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Ideas for 'Structures and Structuralism in Phil of Maths', 'fragments/reports' and 'Conditionals'

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3 ideas

3. Truth / B. Truthmakers / 10. Making Future Truths
Future events are true if one day we will say 'this event is happening now' [Carneades]
     Full Idea: We call those past events true of which at an earlier time this proposition was true: 'They are present now'; similarly, we shall call those future events true of which at some future time this proposition will be true: 'They are present now'.
     From: Carneades (fragments/reports [c.174 BCE]), quoted by M. Tullius Cicero - On Fate ('De fato') 9.23-8
     A reaction: This is a very nice way of paraphrasing statements about the necessity of true future contingent events. It still relies, of course, on the veracity of a tensed assertion
We say future things are true that will possess actuality at some following time [Carneades, by Cicero]
     Full Idea: Just as we speak of past things as true that possessed true actuality at some former time, so we speak of future things as true that will possess true actuality at some following time.
     From: report of Carneades (fragments/reports [c.174 BCE]) by M. Tullius Cicero - On Fate ('De fato') 11.27
     A reaction: This ducks the Aristotle problem of where it is true NOW when you say there will be a sea-fight tomorrow, and it turns out to be true. Carneades seems to be affirming a truth when it does not yet have a truthmaker.
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
     Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models.
     From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
     A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc.