9 ideas
| 12427 | All of mathematics is properties of the whole numbers [Kronecker] |
| Full Idea: All the results of significant mathematical research must ultimately be expressible in the simple forms of properties of whole numbers. | |
| From: Leopold Kronecker (works [1885], Vol 3/274), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 09.5 | |
| A reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date. Natural numbers have a special status, but not sufficient to support this claim. |
| 10091 | God made the integers, all the rest is the work of man [Kronecker] |
| Full Idea: God made the integers, all the rest is the work of man. | |
| From: Leopold Kronecker (works [1885]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Intro | |
| A reaction: This famous remark was first quoted in Kronecker's obituary. A response to Dedekind, it seems. See Idea 10090. Did he really mean that negative numbers were the work of God? We took a long time to spot them. |
| 17771 | How we evaluate evidence depends on our background beliefs [Bayne] |
| Full Idea: A claim that might be very plausible given one set of background beliefs might be highly implausible when evaluated in the light of a different set of background beliefs. | |
| From: Tim Bayne (Thought: a very short introduction [2013], Ch.7) |
| 17770 | Clifford's dictum seems to block our beliefs in morality, politics and philosophy [Bayne] |
| Full Idea: Endorsing Clifford's dictum threatens to undermine our right to hold many of our most cherished beliefs about morality, politics, and philosophy, for these are domains in which it is notoriously difficult to secure consensus. | |
| From: Tim Bayne (Thought: a very short introduction [2013], Ch.7) | |
| A reaction: I would say that those beliefs are amenable to evidence, but the evidence is often highly generalised, which is what makes those subjects notoriously difficult. The existence of a convention is a sort of evidence. |
| 17766 | Physicalism correlates brain and mind, explains causation by thought, and makes nature continuous [Bayne] |
| Full Idea: The motivations for physicalism about the mind are that it accounts for correlations between states of the brain and states of thought, ...that it accounts for the causal role of thoughts, ...and that it does justice to the continuity of nature. | |
| From: Tim Bayne (Thought: a very short introduction [2013], Ch.2) | |
| A reaction: [summary] That is a pretty good summary of why I am a physicalist about the mind. I take all other theories to be dead footnotes in the history of thought - unless someone can produce a really good new argument. Which they can't. |
| 17768 | Perception reveals what animals think, but humans can disengage thought from perception [Bayne] |
| Full Idea: One striking feature of human thought involves our ability to disengage the focus of thought from that of our perceptual attention. ...To get a fix on what an animal is thinking about, one need only determine the object of its perceptual attention. | |
| From: Tim Bayne (Thought: a very short introduction [2013], Ch.4) | |
| A reaction: What happens when an animal closes its eyes, or stirs violently during sleep? I take the hallmark of human thought to be its multi-level character, and this offers nice evidence for that view. Doing philosophy while driving a car is very revealing. |
| 17769 | Some people centre space on themselves; others centre space on the earth [Bayne] |
| Full Idea: Egocentric conceptions of space employ a frame of reference that is focused on oneself; ...geocentric conceptions of space, by contrast, employ a frame of reference that is centred on the earth. | |
| From: Tim Bayne (Thought: a very short introduction [2013], Ch.5) | |
| A reaction: Famously, Europeans nearly always employ the egocentric conception, but many other cultures are geocentric. Thus the salt cellar is either 'to my left' or 'to the west'. In the latter view, everyone always knows their orientation (even indoors?). |
| 17767 | The alternative to a language of thought is map-like or diagram-like thought [Bayne] |
| Full Idea: One could think that the structure of thought has more in common with that of maps or diagrams, and is not particularly language-like. | |
| From: Tim Bayne (Thought: a very short introduction [2013], Ch.2) | |
| A reaction: It seems unwise to be ensnared by analogies on this one, since the phenomenon is buried deep. You can no more infer what goes on underneath than you can infer electrons from looking at trees? |
| 3029 | Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius] |
| Full Idea: Stilpo asked a man whether Athena is the daughter of Zeus, and when he said yes, said,"But this statue of Athena by Phidias is the child of Phidias, so it is not a god." | |
| From: report of Stilpo (fragments/reports [c.330 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.10.5 |