5 ideas
18004 | We can't do philosophy without knowledge of types and categories [Ryle] |
Full Idea: We are in the dark about the nature of philosophical problems and methods if we are in the dark about types and categories. | |
From: Gilbert Ryle (Categories [1938], p.189), quoted by Ofra Magidor - Category Mistakes 1.2 | |
A reaction: Magidor and others take this to be an assertion about language and logic, but I take it to be an assertion about reality. It is an early assertion of Schaffer's claim that ontology concerns the structure of existence, and not just what exists. |
9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
Full Idea: Most accounts of the concept of mathematical truth can be identified with serving one or another of either semantic theory (matching it to ordinary language), or with epistemology (meshing with a reasonable view) - always at the expense of the other. | |
From: Paul Benacerraf (Mathematical Truth [1973], Intro) | |
A reaction: The gist is that language pulls you towards platonism, and epistemology pulls you towards empiricism. He argues that the semantics must give ground. He's right. |
17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
Full Idea: Benacerraf argues that realists about mathematical objects have a nice normal semantic but no epistemology, and anti-realists have a good epistemology but an unorthodox semantics. | |
From: report of Paul Benacerraf (Mathematical Truth [1973]) by Mark Colyvan - Introduction to the Philosophy of Mathematics 1.2 |
9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
Full Idea: The principle defect of the standard (platonist) account of mathematical truth is that it appears to violate the requirement that our account be susceptible to integration into our over-all account of knowledge. | |
From: Paul Benacerraf (Mathematical Truth [1973], III) | |
A reaction: Unfortunately he goes on to defend a causal theory of justification (fashionable at that time, but implausible now). Nevertheless, his general point is well made. Your theory of what mathematics is had better make it knowable. |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |