Are there any strong reasons to still consider logical monism or a “One True Logic” in light of all the non-classical logics that have been developed?

Question

I know there has always been some debate concerning whether or not a certain logical system (like classical logic) is the correct one, especially when it comes to propositional claims about the external world we inhabit. The Philpapers survey from 2009 shows a clear majority (51.6% classical : 33.1% other : 15.4% non-classical) in favor of classical logic (I'll assume the question refers to which logic they believe to be correct when it comes to reasoning, but there are really several different interpretations of that particular question, which may have influenced the results).

I would also consider myself a proponent of classical logic as the correct logic when it comes to evaluating the world as it is (though not necessarily how it relates to reasoning, especially when it comes to the inconsistent beliefs many individuals hold). I would say that my philosophical worldview (there is a mind-independent external reality that operates on some deep, fundamental principles) heavily influences this, as I don't believe in any inherent fuzziness that might be amenable to a multi or many-valued logic, and I certainly don't believe in true contradictions (whatever the hell that would even mean).

With that being said, what are the best avenues one could take if they wanted to show that classical logic (or another logic, as Alan Ross Anderson was a platonist with respect to relevant logic) was "better" than all the others when applied to uncovering the nature of reality? In addition, has any progress been made when it comes to the program of Universal Logic, which would uncover the foundations or similarities between every logical system conceivable?

Any input on this is greatly appreciated.

Answer 1

THe program of Universal Logic is mostly considered a joke by the professional logicians I have talked to.

There seem to be two popular conceptions of logic among philosophers who think about logic. But before going into these, you have to understand first that, among present-day logicians, the philosophical concerns are most frequently secondary or tertiary if they are even taken into consideration at all. Today mathematical logic has taken on a life of its own and has merged for many with computer science in particular ways. It is, in general, a branch of mathematics. Thus, for a good majority of logicians, engaging in the study of the properties of a non-classical logic is frequently done for its own sake, not much different from studying the properties of any mathematical structure. It's also frequently done in view of computer science. The point here being that much logic done today is not motivated primarily by philosophical concerns, and rarely will you see logicians even engaging in the kinds of arguments you are talking about.

But among philosophical logicians and philosophers who think about logic, there seem to be two streams of thought. First, there seems to be the view that logic can form the structural core of a metaphysics. This view is that of Williamson and his followers in his Modal Logic as Metaphysics. It is in this sense that there could be a correct logic for propositions that you are looking for. But today I think you'll have trouble finding anyone who thinks classical logic forms the core of a metaphysics, since modal metaphysics is in. So it's usually modal logics dealing with necessity that are taken to be a structural core of a metaphysics, since they can deal with dependence and grounding structures in a way that non-intensional classical logics cannot.

The other guiding conception of logic that has emerged with the dominance of mathematical logic is logic as a tool, either in the sense of an organon or in the sense of an intellectual tool-kit. On this conception of logic is the device by which philosophers start from premises and draw conclusions. In the sense of organon, then, logic prepares the way for science by providing the device by which one may generate new conclusions from premises. With the proliferation of non-classical logics, many take a quite pluralistic approach. Any logical system has paradigm cases and problem cases. With a pluralistic conception, one simply uses whichever logical system’s paradigm cases conform most closely to the matters at hand, be it a classical or non-classical mathematical logic, a dialectical or Hegelian logic, or something else.

Personally the last time I have seen arguments regarding the "correct" logic in the sense you are discussing is back in the Quine-Montague days. Quine's arguments were quite frequently motivated by a concern with preserving the classical meanings of the first-order logical terms, which indicates his endorsement of classical logic as the "correct" one. But these arguments are not really going on today, and certainly not among logicians.

Answer 2

As much as we would like to believe otherwise, logic, like science is descriptive not formative. Science does not tell us what is going on, it captures the information from observations of what tends to go on. Logic is of the same cloth. As in applied science, the best logic is the one for which the intended purpose is as close as possible to the source from which it derives.

The logic isolates and clarifies some aspect of thought or language. That part of thought would still be there without being formalized, and would pretty much act the same way, perhaps less efficiently, except to the extent that the formalism feeds back into the content that the reasoning has at its disposal.

Like your example of algebra, where there is no universally best choice between Module Theory and K-Theory or between Fields and Groups, logic as a whole is driven by deployment. There can be generalizations that combine or classify logics, as we see links like Galois Theory, etc. where algebras merge or apply to one another. And following those down, it is not hard to see that there could be a single underlying structure that unifies the whole.

But it would not answer this question. Universal Algebra and its cohorts Model Theory and Category Theory are fascinating in that they highlight commonalities we see between different logical structures we never imagined were so similar, and lets us classify them in a clean and compelling way.

But they do not give those classified objects more structure or more power, and they cannot capture all the detail of any one of those domains. So in the end, they provide leverage, but no new power. And they do not replace the separate domains. Nor do they give an overall view that would choose one to be best. The equivalent Universal Logic would have the same nature.

In fact, since most logics are algebras in the UA sense, it is ambiguous whether the two are even different. So people seem to be looking for this structure inside Category Theory, which is just one of the three faces of Universal Algebra itself, a domain that, for all its theoretical power, finds limited real application.

Answer 3

I think the question is whether there is one human logic to begin with and whether we could conceive of a better one.

That there is only one human logic seems attested by the history of logic between Aristotle and Kant. Each of us can test for himself this idea on the small set of logical truths uncovered by the tradition, such as the modus ponens, the modus tollens, and such basic relations as "A → A", "(A ∧ B) → A" or "A → (A ∨ B)", and this by considering how these logical truths could possibly not be true after all.

Mathematical logic may seem to disprove this thesis. However, while there is little doubt that mathematical logic is mathematics, it is unclear that it is also logic proper. As I see it, mathematical logic is the study of various mathematical extensions of and beyond logic, which can be said of the whole of mathematics. Some of those extensions will perhaps prove useless, others already have applications. The question is whether some of these theories are proper logics, i.e. operational alternatives to human logic rather, than mere extensions of human logic, or even fanciful theories without any real application.

Supposing we are effectively able to even conceive coherently of a different logic, your question becomes whether any such alternative to human logic could be somehow more effective.

One reason to suspect not is to consider that human logic is the result of more than 550 million years of natural selection of nervous systems. As such, it has to be very effective in allowing us to understand nature if, that is, nature is at all logically consistent. The possibility of conceiving of a logic more effective than human logic seems conceivable but a very, very tall order. The key aspect of logic has to be validity. To conceive of an alternative logic superior to human logic, we would probably have to understand logical validity first.

We could also conceive of alternative logics as only applicable to particular questions or fields. However, human logic seems applicable to all conceivable questions, through theology, metaphysics, philosophy, mathematics, science and technology. All mathematical theories rely on human logic, and so all human theories of logic also rely on human logic. And the few theories that seem incompatible with human logic still have to show first that they are pure logic and not mathematics in disguise and, second, how they could be conceived of coherently.

One last (barely) conceivable possibility would for us to just discover an alternative to human logic in nature itself. This might happen if for example we came to realise that human logic doesn't apply to some natural phenomenon. Easy to say it, much less to conceive of it, although this could also be said of all major scientific discoveries. So, it might happen but that would come as a very big surprise and one that we would perhaps be unable to understand.