The notion of validity that comes out of the orthodox account is a strangely perverse one according to which any rule whose conclusion is a logical truth Is valid and, conversely, any rule whose premises contain a contradiction is valid. By a process that does not fall far short of indoctrination most logicians have now had their sensibilities dulled to these glaring anomalies. However, this is possible only because logicians have also forgotten that logic isa normative subject: it is supposed to provide an account of correct reasoning. When seen in this light the full force of these absurdities can be appreciated. Anyone who actually reasoned from an arbitrary premise to, e.g., the infinity of prime numbers, would not last long in an undergraduate mathematics course.
The opening lines of the SEP article on logical pluralism acknowledge that the idea seems crazy at first glance, but that it becomes more plausible on further examination. I found myself getting more of a handle on it when reading the objections to it. It's all pretty technical, and that's not really something I'm super familiar with, but I did get that logical pluralism isn't taking anything away from the regular logic.
The best way of summarising the difference between monism, pluralism, and nihilism is as follows:
Monism: there is only one true logic.
Pluralism: there are at least two true logics.
Nihilism: there are no true logics.
Whether one is a monist, pluralist, or nihilist will depend a lot on what one takes a logic to be about and whether logics have to satisfy certain properties, like being universal, normative (capturing "rules of good thought"), and so on. Certain kinds of nihilism have a lot in common with certain kinds of pluralism (Aaron Cotnoir's nihilism is very close to a view of pluralism called logic-as-modelling, for example).
I think thinking in terms of "laws" is probably unhelpful here and I have never seen a monist argument that tries to define itself in this way. If by laws we mean "true for all existing logics," then there are clearly no such laws. The monist doesn't argue that such laws "hold in generality," except insofar as they hold for "correct logic" (as they variously define it; note also that most monists embrace many logics, the question is more about consequence). So, Russell's paper is fine overall, but I think this part has just confused people because it's easy to read it in a way that seems to make the answer trivial. But based on the fact that even pluralists themselves very often claim that they are in the minority, it should give us pause if monism seems very obviously false. — Count Timothy von Icarus
I think part of the confusion is that, just as idealism is much more popular on TPF than in metaphysics as a discipline, highly deflationary conceptions of logic's subject matter are also much more common. But one might agree to a deflation of truth for the purposes of doing logic without embracing any robust notion of deflation, e.g. that "on 9/11 the Pentagon was struck by an airliner not a cruise missile," is true or false in a sense transcending any formal construct or social practice. Maybe not, I only know of two surveys on this question, but they do seem to bear this out, as does the way authors actually talk about non-classical logics (i.e. they spend a lot of time making plausibility arguments, which are superfluous of logic is just about formalism). — Count Timothy von Icarus
Ontologically, the pluralist is going to be the one who thinks that objective/external reality is chaotic or random enough to support all sorts of anomalies and fluxes with respect to the relations between its constituent facts. (Logical nihilism, or rather logical asemanticism, seems more accurate in this context, though, if it is not accurate to think that reality is structured according to any completely specifiable system of logic at all. Or maybe there are a few rules that are universal as such, i.e. exactly those pertaining to universal quantification, if this be doable in an unrestricted way.)
↪@Leontiskos ↪Banno To what extent does your disagreement on this involve, perhaps, one being a conservative and the other liberal? — Tom Storm
So it remains that logical monism is an act of faith rather than a conclusion.
But the view that there are multiple correct logics or none wouldn't require act of faith? — Count Timothy von Icarus
Now it seems to me that Pluralism is the better of these options, but the devil is in the detail, and the discussion is on-going. — Banno
There is a correlation between philosophers who reject abortion and accept only classical logic. What to make of that? — Banno
Isn't a tautology as much a contradiction as anything? (p or ~p) — Cheshire
Godel concluded that no system really has a foundation — Cheshire
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. — frank
I don't recall the post, but in this thread (or another?) someone mentioned LEM in relation to the liar paradox. We don't need to refer to LEM for the liar's paradox. The contradiction is obtained even without LEM. — TonesInDeepFreeze
None. I thought that was the result of his numbering system for mathematical proofs. The Godel numbers, lead to a conclusion that you can't in fact provide support for every mathematical assertion. Without reaching some paradox. I don't remember the details.What specific remarks by Godel are you referring to? — TonesInDeepFreeze
Fair point. Trying to see if I could argue it. Boolean logic is pretty solid.No. A tautology is a formula that is satisfied by every interpretation. No contradiction is satisfied by any interpretation. Therefore, no tautology is a contradiction. — TonesInDeepFreeze
lead to a conclusion that you can't in fact provide support for every mathematical assertion. Without reaching some paradox. — Cheshire
Of course LNC and LEM are different. — TonesInDeepFreeze
I can't find the post about the liar paradox; my own point was merely the technical one that the contradiction of the liar does not require LEM.
I don't think it's that hard to define at all. — Count Timothy von Icarus
Their argument is roughly that the intuitive/informal notion of logical consequence is multiply-realizable (granted it is more technical in its details). — Count Timothy von Icarus
I haven't seen anyone define any of the positions in a clear and non-vacuous way, much less go on to argue in favor of one or another. — Leontiskos
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