Logical relativism ≠ logical pluralism = logical inclusivism?

Question

Logical pluralism, in an attempted slogan, is, "There is no One True Logic, but a plurality of 'true' logics." But so on this site I have seen the phrase "logical pluralism" applied to what seems more like logical relativism, or, "There are different true logics for different fields of inquiry," e.g. perhaps independence-friendly logic for mathematics and some flavor of Schrödinger logic for quantum physics.

And though for a while I've thought of myself as a logical pluralist in a sort of "political" fashion—I comfortably give the time of day to dialethists and try (with admittedly not the best of luck) to empathize with intuitionists—yet then now it's occurred to me that I might actually be a logical inclusivist instead.

To clarify what that would mean, here are my working definitions of logical relativism and logical pluralism, followed up by the third relevant category:

1. Logical relativism: different logics are strongly normative for reasoning about different subjects. (I say "strongly normative" in lieu of "obligatory" to try to avoid misunderstanding, yet see (2)).

2. Logical pluralism: different logics are permissible for use in reasoning about most any subject matter. In the limit, there is no absolutely impersonal, transcendent standard of logic for anything under the sun, and so in fact anyone can adopt whichever logic they please for whatever reason, for the sake of any topic, and there's nothing to gainsay them with in the end—not even the charge of hypocrisy, perhaps, in the event that someone adopts dialethic logic at will and tout court. (For example, a logical relativist might think that we can perceive quantum-physical reality to obey a certain type of logic; the radical pluralist says that the theory of perception-grounded inference is itself pluralized in such a way that an empirical observation by person A licenses A to infer X but can license some B to infer Y instead, even with respect to the question of which theory of inference applies to perception itself!)

3. Logical inclusivism: the question of "One True Logic" is not well-defined because "logic" is (or should be) used more as a mass noun than a count noun. It makes no more sense to ask how many "true" or "correct" logics there are than to ask, "How many iron are there?" (Though c.f., "How much iron is there?") Accordingly, rather than try to sharply demarcate theories of inference one from another, we would do best to review individual rules of inference, e.g. explosion arguments, double-negation eliminations, etc., and see if we can't combine as many rules as possible into an indefinitely expanding theoretical system of inference. (Case-in-point: as of my current writing of this post, I am willing to suspend the argument from explosions for finitary reasoning but accept it wholeheartedly for reasoning about infinite sets.)

(1) allows criticism of others to proceed apace, if an absolutely transcendent standard of relative correctness can be arrived at. (2) does away with criticism (in the limit), and I doubt it would be openly popular among Internet-goers, seeing how much of the Internet worships contempt and hatred for others. But how would (3) actually be worked out? Does it too need a sort of "litmus test" for its inclusions? If it does, how much does it differ from (1)? If it doesn't, how much does it differ from (2)? Or do (1) and (2) differ all that much, besides the emphasized normative status in play per each ("obligation" for (1) and "permission" for (2))?

Answer 1

The original debate within logic was whether there was One True logic, or if there were multiple logics. This debate has been decisively settled in favor of multiple logics. One can start with a seemly infinite number of different sets of postulates and rules and derive subsequent logic systems using them.

There are subsequent questions that remain in logic, some of which your questions ask about. For instance, can we really distinguish logics from each other, are there logics that we intrinsically cannot understand, so can't even specify, or whether a meta logic can encompass a set of apparently diverse logics. The "can we distinguish" is true for many logics, but probably not all. The "are there unknowable logics" is very plausible, but of course we don't know... And the encompassing of diverse logics by a meta logic also seems plausible, for at least some subsets of logic. A GLOBAL meta logic that encompasses all logics -- strikes me as unlikely though, particularly in the face of "are there unknowable logics".

The second set of questions that you are dealing with is what is the relationship of logic to the material world. the original One True Logic advocates considered logic to be necessary, and intrinsic to the material world. But logic pluralism puts logic at the same level as all other hypotheses about our world -- whether a given logic applies or not to it, is a contingent fact, discoverable empirically.

That empirical investigation could have discovered many possible states of our universe.

a) It is possible that our universe could have only had one logic apply to it, despite the theoretical infinitude of others. The One True Logic advocates have in most cases fallen back on this view, and assert there can be a single logic that addresses all questions in the physical world.

b) It is possible that our world is logically chaotic, and NO logics apply to it, or any part of it.

c) It is possible that up to an infinitude of logics apply to our world, and one can construct multiple equally valid and contradictory models and evaluations of our world.

d) It is possible that our world has sub-regions of itself, where one logic applies, and other regions where a second logic applies., then a third, up to N such regions.

We could also discover that we are in a variant of one of the above, or a combination of them. One variant that is discussed for c), is that there may be infinite logics applicable to a part of our world, but one of those logics may be better at performing evaluations between them, so one of the infinite number is prioritized.

What I believe we have actually discovered about our world, is that both b) and d) are true of it, and c) may be true for some regions for several (not infinite) logics. Note that b) contradicts c) and d) if one uses absolutist classical logic. But if one uses approximate pragmatic logic, then the utility of a logic to address practical problems in most of our world is not refuted by its breakdown in rare or limit cases. Explaining further: overall, our material world is not something that adheres to A = A over any time duration, making it a not very forgiving place for logic in absolutist terms. But over short time periods, where A's are somewhat stable, logics can be highly effective. But this is true of different logics, for different problems -- d) seems to be approximately the case, for much of our world. But there also seem to be a least a few cases where multiple contrary logics can be applied as approximations validly to the SAME part of our world. AND some of those are better for sorting between logics than others.

So, to summarize. Pluralism is true, so yes to part of 2). And we can identify different logics, contra part of 3). And putting aside the further solely logic questions from th rest of 3), the empirical ones of what logic to apply to our world -- leads to pragmatic logic, with sub-regions that your norms of 1) apply to.

Answer 2

This is not so much an answer to your question, but a series of observations.

There are many logics. It is a live issue in the philosophy of logic to enquire as to why there are so many. The logical monist is committed to the claim that only one is correct, and of identifying which one. They face the task of explaining why all the others are wrong. The pluralist has to explain how it is possible for multiple logics to coexist. This problem becomes particularly sharp if we also believe that logical truths are necessary truths, and/or if we believe that logic is normative in some fashion.

But we really need to start with the question: why are there any logics at all? What is the project of formulating a logic about, and why do we do it? Logic was originally conceived as the art of distinguishing good arguments from bad. It developed into the business of saying under what conditions the truth of some proposition follows from the truth of other propositions. Then it mushroomed into a more general activity of accounting for how some things are the consequence of other things and of showing how such relationships can be proved or computed.

It is uncontroversial to say that there are different logics for different modalities or properties. Bivalent propositions, obligations, partial belief, warranted assertability, vague statements, etc., all have different logics. You refer to this as logical relativism though this is probably not the best term, since that suggests that the acceptance of a particular logic is governed by something like cultural norms. It is also possible to say that different logics do not conflict because their logical constants mean different things. It is commonplace for example to say that the intuitionistic meaning of negation differs from the classical, or that the meaning of relevant implication differs from the material conditional.

The position defended by Beall and Restall in their book Logical Pluralism is stronger. They propose that even for a given property, such as truth, the fact that we can understand a valid argument to be one that preserves truth in all cases leaves open the possibility of taking 'cases' to be different things in different circumstances. This in turn allows that, for example, classical and relevance logics might both be correct, even though they conflict.

Carnap in The Logical Syntax of Language famously espoused a version of logical pluralism that is usually called the principle of tolerance. According to Carnap, "Everyone is at liberty to build his own logic, i.e. his own form of language, as he wishes. All that is required of him is that, if he wishes to discuss it, he must state his methods clearly, and give syntactical rules instead of philosophical arguments." For Carnap, a logico-linguistic framework cannot be assessed on the basis of its correctness but on some other criterion of expedience. Ultimately, this might be something like how successfully it contributes to decision theory.

Within the philosophy of logic, there are many different approaches to understanding what logic is about. One of these is called 'anti-exceptionalism' and is basically the view that logic is continuous with science, that its methods are the same as those of science, that it is not a priori, and that it does not have any special epistemological status. If we combine this with the thesis of the underdetermination of theories by data, then we may allow that there are rival incommensurable logics about which we have no basis to judge which is correct, or even which is better.