a confusion, it could be an insistence on a unified metalanguage having a single truth concept in it which sublanguages, formal or informal, necessarily ape. — fdrake
We could say that a circle is a [closed] figure whose roundness is perfectly consistent.* There is no part of it which is more or less round than any other. — Leontiskos
Presumably it is an intuitive concept, and are intuitive concepts mathematical formalisms? — Leontiskos
not a prepackaged formalism. — Leontiskos
But you also seem to think the context you have in mind for any question that arises is the only context it can possibly arise in. — Srap Tasmaner
That reads disingenuously to me. Your use of "roundness" previously read as a completely discursive notion. If you would've said "I think of a circle as a closed curve of constant curvature" when prompted for a definition, and didn't give Euclid's inequivalent definition, we would've had a much different discussion. I just don't get why you'd throw out Euclid's if you actually thought of the intrinsic curvature definition... It seems much more likely to me that you're equating the definition with your previous thought now that you've seen it. — fdrake
The latter of which is fair, but that isn't a point in the favour of pretheoretical reasoning, because constant roundness isn't a concept applicable to a circle in Euclid's geometry, is it? Roundness isn't quantified... — fdrake
Mathematical concepts tend to be expressible as mathematical formalisms, yeah. And if they can't, it's odd to even think of them as mathematical concepts. It would be like thinking of addition without the possibility of representing it as +. — fdrake
And therein lies a relevant distinction. Formalisms aren't prepackaged at all. In fact I believe you can think of producing formalisms as producing discursive knowledge! — fdrake
You are the one who brought up Euclid in the first place, but I really don't see the two descriptions as competing. — Leontiskos
Pretheoretical or intuitive reasoning need not be quantified, does it? In making that comment I was making the point that pretheoretical reasoning represents the same basic idea as the calculus definition you gave. "...In calculus [consistent roundness] cashes out as a derivative, but folks do not need calculus to understand circles. Calculus just provides one way of conceptualizing a circle." — Leontiskos
Or rather, producing thing that can produce discursive knowledge. And knowing a true logical system is a kind of knowledge, which is probably discursive. I think that's right. But they are prepackaged in a very relevant sense, particularly for those of us who are not their inventors. — Leontiskos
But I also don't think a logic like Frege's is merely a model, nor that it could be. To invent a logical system is to attempt to capture a (or the?) bridge to discursive knowledge, and I don't know that any success or failure is complete.
Now what do you make of this? I've understood you as saying Tarski is unavoidably deflationary, and that this is a bad thing.
This seems like a useful clarification of terms. Where I have seen the term used, and how it is used in the papers we have been discussing, the idea is that there is no logical consequence relationship. It is not that there is no general consequence relationship that obtains in all cases. The idea that there are truth-preserving rules of logical consequence but that they might vary is called logical pluralism. — Count Timothy von Icarus
Nihilism seems more to me like we all have wood blocks and jigsaws and we can cut out whatever we please. Which, as an analogy for "how does one derive conclusions from true premises," seems like a poor one if one has any notion that truth is not some sort of post-modern "creative act." — Count Timothy von Icarus
This is why deflationism is question begging. You can set up the argument like so:
1. Truth is defined relative to different formalisms.
2. Different formalisms each delete some supposed "laws of logic," such that there are no laws that hold across all formalisms.
3. The aforementioned formalisms each have their own definition of truth and their systems preserve their version of truth.
C: There are no laws vis-á-vis inference from true premises to true conclusions. — Count Timothy von Icarus
So, formulation doesn't cause the truth of something. It simply presents the reasoning in an arguably unnatural way. The truth of things is constrained by the facts and the state of affairs, not the way I choose to write it down.
But again, virtually no one wants to claim that truth should be both deflated and allowed to be defined arbitrarily. So we still have the question (even in the permissive case of Shapiro) about what constitutes a "correct logic." The orthodox position is that this question is answered in terms of the preservation of "actual truth." But we also see it defined in terms of "being interesting" (e.g. Shapiro). Either way, we are right back to an ambiguous metric for determining "correct logics," hence to common appeals to popular opinion in these papers. — Count Timothy von Icarus
There is also a really odd thing that happens constantly on TPF (and it usually happens with SEP). Someone will champion a position like logical pluralism or dialetheism or something like that, but when it comes down to the question of what exactly they are promoting they are at a loss for words. They don't have any clear definition of, say, logical pluralism. — Leontiskos
I agree with underlined point completely. The scientific and metaphysical arguments for monism tend to be abductive arguments based on this idea. This is why deflation is problematic as a background assumption. It needs to be an explicit premise, else we end up talking past each other, since the disagreement is really about what is properly "truth-preserving" in the most perfect* sense, not about what is true of formal systems and the logical consequence relationships each uses. — Count Timothy von Icarus
Anyhow, I think you get at a good point, in that I can imagine that many who subscribe to "classical metaphysics" (i.e. the serious "neo-neoplatonists" today, or Thomists) might actually agree with the nihilist that laws, as in short, stipulated formulae, are incapable of capturing the logical consequence relationship because they cannot capture analogical predication of truth and being properly. But I think they would disagree in concluding that the logical consequence relationship can be either arbitrary or unintelligible as a unity. Just for an example, I don't think Eriugena's four-fold distinction of being where "to say 'angels exist' is to negate 'man exists'" (when using exists univocally) is going to fit nicely into formal context. You could add four distinct existential quantifiers related by some sort of formalism of analogy, but I don't think that's going to cut it. — Count Timothy von Icarus
One of the great things about producing formalisms is that they're coordinative. — fdrake
I think such things are useful, but I also think that at some point we have to venture out beyond the bay and into the open sea. — Leontiskos
I would agree that every quantification is into a domain, and I don't think there are context independent utterances. I do not think it follows that there is no metaphysics. I'm rather fond of it in fact, but the perspective I take on it is more like modelling than spelling out the Truth of Being. I think of metaphysics as, roughly, a manner of producing narratives that has the same relation to nonfiction that writing fanfiction has to fiction. You say stuff to get a better understanding of how things work in the abstract. That might be by clarifying how mental states work, how social structures work, or doing weird concept engineering like Deleuze does. It could even include coming up with systems that relate lots of ideas together into coherent wholes! Which it does in practice obv. — fdrake
And this sounds a lot like Srap's approach. I was encouraging him to write a new thread on the topic.
Plato's phrase, "carving nature at it's joints," seems appropriate here. I would say more but in this I would prefer a new or different thread (in the Kimhi thread I proposed resuscitating the QV/Sider thread if we didn't make a new one). I don't find the OP of this thread helpful as a context for these discussions touching on metaphysics. — Leontiskos
and are you willing to say that the fanfiction can be good or bad? — Leontiskos
As I've said repeatedly, STT need not be deflationary. It is often taking as a means of modeling correspondence truth and this leaves the door open for judging "correct logics" in terms of their ability to preserve correspondence truth not simply truth relative to some formal context. — Count Timothy von Icarus
Affirming coherence and denying absurdity is an act, a job for human beings.
Does that mean that correspondence gets to decide between logics?
Is the correctness of logic to be decided empirically?
And it remains unclear to me why you introduced deflation into the conversation.
To be sure, it's not a term I would use. Logics are useful, applicable, valid, consistent, incomplete and so on, but not so much "correct".When people writing on this topic discuss "correct logics," what exactly is it you think they are referring to? — Count Timothy von Icarus
Why? IfIf all logics are correct logics then nihilism is obvious. — Count Timothy von Icarus
what follows is that there are logical laws that apply within each system. What does not follow is that there are no logical laws.Truth just is truth as defined by some system. — Count Timothy von Icarus
So there are multiple logics?Is the correctness of logic to be decided empirically?
Yes, — Count Timothy von Icarus
When people writing on this topic discuss "correct logics," what exactly is it you think they are referring to? If all logics are correct logics then nihilism is obvious. — Count Timothy von Icarus
If you assume deflation, I don't get how nihilism isn't a consequence. Truth just is truth as defined by some system — Count Timothy von Icarus
In the same way moral pluralism is nihilism? Yes
Truth deflationists usually think of truth as having a social function. It's just something people say. That's different from using the truth predicate in a technical way as Tarski did.
To be sure, it's not a term I would use. Logics are useful, applicable, valid, consistent, incomplete and so on, but not so much "correct".
what follows is that there are logical laws that apply within each system. What does nto follow is tha there are no logical laws.
So there are multiple logics?
To be sure, it's not a term I would use. Logics are useful, applicable, valid, consistent, incomplete and so on, but not so much "correct".
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