3 ms·

A mathematician's (or, at least, this mathematician's) instinctive response to a paper titled "Against set theory" is to think that it must be the work of a cra

by JadeNB 6y ago

A mathematician's (or, at least, this mathematician's) instinctive response to a paper titled "Against set theory" is to think that it must be the work of a crank (not to disparage the work of reputable mathematicians exploring alternative foundations—but I think that most of them know that, to earn their ideas a receptive foundation, they had better focus at least on what they are for rather than what they are against), but it should probably be noted that this is against set theory from a philosopher's point of view, not a mathematician's. (With which I can't quibble, though neither can I agree; I am no philosopher, and the fact that mathematics can be used fruitfully in philosophy doesn't mean that it always should.) Indeed, at a skim, the complaint seems to be much more about the mathematisation of philosophy broadly speaking, rather than about the encroachment of set theory in particular. (I also take issue with the claim on p. 3 that Cauchy was doing only unconscious set theory. It is true that he came before what we might call Cantor's formalisation of the subject, but I think he probably thought in something much closer to a modern "naïvely set theoretic" way about mathematics than almost all o his predecessors.)

throwaway_pdp09 6y ago
Introducing mathematical notation into philosophy gives, not the firm foundation, but some firm foundation, upon which to argue. Otherwise a whole lot of shite is spewed and no progress is made. In its are sentences of long words that serve to emote, cajole and frankly baffle rather than enlighten. There's some of it here but it's not the worst. What I can't accept is stuff like " has been to persuade many philosophers that the rich panoply of entities the world throws at us can be reduced to individuals and sets of various sorts, for example sets as properties, sets of ordered tuples as relations, sets of possible worlds as propositions, and so on and so forth. It is hard to know where to start in revealing the scope of the damage caused to ontology by the thoughtless or supposedly scientifically economic reduction of various entities to sets" To model something you need to simplify it. What's he suggesting instead? Other oddities " Richmond Thomason notes that Montague saw grammar as a branch of mathematics and not (as in Chomsky) of psychology". Pretty sure Chomsky's hierarchy of grammars, types 3 to 0, are considered by him as mathematical, not psychological. Not my area but I'm not convinced it's worth digging into this paper. (edit) Further down we get to the bullshit. The emotive crap: "tiresome to continue citing further absurdities in philosophy resulting from the over-zealous application" so instead we replace defined set theoretic terms with english, delights such as, replacing <x,y> with x followed by y; x and y in that order. Ha ha ha now explain what logical implication means without being formal. (edit: and then show me some symbol manipulation using it, without the symbols) Not happening. I do understand the terminology is intimidating, and there's much to be said for annotating the set-theoretic with plain english as he suggests but to replace it... that would be a massive step backwards.
- einpoklum 6y ago
  > To model something you need to simplify it. What's he suggesting instead? But is set theory "simple"? The author mentions several ways in which it is the opposite of simple. Also - if you need to model _something_, that doesn't mean you should try to model _everything_ with the same kind of model.
  - throwaway_pdp09 6y ago
    Could you point to those ways? I guess I missed them.
- sinkasapa 6y ago
  > Other oddities " Richmond Thomason notes that Montague saw grammar as a branch of mathematics and not (as in Chomsky) of psychology". Pretty sure Chomsky's hierarchy of grammars, types 3 to 0, are considered by him as mathematical, not psychological. I would suggest looking up Chomsky and mentalism. This is a core feature of his theory. Early in his career Chomsky did have interesting things to say about formal language theory and you're right that Chomsky would not consider regular languages or the grammar of Python, for instance, to be psychological but this isn't the grammar that the author is concerned with here.

by JadeNB 6y ago

throwaway_pdp09 6y ago

Introducing mathematical notation into philosophy gives, not the firm foundation, but some firm foundation, upon which to argue. Otherwise a whole lot of shite is spewed and no progress is made. In its are sentences of long words that serve to emote, cajole and frankly baffle rather than enlighten. There's some of it here but it's not the worst. What I can't accept is stuff like " has been to persuade many philosophers that the rich panoply of entities the world throws at us can be reduced to individuals and sets of various sorts, for example sets as properties, sets of ordered tuples as relations, sets of possible worlds as propositions, and so on and so forth. It is hard to know where to start in revealing the scope of the damage caused to ontology by the thoughtless or supposedly scientifically economic reduction of various entities to sets" To model something you need to simplify it. What's he suggesting instead? Other oddities " Richmond Thomason notes that Montague saw grammar as a branch of mathematics and not (as in Chomsky) of psychology". Pretty sure Chomsky's hierarchy of grammars, types 3 to 0, are considered by him as mathematical, not psychological. Not my area but I'm not convinced it's worth digging into this paper. (edit) Further down we get to the bullshit. The emotive crap: "tiresome to continue citing further absurdities in philosophy resulting from the over-zealous application" so instead we replace defined set theoretic terms with english, delights such as, replacing <x,y> with x followed by y; x and y in that order. Ha ha ha now explain what logical implication means without being formal. (edit: and then show me some symbol manipulation using it, without the symbols) Not happening. I do understand the terminology is intimidating, and there's much to be said for annotating the set-theoretic with plain english as he suggests but to replace it... that would be a massive step backwards.

einpoklum 6y ago
> To model something you need to simplify it. What's he suggesting instead? But is set theory "simple"? The author mentions several ways in which it is the opposite of simple. Also - if you need to model _something_, that doesn't mean you should try to model _everything_ with the same kind of model.
- throwaway_pdp09 6y ago
  Could you point to those ways? I guess I missed them.
sinkasapa 6y ago
> Other oddities " Richmond Thomason notes that Montague saw grammar as a branch of mathematics and not (as in Chomsky) of psychology". Pretty sure Chomsky's hierarchy of grammars, types 3 to 0, are considered by him as mathematical, not psychological. I would suggest looking up Chomsky and mentalism. This is a core feature of his theory. Early in his career Chomsky did have interesting things to say about formal language theory and you're right that Chomsky would not consider regular languages or the grammar of Python, for instance, to be psychological but this isn't the grammar that the author is concerned with here.