21 ideas
| 2546 | Philosophy is a magnificent failure in its attempt to overstep the limits of our knowledge [McGinn] |
| Full Idea: Philosophy marks the limits of human theoretical intelligence. Philosophy is an attempt to overstep our cognitive bounds, a kind of magnificent failure. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.209) | |
| A reaction: No one attempts to overstep boundaries once they are confirmed as such. The magnificent attempts persist because failure is impossible to demonstrate (except, perhaps, by Gödel's Theorem). |
| 10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
| Full Idea: It is generally accepted that mathematics reduces to set theory, and I argue that set theory in turn reduces, with some aid of mereology, to the theory of the singleton function. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) |
| 10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
| Full Idea: In my usage of 'class', there is no such things as the null class. I don't mind calling some memberless thing - some individual - the null set. But that doesn't make it a memberless class. Rather, that makes it a 'set' that is not a class. | |
| From: David Lewis (Mathematics is Megethology [1993], p.05) | |
| A reaction: Lewis calls this usage 'idiosyncratic', but it strikes me as excellent. Set theorists can have their vital null class, and sensible people can be left to say, with Lewis, that classes of things must have members. |
| 10811 | The null set plays the role of last resort, for class abstracts and for existence [Lewis] |
| Full Idea: The null set serves two useful purposes. It is a denotation of last resort for class abstracts that denote no nonempty class. And it is an individual of last resort: we can count on its existence, and fearlessly build the hierarchy of sets from it. | |
| From: David Lewis (Mathematics is Megethology [1993], p.09) | |
| A reaction: This passage assuages my major reservation about the existence of the null set, but at the expense of confirming that it must be taken as an entirely fictional entity. |
| 10812 | The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis] |
| Full Idea: Should we accept the null set as a most extraordinary individual, a little speck of sheer nothingness, a sort of black hole in the fabric of Reality itself? Not that either, I think. | |
| From: David Lewis (Mathematics is Megethology [1993], p.09) | |
| A reaction: Correct! |
| 10813 | What on earth is the relationship between a singleton and an element? [Lewis] |
| Full Idea: A new student of set theory has just one thing, the element, and he has another single thing, the singleton, and not the slightest guidance about what one thing has to do with the other. | |
| From: David Lewis (Mathematics is Megethology [1993], p.12) |
| 10814 | Are all singletons exact intrinsic duplicates? [Lewis] |
| Full Idea: Are all singletons exact intrinsic duplicates? | |
| From: David Lewis (Mathematics is Megethology [1993], p.13) |
| 10806 | Megethology is the result of adding plural quantification to mereology [Lewis] |
| Full Idea: Megethology is the result of adding plural quantification, as advocated by George Boolos, to the language of mereology. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) |
| 2544 | Thoughts have a dual aspect: as they seem to introspection, and their underlying logical reality [McGinn] |
| Full Idea: Our thoughts have a kind of duality, corresponding to their surface appearance to introspection and their underlying logical reality. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.147) |
| 10816 | We can use mereology to simulate quantification over relations [Lewis] |
| Full Idea: We can simulate quantification over relations using megethology. Roughly, a quantifier over relations is a plural quantifier over things that encode ordered pairs by mereological means. | |
| From: David Lewis (Mathematics is Megethology [1993], p.18) | |
| A reaction: [He credits this idea to Burgess and Haven] The point is to avoid second-order logic, which quantifies over relations as ordered n-tuple sets. |
| 10808 | Mathematics is generalisations about singleton functions [Lewis] |
| Full Idea: We can take the theory of singleton functions, and hence set theory, and hence mathematics, to consist of generalisations about all singleton functions. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) | |
| A reaction: At first glance this sounds like a fancy version of the somewhat discredited Greek idea that mathematics is built on the concept of a 'unit'. |
| 10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
| Full Idea: We needn't believe in 'abstract structures' to have general structural truths about all successor functions. | |
| From: David Lewis (Mathematics is Megethology [1993], p.16) |
| 10810 | I say that absolutely any things can have a mereological fusion [Lewis] |
| Full Idea: I accept the principle of Unrestricted Composition: whenever there are some things, no matter how many or how unrelated or how disparate in character they may be, they have a mereological fusion. ...The trout-turkey is part fish and part fowl. | |
| From: David Lewis (Mathematics is Megethology [1993], p.07) | |
| A reaction: This nicely ducks the question of when things form natural wholes and when they don't, but I would have thought that that might be one of the central issues of metaphysicals, so I think I'll give Lewis's principle a miss. |
| 3158 | Theories of intentionality presuppose rationality, so can't explain it [Dennett] |
| Full Idea: Intentional theory is vacuous as psychology because it presupposes and does not explain rationality or intelligence. | |
| From: Daniel C. Dennett (Brainstorms:Essays on Mind and Psychology [1978], p.15?) | |
| A reaction: Virtually every philosophical theory seems to founder because it presupposes something like the thing it is meant to explain. I agree that 'intentionality' is a slightly airy concept that would probably reduce to something better. |
| 2539 | Mental modules for language, social, action, theory, space, emotion [McGinn] |
| Full Idea: The prevailing view in cognitive psychology is that the mind consists of separate faculties, each with a certain cognitive task: linguistic, social, practical, theoretical, abstract, spatial and emotional. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.40) | |
| A reaction: 'Faculties' are not quite the same as 'modules', and this list mostly involves more higher-order activities than a modules list (e.g. Idea 2495). The idea that emotion is a 'faculty' sounds old-fashioned. |
| 2545 | Free will is mental causation in action [McGinn] |
| Full Idea: Free will is mental causation in action. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.167) |
| 2543 | Brains aren't made of anything special, suggesting panpsychism [McGinn] |
| Full Idea: All matter must contain the potential to underlie consciousness, since there is nothing special about the matter that composes brain tissue. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.100) | |
| A reaction: This seems to me one of the most basic assumptions which we should all make about the mind. The mind is made of the brain, and the brain is made of food. However, there must be something 'special' about the brain. |
| 3159 | Beliefs and desires aren't real; they are prediction techniques [Dennett] |
| Full Idea: Intentional systems don't really have beliefs and desires, but one can explain and predict their behaviour by ascribing beliefs and desires to them. This strategy is pragmatic, not right or wrong. | |
| From: Daniel C. Dennett (Brainstorms:Essays on Mind and Psychology [1978], p.7?) | |
| A reaction: If the ascription of beliefs and desires explains behaviour, then that is good grounds for thinking they might be real features of the brain, and even if that is not so, they are real enough as abstractions from brain events, like the 'economic climate'. |
| 2540 | Examining mind sees no brain; examining brain sees no mind [McGinn] |
| Full Idea: You can look into your mind until you burst and not discover neurons and synapses, and you can stare at someone's brain from dawn till dusk and not perceive the consciousness that is so apparent to the person whose brain it is. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.47) | |
| A reaction: This is a striking symmetry of ignorance, though hardly enough to justify McGinn's pessimism about understanding the mind. 'When you are in the grass you can't see the whole of England; if you can see the whole of England, you won't see the grass'. |
| 2547 | There is information if there are symbols which refer, and which can combine into a truth or falsehood [McGinn] |
| Full Idea: There is information in a system if there are symbols in it that refer to things and that together form strings that can be true or false. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.225) | |
| A reaction: We can also directly apprehend information by perception. Are facts identical with correct information? Can a universal generalisation be information? |
| 2542 | Causation in the material world is energy-transfer, of motion, electricity or gravity [McGinn] |
| Full Idea: Causation in the material world works by energy transfer of some sort: transfer of motion, of electrical energy, of gravitational force. | |
| From: Colin McGinn (The Mysterious Flame [1999], p.92) |