Combining Texts

All the ideas for 'Through the Looking Glass', 'Sets and Numbers' and 'Laughter'

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14 ideas

1. Philosophy / D. Nature of Philosophy / 8. Humour
Amusement rests on superiority, or relief, or incongruity [Scruton]
     Full Idea: There are three common accounts of amusement: superiority theories (Hobbes's 'sudden glory'), 'relief from restraint' (Freud on jokes), and 'incongruity' theories (Schopenhauer).
     From: Roger Scruton (Laughter [1982], §5)
     A reaction: All three contain some truth. But one need not feel superior to laugh, and one may already be in a state of unrestraint. Schopenhauer seems closest to a good general account.
The central object of amusement is the human [Scruton]
     Full Idea: There are amusing buildings, but not amusing rocks and cliffs. If I were to propose a candidate for the formal object of amusement, then the human would be my choice, ...or at least emphasise its centrality.
     From: Roger Scruton (Laughter [1982], §9)
     A reaction: Sounds good. Animal behaviour only seems to amuse if it evokes something human. Plants would have to look a bit human to be funny.
Since only men laugh, it seems to be an attribute of reason [Scruton]
     Full Idea: Man is the only animal that laughs, so a starting point for all enquiries into laughter must be the hypothesis that it is an attribute of reason (though that gets us no further than our definition of reason).
     From: Roger Scruton (Laughter [1982], §1)
     A reaction: I would be inclined to say that both our capacity for reason and our capacity for laughter (and, indeed, our capacity for language) are a consequence of our evolved capacity for meta-thought.
Objects of amusement do not have to be real [Scruton]
     Full Idea: It is a matter of indifference whether the object of amusement be thought to be real.
     From: Roger Scruton (Laughter [1982], §7)
     A reaction: Sort of. If I say 'wouldn't it be funny if someone did x?', it is probably much less funny than if I say 'apparently he really did x'. The fantasy case has to be much funnier to evoke the laughter.
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
The master science is physical objects divided into sets [Maddy]
     Full Idea: The master science can be thought of as the theory of sets with the entire range of physical objects as ur-elements.
     From: Penelope Maddy (Sets and Numbers [1981], II)
     A reaction: This sounds like Quine's view, since we have to add sets to our naturalistic ontology of objects. It seems to involve unrestricted mereology to create normal objects.
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy]
     Full Idea: If you wonder why multiplication is commutative, you could prove it from the Peano postulates, but the proof offers little towards an answer. In set theory Cartesian products match 1-1, and n.m dots when turned on its side has m.n dots, which explains it.
     From: Penelope Maddy (Sets and Numbers [1981], II)
     A reaction: 'Turning on its side' sounds more fundamental than formal set theory. I'm a fan of explanation as taking you to the heart of the problem. I suspect the world, rather than set theory, explains the commutativity.
Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy]
     Full Idea: The standard account of the relationship between numbers and sets is that numbers simply are certain sets. This has the advantage of ontological economy, and allows numbers to be brought within the epistemology of sets.
     From: Penelope Maddy (Sets and Numbers [1981], III)
     A reaction: Maddy votes for numbers being properties of sets, rather than the sets themselves. See Yourgrau's critique.
Numbers are properties of sets, just as lengths are properties of physical objects [Maddy]
     Full Idea: I propose that ...numbers are properties of sets, analogous, for example, to lengths, which are properties of physical objects.
     From: Penelope Maddy (Sets and Numbers [1981], III)
     A reaction: Are lengths properties of physical objects? A hole in the ground can have a length. A gap can have a length. Pure space seems to contain lengths. A set seems much more abstract than its members.
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Sets exist where their elements are, but numbers are more like universals [Maddy]
     Full Idea: A set of things is located where the aggregate of those things is located, ...but a number is simultaneously located at many different places (10 in my hand, and a baseball team) ...so numbers seem more like universals than particulars.
     From: Penelope Maddy (Sets and Numbers [1981], III)
     A reaction: My gut feeling is that Maddy's master idea (of naturalising sets by building them from ur-elements of natural objects) won't work. Sets can work fine in total abstraction from nature.
Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy]
     Full Idea: I am not suggesting a reduction of number theory to set theory ...There are only sets with number properties; number theory is part of the theory of finite sets.
     From: Penelope Maddy (Sets and Numbers [1981], V)
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
If mathematical objects exist, how can we know them, and which objects are they? [Maddy]
     Full Idea: The popular challenges to platonism in philosophy of mathematics are epistemological (how are we able to interact with these objects in appropriate ways) and ontological (if numbers are sets, which sets are they).
     From: Penelope Maddy (Sets and Numbers [1981], I)
     A reaction: These objections refer to Benacerraf's two famous papers - 1965 for the ontology, and 1973 for the epistemology. Though he relied too much on causal accounts of knowledge in 1973, I'm with him all the way.
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy]
     Full Idea: Number words are not like normal adjectives. For example, number words don't occur in 'is (are)...' contexts except artificially, and they must appear before all other adjectives, and so on.
     From: Penelope Maddy (Sets and Numbers [1981], IV)
     A reaction: [She is citing Benacerraf's arguments]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
     Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people."
     From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7
     A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork.
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Only rational beings are attentive without motive or concern [Scruton]
     Full Idea: It is only rational beings who can be attentive without a motive; only rational beings who can be interested in that in which they have no interest.
     From: Roger Scruton (Laughter [1982], §12)
     A reaction: Rational beings make long term plans, so they cannot prejudge which things may turn out to be of interest to them. Scruton (a Kantian) makes it sound a little loftier than it actually is.