A master ‘set’

I have a question to which I have no answer to (because its not my area).

 

Does it make sense to talk of a set which contains all true statements about the world?

 

Destrean comments:

1. To have a fact in it does not necessarily entail the justification/demonstration of that fact (e.g. base principles like F=ma), but it will iff we are to accept the proof of any given fact as true in itself.

2. I’m deserving to be reminded of the conclusions of the 2nd Incompleteness theoremt; but I want a better explanation than the crappy folk explanation I have

3. I’m aware of Russell’s paradox; is this relevant? Furthermore, is it desirable (quid juris) to incorporate this by limiting he notion of the master set?

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4 thoughts on “A master ‘set’

  1. This is early twentieth century stuff, isn’t it (you mention Russell, so I reckon you know this). Wittgenstein’s Tractatus of course makes this assertion right at the beginning – but then, Ludwig spent the rest of his life trying to undo his mistakes here.

    It is my opinion that no, it does not make sense to talk of a set of all the true statements about the world. A statement is true only relative to its frame of reference, so without specifying a frame of reference how would one construct a set?

    Case in point, such a set made 200 years ago would be based on very different axioms than such a set made today – so what basis for asserting that either set contains “true statements”?

    Nietzsche says “there are no facts, only interpretations” – I believe he is fundamentally correct in this assertion, although one could easily misunderstand his claim.

    Sorry, out of time – must dash! *waves*

  2. Chris: Issues that come up from you:

    1. A ‘master set’ must have elicited various axioms; what they are is indeed a good question.
    2. ‘We can pose the existence of a master set iff there is a master set’ is a true proposition; whether we know anything about the master set is irrelevant. An formally isomorphic claim is the following: ‘there exist laws of nature given the following [x,y,z] reasons; we do not, however, know these laws in virtue of [x,y,z]’
    3. Lets not bring Nietzsche into this…he’s a philosopher that is too easily misinterpreted. My man is Kant, and he’s exegetically hard enough, thank you :). I don’t understand what Nietzsche means in that aphorism anyway.
    4. The motivation of this question is Spinoza’s God

    Sinistre/Destre

  3. I agree that Nietzsche is too easily misinterpreted, but I still felt that quote was apposite. 🙂

    I really should give Spinoza a try. He was an influence on both Nietzsche and Einstein, but a quick glance at his major work makes it look pretty impenetrable – I think I’d rather make a start on another Kant first.

  4. I think it is possible with caveats:

    Firstly you must pin down how you code your universe (this is essentially picking an observational standpoint).

    Secondly you must pin down the languange you are using (it needs to be rigorous and it needs to lack ambiguous propositions. There may be additional requirements). I shall be assuming that the language is reasonably expressive in later caveats.

    Thirdly we probably can’t expect such a truth set to be definable from within the system (Tarski’s undefinability of truth).

    Fourthly the existence of such a truth set will probably be unprovable due to Godel’s second incompleteness theorem (the existence of a truth set would validate the consistency of your underlying mathematical theory).

    One could try to develop a theory of truth to allow the dropping of the second caveat by refraining from pinning down ones language entirely but rather introducing axioms describing features of the language sufficient to imply that it is rigorous and unamibuous and so on.

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