Combining Texts

All the ideas for 'fragments/reports', 'The Source of Necessity' and 'Intro to 'Provenance of Pure Reason''

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8 ideas

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

13416	Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C]
	Full Idea: The axiomatic conception of mathematics is the only viable one. ...But they are true because they are axioms, in contrast to the view advanced by Frege (to Hilbert) that to be a candidate for axiomhood a statement must be true.
	From: report of William W. Tait (Intro to 'Provenance of Pure Reason' [2005], p.4) by Charles Parsons - Review of Tait 'Provenance of Pure Reason' §2
	A reaction: This looks like the classic twentieth century shift in the attitude to axioms. The Greek idea is that they must be self-evident truths, but the Tait-style view is that they are just the first steps in establishing a logical structure. I prefer the Greeks.

10. Modality / C. Sources of Modality / 1. Sources of Necessity

12432	Explanation of necessity must rest on something necessary or something contingent [Hale]
	Full Idea: The dilemma is that to give the ultimate source of any necessity, we must either appeal to something which could not have been otherwise (i.e. is itself necessary), or advert to something which could have been otherwise (i.e. is itself merely contingent).
	From: Bob Hale (The Source of Necessity [2002], p.301)
	A reaction: [Hale is summarising Blackburn's view, and going on to disagree with it] Hale looks for a third way, but Blackburn seems to face us with quite a plausible dilemma.

12434	Why is this necessary, and what is necessity in general; why is this necessary truth true, and why necessary? [Hale]
	Full Idea: We must distinguish between explaining particular necessities and explaining necessity in general; and we ought to distinguish between explaining, in regard to any necessary truth, why it is true, and explaining why it is necessary.
	From: Bob Hale (The Source of Necessity [2002], p.308)
	A reaction: Useful. The pluralist view I associate with Fine says we can explain types of necessity, but not necessity in general. If we seek truthmakers, there is a special case of what adds the necessity to the truth.

12435	The explanation of a necessity can be by a truth (which may only happen to be a necessary truth) [Hale]
	Full Idea: My claim is that there are non-transitive explanations of necessities, where what explains is indeed necessary, but what explains the necessity of the explanandum is not the explanation's necessity, but its truth simpliciter.
	From: Bob Hale (The Source of Necessity [2002], p.311)
	A reaction: The big idea is to avoid a regress of necessities. The actual truths he proposes are essentialist. An interesting proposal. It might depend on how one views essences (as giving identity, or causal power)

10. Modality / C. Sources of Modality / 3. Necessity by Convention

12433	If necessity rests on linguistic conventions, those are contingent, so there is no necessity [Hale]
	Full Idea: If the alleged necessity, e,g, 2+2=4, really does depend upon a convention governing the use of the words in which we state it, and the existence of that convention is merely a contingent matter, then it can't after all be necessary.
	From: Bob Hale (The Source of Necessity [2002], p.302)
	A reaction: [Hale is citing Blackburn for this claim] Hale suggests replies, by keeping truth and meaning separate, and involving laws of logic. Blackburn clearly has a good point.

10. Modality / C. Sources of Modality / 4. Necessity from Concepts

12436	Concept-identities explain how we know necessities, not why they are necessary [Hale]
	Full Idea: It seems to me that identity-relations among concepts have more to do with explaining how we know that vixens are female foxes etc., than with explaining why it is necessary, and, more generally, with explaining why some necessities are knowable a priori.
	From: Bob Hale (The Source of Necessity [2002], P.313)
	A reaction: Hale rejects the conceptual and conventional accounts of necessity, in favour of the essentialist view. This strikes me as a good suggestion of Hale's, since I agree with him about the essentialism.

25. Social Practice / E. Policies / 5. Education / b. Education principles

13304	Learned men gain more in one day than others do in a lifetime [Posidonius]
	Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes.
	From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078
	A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book.

27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure

20820	Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
	Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness.
	From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42
	A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them.