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All the ideas for 'Abstract Objects: a Case Study', 'Aspects of the Theory of Syntax' and 'works'

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10 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
Do not multiply entities beyond necessity [William of Ockham]
     Full Idea: Do not multiply entities beyond necessity.
     From: William of Ockham (works [1335])
     A reaction: This is the classic statement of Ockham's Razor, though it is not found in his printed works. It appears to be mainly aimed at Plato's Theory of Forms. It is taken to refer to types of entities, not numbers. One seraph is as bad as a hundred.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
     Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10)
     A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity.
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
     Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08)
     A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
     Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01)
We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
     Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02)
8. Modes of Existence / D. Universals / 5. Universals as Concepts
Species and genera are individual concepts which naturally signify many individuals [William of Ockham]
     Full Idea: In his mature nominalism, species and genera are identified with certain mental qualities called concepts or intentions of the mind. Ontologically they are individuals too, like everthing else, ...but they naturally signify many different individuals.
     From: William of Ockham (works [1335]), quoted by Claude Panaccio - William of Ockham p.1056
     A reaction: 'Naturally' is the key word, because the concepts are not fictions, but natural responses to encountering individuals in the world. I am an Ockhamist.
19. Language / C. Assigning Meanings / 1. Syntax
Chomsky's 'interpretative semantics' says syntax comes first, and is then interpreted [Chomsky, by Magidor]
     Full Idea: Chomsky and his followers (whose position was labelled 'interpretative semantics') claimed that a sentence is first assigned a syntactic structure by an autonomous syntactic module, and this structure is then provided as input for semantic interpretation.
     From: report of Noam Chomsky (Aspects of the Theory of Syntax [1965]) by Ofra Magidor - Category Mistakes 1.3
     A reaction: This certainly doesn't fit the experience of introspecting speech, but then I suppose good pianists focus entirely on the music, and overlook the finger movements which have obvious priority. But I don't know the syntax of the sentence when I begin it.
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham]
     Full Idea: Time is composed of non-entities, because it is composed of the past which does not exist now, although it did exist, and of the future, which does not yet exist; therefore time does not exist.
     From: William of Ockham (works [1335], 6:496), quoted by Richard T.W. Arthur - Leibniz 7 'Nominalist'
     A reaction: I've a lot of sympathy with this! I favour Presentism, so the past is gone and the future is yet to arrive. But we have no coherent concept of a present moment of any duration to contain reality. We are just completely bogglificated by it all.
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
William of Ockham is the main spokesman for God's commands being the source of morality [William of Ockham]
     Full Idea: The most notable philosopher who makes God's commandment the basis of goodness, rather than God's goodness a reason for obeying him, is William of Occam.
     From: William of Ockham (works [1335]), quoted by Alasdair MacIntyre - A Short History of Ethics Ch.9
     A reaction: Either view has problems. Why choose God to obey? Obey anyone who is powerful? But how do you decide that God is good? How do we know the nature of God's commands, or the nature of God's goodness? Etc.
29. Religion / B. Monotheistic Religion / 4. Christianity / c. Angels
Even an angel must have some location [William of Ockham, by Pasnau]
     Full Idea: Ockham dismisses the possibility of non-location out of hand, remarking that even an angel has some location.
     From: report of William of Ockham (works [1335]) by Robert Pasnau - Metaphysical Themes 1274-1671 14.4