9 ideas
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. |
7401 | Heat and colour don't exist, so cannot mislead about the external world [Galileo, by Tuck] |
Full Idea: Galileo argued that there is no such thing as heat (and hence also as colour) in the external world, so there is no reason to conclude from colour-blindness that we cannot know the truth about the world. | |
From: report of Galileo Galilei (Il Saggiatore ('The Assayer') [1623]) by Richard Tuck - Hobbes Ch.1 | |
A reaction: This key idea, taken up by Gassendi, Descartes and Locke, seems to me to be one of the most important (and, in retrospect, rather obvious) facts ever worked out by the human mind. Why does anyone still doubt it? |
5454 | Tastes, odours and colours only reside in consciousness, and would disappear with creatures [Galileo] |
Full Idea: I think tastes, odours, colours, and so on are mere names as far as the objects are concerned, and only reside in consciousness. Hence if the living creature were removed, all these qualities would be wiped away and annihilated. | |
From: Galileo Galilei (Il Saggiatore ('The Assayer') [1623]), quoted by Brian Ellis - The Philosophy of Nature: new essentialism Ch.3 | |
A reaction: A nice bold assertion of the primary/secondary distinction from the first great scientist. I agree, and to disagree (and hence side with Berkeley and Hume) is to head for metaphsical and epistemological confusion. |
21513 | We can no more expect a precise definition of coherence than we can of the moral ideal [Ewing] |
Full Idea: I think it is wrong to tie down the advocates of the coherence theory to a precise definition. ...It would be altogether unreasonable to demand that the moral ideal should be exhaustively defined, and the same may be true of the ideal of thought. | |
From: A.C. Ewing (Idealism: a critical survey [1934], p.231), quoted by Erik J. Olsson - Against Coherence 7.6 | |
A reaction: I strongly agree. It is not a council of despair. I think the criteria of coherence can be articulated quite well (e.g by Thagard), and the virtues of enquiry can also be quite well specified (e.g. by Zagzebski). Very dissimilar evidence must cohere. |
21497 | If undetailed, 'coherence' is just a vague words that covers all possible arguments [Ewing] |
Full Idea: Without a detailed account, coherence is reduced to the mere muttering of the word 'coherence', which can be interpreted so as to cover all arguments, but only by making its meaning so wide as to rob it of almost all significance. | |
From: A.C. Ewing (Idealism: a critical survey [1934], p.246), quoted by Erik J. Olsson - Against Coherence 2.2 | |
A reaction: I'm a fan of coherence, but it is a placeholder, involving no intrinsic or detailed theory. I just think it points to the reality of how we make judgements, especially practical ones. We can categorise the inputs, and explain the required virtues. |
16560 | Galileo introduced geometrico-mechanical explanation, based on Archimedes [Galileo, by Machamer/Darden/Craver] |
Full Idea: The modern idea of explaining with mechanisms became current in the 17th century when Galileo articulated a geometrico-mechanical form of explanation based on Archimedes' simple machines. This became the 'mechanical philosophy'. | |
From: report of Galileo Galilei (Il Saggiatore ('The Assayer') [1623]) by Machamer,P/Darden,L/Craver,C - Thinking About Mechanisms 5.2 | |
A reaction: So is Archimedes the source? I would say that mechanical explanation is just commonsense, and is predominant in all human thinking, even in tiny infants. |
3645 | To understand the universe mathematics is essential [Galileo] |
Full Idea: The great book of the universe cannot be understood unless one can understand the language in which it is written - the language of mathematics. | |
From: Galileo Galilei (Il Saggiatore ('The Assayer') [1623], VI.232) | |
A reaction: Nice, though one might say that humans created the language of maths to help them discuss the patterns they perceived in nature. Maybe what is special is order, and all order can be described mathematically. |