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THE QUANTUM of EXPLANATION

~ Science, logic, and ethics, from a Whiteheadian Pragmatist perspective (go figure)

THE QUANTUM of EXPLANATION

Tag Archives: Modal Logic

A = B

10 Monday Jun 2019

Posted by Gary Herstein in Logic, Mathematics, measurement, Philosophy of Logic

≈ 8 Comments

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measurement, Modal Logic, Philosophy of Logic

Anyone who is reading this post – indeed, anyone who can read at all – has some minimal exposure to mathematical ideas, even if that exposure goes no further than elementary arithmetic and not, as I am only half-jokingly known to say, actual mathematics. (Well, since I’ve mentioned it: the thing I’m known to say is, “that’s not mathematics, that’s arithmetic.” This is always in response to someone who has protested something along the lines, “I’m no good at mathematics; I can’t even balance my checkbook.” The humorous, yet legitimately educative nature of MY statement always strikes me as obvious, yet I am constantly amazed by the numbers of people who get lost in the elementary rhetoric of my statement.)A equals B

In any event, even such minimal exposure is typically enough to satisfy most people, even most mathematicians (I suspect), that they have a pretty good handle on what that equals sign (“=”) means as it is expressed in, say, the title of this little essay. Clearly I wouldn’t be writing about it if such an impression was even remotely true. For one thing, how do we read “A = B”? Does it say, “A equals B”, or does it say “A is B”, and is there a difference between those two? Spoiler: yes. Yes to both questions, depending on how crudely one is using one’s language, which makes the fact that “equals” does not equal “is” an especially problematic conflation of terms. “Is” tends to mean “identity” in such a context, which is tricky enough in its own right (I wrote an MA thesis on the subject). The reading of “=” as “equals” helps to emphasize a somewhat more functional approach to matters, though it is still more rigid and “substantive” than such formal notions as “equivalence” and “isomorphism.” topics I’ll likely blog about in the future because I can already hear the math-phobes screaming in horror. For now, I want to focus on the logical issues of “equals,” as a formal relation. Thus, the word “equality” may also find a use here, but that use should not be mistaken for the political, economic, cultural, &/or social senses of the term. (On the other hand, I do not preclude in advance that what I say here will have no bearing on those uses, either.) Obviously, the starting point for the primary discussion is with the work of Alfred North Whitehead. Continue reading →

The Logic of Possibility

28 Monday Dec 2015

Posted by Gary Herstein in Logic, Philosophy of Logic

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Logic, Modal Logic, Philosophy of Logic

There is a large, nested, complexly intersecting, multidimensional area of logic known as “modal logic.” Standard (“assertoric” – dealing with comparatively simple assertions) logic essentially forgoes any considerations of the modes (hence, “modal”) in which an assertion is considered to be true or false; it simply is, or it is not (true or false). Modal logics are intended to examine the ways (modes) in which a proposition or assertion might express such truth or falsity. A great deal of very good work has been done in this area of study, but it remains a long way from solving its most basic problems; indeed, most proposed “solutions” do not so much “solve” their problems as strangle them.i I am at once deeply impressed by the technical sophistication of contemporary work on modality, and profoundly dissatisfied with the narrowness of its vision. Because one of the “modes” in which an assertion or proposition might be true or false is whether it is possibly true or false.baby-steps

I can certainly inundate any interested party with citations, but anyone capable of following those citations would most likely already be familiar with them. It takes years of dedicated study to bootstrap one’s self up through propositional, into quantificational, and finally on to modal logics. On the other hand, it takes nothing more than the most elementary capacity for cognition to instantly see that there is a difference between saying that “X is the case,” and “X might be the case.” Just as we can talk about Jazz without mastering the saxophone, or relativity without deriving proofs related to the Ricci tensor, we can talk about possibility without becoming research mathematicians in formal logic. One might even argue that mastering such mathematics would not ideally equip us to talk about possibility which is, after all, a metaphysical, rather than a mathematical topic. Continue reading →

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