11 ideas
10304 | Very few things in set theory remain valid in intuitionist mathematics [Bernays] |
Full Idea: Very few things in set theory remain valid in intuitionist mathematics. | |
From: Paul Bernays (On Platonism in Mathematics [1934]) |
10303 | Restricted Platonism is just an ideal projection of a domain of thought [Bernays] |
Full Idea: A restricted Platonism does not claim to be more than, so to speak, an ideal projection of a domain of thought. | |
From: Paul Bernays (On Platonism in Mathematics [1934], p.261) | |
A reaction: I have always found Platonism to be congenial when it talks of 'ideals', and ridiculous when it talks of a special form of 'existence'. Ideals only 'exist' because we idealise things. I may declare myself, after all, to be a Restricted Platonist. |
10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
Full Idea: Mathematical abstraction does not have a lesser degree than logical abstraction, but rather another direction. | |
From: Paul Bernays (On Platonism in Mathematics [1934], p.268) | |
A reaction: His point is that the logicists seem to think that if you increasingly abstract from mathematics, you end up with pure logic. |
7720 | Two things can only resemble one another in some respect, and that may reintroduce a universal [Lowe] |
Full Idea: A problem for resemblance nominalism is that in saying that two particulars 'resemble' one another, it is necessary to specify in what respect they do so (e.g. colour, shape, size), and this threatens to reintroduce what appears to be talk of universals. | |
From: E.J. Lowe (Locke on Human Understanding [1995], Ch.7) | |
A reaction: We see resemblance between faces instantly, long before we can specify the 'respects' of the resemblance. This supports the Humean hard-wired view of resemblance, rather than some appeal to Platonic universals. |
7712 | On substances, Leibniz emphasises unity, Spinoza independence, Locke relations to qualities [Lowe] |
Full Idea: Later philosophers emphasised different strands of Aristotle's concept of substances: Leibniz (in his theory of monads) emphasised their unity; Spinoza emphasised their ontological independence; Locke emphasised their role in relation to qualities. | |
From: E.J. Lowe (Locke on Human Understanding [1995], Ch.4) | |
A reaction: Note that this Aristotelian idea had not been jettisoned in the late seventeenth century, unlike other Aristotelianisms. I think it is only with the success of atomism in chemistry that the idea of substance is forced to recede. |
7710 | Perception is a mode of belief-acquisition, and does not involve sensation [Lowe] |
Full Idea: According to one school of thought, perception is simply a mode of belief-acquisition,and there is no reason to suppose that any element of sensation is literally involved in perception. | |
From: E.J. Lowe (Locke on Human Understanding [1995], Ch.3) | |
A reaction: Blindsight would be an obvious supporting case for this view. I think this point is crucial in understanding what is wrong with Jackson's 'knowledge argument' (involving Mary, see Idea 7377). Sensation gives knowledge, so it can't be knowledge. |
7711 | Science requires a causal theory - perception of an object must be an experience caused by the object [Lowe] |
Full Idea: Only a causal theory of perception will respect the facts of physiology and physics ...meaning a theory which maintains that for a subject to perceive a physical object the subject should enjoy some appropriate perceptual experience caused by the object. | |
From: E.J. Lowe (Locke on Human Understanding [1995], Ch.3) | |
A reaction: If I hallucinate an object, then presumably I am not allowed to say that I 'perceive' it, but that seems to make the causal theory an idle tautology. If we are in virtual reality then there aren't any objects. |
7714 | Personal identity is a problem across time (diachronic) and at an instant (synchronic) [Lowe] |
Full Idea: There is the question of the identity of a person over or across time ('diachronic' personal identity), and there is also the question of what makes for personal identity at a time ('synchronic' personal identity). | |
From: E.J. Lowe (Locke on Human Understanding [1995], Ch.5) | |
A reaction: This seems to me to be the first and most important distinction in the philosophy of personal identity, and they regularly get run together. Locke, for example, has an account of synchronic identity, which is often ignored. It applies to objects too. |
7715 | Mentalese isn't a language, because it isn't conventional, or a means of public communication [Lowe] |
Full Idea: 'Mentalese' would be neither conventional nor a means of public communication so that even to call it a language is seriously misleading. | |
From: E.J. Lowe (Locke on Human Understanding [1995], Ch.7) | |
A reaction: It is, however, supposed to contain symbolic representations which are then used as tokens for computation, so it seems close to a language, if (for example) symbolic logic or mathematics were accepted as languages. But who understands it? |
7722 | If meaning is mental pictures, explain "the cat (or dog!) is NOT on the mat" [Lowe] |
Full Idea: If meaning is a private mental picture, what does 'the cat is NOT on the mat' mean, and how does it differ from 'the dog is not on the mat?'. | |
From: E.J. Lowe (Locke on Human Understanding [1995], Ch.7) | |
A reaction: Not insurmountable. We picture an empty mat, combined with a cat (or whatever) located somewhere else. A mental 'picture' of something shouldn't be contrued as a single image in a neat black frame. |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |