Combining Texts

All the ideas for 'fragments/reports', 'Intro to 'Provenance of Pure Reason'' and 'Modal Realism at Work: Properties'

unexpand these ideas     |    start again     |     specify just one area for these texts

4 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.
8. Modes of Existence / B. Properties / 11. Properties as Sets
4038 Properties are sets of their possible instances (which separates 'renate' from 'cordate') [Lewis, by Mellor/Oliver]
     Full Idea: Lewis agrees that properties cannot be sets of their actual instances, but claims they can be sets of their possible instances. This would distinguish coextensive properties like being cordate and renate, since they might be separated.
     From: report of David Lewis (Modal Realism at Work: Properties [1986]) by DH Mellor / A Oliver - Introduction to 'Properties' §10
     A reaction: Sounds wrong. Two properties could be obviously different even if they could never be separated. In this world a creature might briefly survive without kidneys.
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
     Full Idea: Archelaus was the first person to say that the universe is boundless.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]
     Full Idea: Archelaus wrote that life on Earth began in a primeval slime.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus
     A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea.