Keith Douglas
Recap
Last time we discussed the pessimistic metainduction. Steve W. further expands various realist theses. The three theses are fine as far as I am concerned as a scientific realist. As a species of what is sometimes called antirealism in philosophy of mathematics, I deny the metaphysical one in that domain (there are no numbers, sets, etc.). I also deny the epistemic thesis (suitably understood). “Formal truth,” as it is sometimes called, is not truth in at all the same way that factual truth is, i.e., the correspondence that I mentioned. I deny this because I deny that there is anything to correspond to. However, since I’m a fictionalist, I don’t get caught up in worrying whether we can construct anything, because I think the language of construction itself can be taken as fictional. In fact, I find it easier to understand transfinite arithmetic at its basic levels than very large finite arithmetic. Why would that be? Steve W. also doubts that the oxidation vs. phlogiston example can be taken as a relativity-of-wrong case. I’m not really wedded to any particular explanation, here, but it seems to me that even with phlogiston, we gained some knowledge. If we are wedded to “complete truth or nothing”, perhaps not, but I think the realist can say we gain some truth even if it is partial. For example, something in the air combines with something solid when rusting occurs. As opposed to, say, something internal to the solid changing state. This seems to be what Aristotle meant by “corruption”, for example. It is of course true that nobody still uses phlogiston chemistry. I am not sure what relevance that has. Do people still use Aristotle’s mechanics? What’s the name for a reverse limiting case: one where the (say) friction is substantially non-zero? In any case, I don’t think the realist has to be committed to the idea that all theories persist. In my view, the antirealist has to explain why one didn’t continue on working as Ptolemy and so on did – epicycles. I had a physicist point out to me that there’s a sense in which Ptolemy invented the Fourier series. The mathematicians in the room laughed at this, but… Finally (taking matters out of order), Steve also addresses whether Hasok Chang is a realist. I don’t know. I’ll have to read his two later books. Incidentally, there’s also a good taxonomy of different sorts of realisms in Critical Scientific Realism by Ikka Niiniluoto, which I can recommend, as a way around the space. Let’s move on.
This time…
I mentioned last time that Susan Haack, one of my philosophical influences, had died recently. I would like to do another personalized intellectual obituary, if I may. I guess I am at the age where large numbers of people of my parents’ generation (and earlier!) are dying off. Sad, but we all know this changing of the guard happens. (Pardon the militaristic metaphor. Maybe it is the tiny bit of Stoicism in me. 😊)
I first encountered Haack’s work in a little book I saw in Montreal’s Paragraphe book store, a little place near the McGill campus. I had a bit of discretionary money (thanks to my parents) and would sometimes buy stuff there. (Also, some of the philosophy instructors couldn’t stand the McGill bookstore’s incompetence and markups, so they used this place to order texts for their students, so I was in a bit more often for that reason as well.) This little book was the 1998 Manifesto of a passionate moderate: unfashionable essays, a collection of papers. I later encountered her two papers in a collection Bunge alluded to, The Flight from Science and Reason and Bunge also praised her book on epistemology: Evidence and Inquiry (this one has a varying, longer title depending on the edition). A short time later, A. Irivine at UBC mentioned her work in philosophy of logic – Deviant Logic, Fuzzy Logic: Beyond the Formalism and Philosophy of Logics, which I understand was her first book. In addition to the epistemology and logic works, her oeuvre includes works in philosophy of literature, philosophy of law, the history of philosophy (particularly pragmatism) and philosophy of science.
I will not of course survey anywhere near all of this work here; I had contemplated looking at each area. However, the reader can go to the journals and look at that sort of matter on their own. I would like to instead address a question provoked in me by Deviant Logic, Fuzzy Logic. Both this and the earlier Philosophy of Logics are works in the philosophy of logic. One important (to me at least) topic in the philosophy of logic is the justification of logic itself. One aspect of this is justifying any particular logical formalism, theory, etc. How one does this is not an easy question, and recently, there has even been movement to try to tie different systems together in a way that I think ultimately has some merit. Be that as it may, that part of the literature is extremely challenging – state-of-the-art research should be!
Haack also gives some discussion of technology that I would like to pick up on. She says that fuzzy logic, whatever its merits, is not justified by its use within engineering applications like thermostats or other control systems. The first argument seems to be something like this: fuzzy logic is really a fuzzy set theory, and such a theory that presupposes classical analysis in order to interpret. (At the time I first read Haack’s book, I had yet to read a textbook, only having read papers on fuzzy logic. I did so much later, and wrote some of this with more hindsight that is justified for me. The textbook I read later came out the same year as the second edition of her book; I bought a used copy.) I
This is immediately problematic to me, as it appears to deny that metatheory is relevant to understanding logic. Or perhaps more charitably, that metatheory should use the same logic as the basic logic. Graham Priest, for example, has tried to study paraconsistent logics with paraconsistent metatheory.
However, there’s another possibility here. Haack also says she considers logic as an attempt to capture truth-preserving inferences. She doesn’t say precisely why she considers (say) a fuzzy thermostat as not performing those. We’ve met critics of AI who would say that it does not, but that is not mentioned here as such. To make the problem clearer, let’s widen the context a little.
Fuzzy logic is not the only non-classical logic that is used in technological applications. For example, a three-valued logic is used in the theory of databases, and in particular, the programming language SQL. This three-valued logic is explicitly used in the context of conditionals in this language and manuals, and textbooks illustrate how it works with truth tables, etc. (One cannot of course write a truth table for the continuum-valued logic of the fuzzy controller.) It is unclear what Haack would say about this case. It seems that she would be forced to say that programming languages don’t use logic either if it is the machine involved that is the problem. However, there is another possibility.
She seems to think that fuzzy controllers work by binning ranges of a relevant measurement into n categories and then using those categories (e.g., high, just right, low, in the case of a thermostat) to take action (lower temperature, no action, raise temperature). This, however, misses the inference, which is that “if in range do…” and the fact that these don’t work categorically. Fuzzy controllers behave fuzzily, as it were (probabilistically). This is to prevent flapping on and off when the temperature is near the edges of the range. In that sense, they recapture the idea that fuzzy sets are not supposed to have precise boundaries.
It is hard to say more about this case; it is all so elliptical, and I’ve not addressed the other criticisms she has of fuzzy logic (some of which I agree with, for sure). I have just been interested in exploring ways in which logic is justified, and via its technological applications seems a promising area.
As usual, I’m up for topics of reader interest, so feel free to send those along.