Combining Texts

All the ideas for 'fragments/reports', 'Truth' and 'Elements of Intuitionism'

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7 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Even pointing a finger should only be done for a reason [Epictetus]
     Full Idea: Philosophy says it is not right even to stretch out a finger without some reason.
     From: Epictetus (fragments/reports [c.57], 15)
     A reaction: The key point here is that philosophy concerns action, an idea on which Epictetus is very keen. He rather despise theory. This idea perfectly sums up the concept of the wholly rational life (which no rational person would actually want to live!).
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
The fact which is stated by a true sentence is not something in the world [Strawson,P]
     Full Idea: The fact which is stated by a true sentence is not something in the world.
     From: Peter F. Strawson (Truth [1950], §2)
     A reaction: Everything is in the world. This may just be a quibble over how we should use the word 'fact'. At some point the substance of what is stated in a sentence must eventually be out there, or we would never act on what we say.
Facts aren't exactly true statements, but they are what those statements say [Strawson,P]
     Full Idea: Facts are what statements (when true) state; they are not what statements are about. ..But it would be wrong to identify 'fact' and 'true statement' for these expressions have different roles in our language.
     From: Peter F. Strawson (Truth [1950], §2)
     A reaction: Personally I like to reserve the word 'facts' for what is out there, independent of any human thought or speech. As a realist, I believe that the facts are quite independent of our attempts to understand the facts. True statements attempt to state facts.
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
The statement that it is raining perfectly fits the fact that it is raining [Strawson,P]
     Full Idea: What could fit more perfectly the fact that it is raining than the statement that it is raining?
     From: Peter F. Strawson (Truth [1950], §2)
3. Truth / F. Semantic Truth / 2. Semantic Truth
The word 'true' always refers to a possible statement [Strawson,P]
     Full Idea: It is of prime importance to distinguish the fact that the use of 'true' always glances backwards or forwards to the actual or envisaged making of a statement by someone.
     From: Peter F. Strawson (Truth [1950], §1)
     A reaction: 'The truth of this matter will never be known'. Strawson is largely right, but it is crazy for any philosopher to use the word 'always' if they can possibly avoid it.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett]
     Full Idea: The platonist destroys the whole essence of infinity, which lies in the conception of a structure which is always in growth, precisely because the process of construction is never completed.
     From: Michael Dummett (Elements of Intuitionism [1977], p.57), quoted by Thomas J. McKay - Plural Predication
     A reaction: I don't warm to intuitionism, but I warm to this conception of infinity. Completed infinities are convenient reifications for mathematicians.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
For intuitionists it is constructed proofs (which take time) which make statements true [Dummett]
     Full Idea: For an intuitionist a mathematical statement is rendered true or false by a proof or disproof, that is, by a construction, and constructions are effected in time.
     From: Michael Dummett (Elements of Intuitionism [1977], p.336), quoted by Shaughan Lavine - Understanding the Infinite VI.2
     A reaction: Lavine is quoting this to draw attention to the difficulties of thinking of it as all taking place 'in time', especially when dealing with infinities.