12 ideas
| 17833 | The first-order ZF axiomatisation is highly non-categorical [Hallett,M] |
| Full Idea: The first-order Sermelo-Fraenkel axiomatisation is highly non-categorical. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1213) |
| 17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M] |
| Full Idea: The non-categoricity of the axioms which Zermelo demonstrates reveals an incompleteness of a sort, ....for this seems to show that there will always be a set (indeed, an unending sequence) that the basic axioms are incapable of revealing to be sets. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1215) | |
| A reaction: Hallett says the incompleteness concerning Zermelo was the (transfinitely) indefinite iterability of the power set operation (which is what drives the 'iterative conception' of sets). |
| 17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
| Full Idea: Unlike earlier writers (such as Fraenkel), Zermelo clearly allows that there might be ur-elements (that is, objects other than the empty set, which have no members). Indeed he sees in this the possibility of widespread application of set-theory. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
| 17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
| Full Idea: In 1938, Gödel showed that ZF plus the General Continuum Hypothesis is consistent if ZF is. Cohen showed that ZF and not-GCH is also consistent if ZF is, which finally shows that neither GCH nor ¬GCH can be proved from ZF itself. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
| 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. |
| 7458 | The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking] |
| Full Idea: The credibility of a witness is in part a function of the story being reported. When the story claims to have infinite value, the temptation to lie for personal benefit is asymptotically infinite. | |
| From: report of Pierre Simon de Laplace (Philosophical Essay on Probability [1820], Ch.XI) by Ian Hacking - The Emergence of Probability Ch.8 | |
| A reaction: Laplace seems to especially have reports of miracles in mind. This observation certainly dashes any dreams one might have of producing a statistical measure of the reliability of testimony. |
| 3441 | If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace] |
| Full Idea: An intelligence knowing at an instant the whole universe could know the movement of the largest bodies and atoms in one formula, provided his intellect were powerful enough to subject all data to analysis. Past and future would be present to his eyes. | |
| From: Pierre Simon de Laplace (Philosophical Essay on Probability [1820]), quoted by Mark Thornton - Do we have free will? p.70 |
| 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? |