Combining Texts

All the ideas for 'Introduction to 'Properties'', 'Letters to Frege' and 'The Structure of Paradoxes of Self-Reference'

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16 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
Ockham's Razor is the principle that we need reasons to believe in entities [Mellor/Oliver]
5. Theory of Logic / L. Paradox / 1. Paradox
Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / b. König's paradox
The 'least indefinable ordinal' is defined by that very phrase [Priest,G]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / d. Richard's paradox
By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G on Russell]
Russell's paradox means we cannot assume that every property is collectivizing [Potter on Russell]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / e. Mirimanoff's paradox
The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
If you know that a sentence is not one of the known sentences, you know its truth [Priest,G]
There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G]
8. Modes of Existence / B. Properties / 6. Categorical Properties
Properties are respects in which particular objects may be alike or differ [Mellor/Oliver]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen]
8. Modes of Existence / B. Properties / 12. Denial of Properties
Nominalists ask why we should postulate properties at all [Mellor/Oliver]
18. Thought / C. Content / 6. Broad Content
We don't assert private thoughts; the objects are part of what we assert [Russell]
18. Thought / E. Abstraction / 5. Abstracta by Negation
Abstractions lack causes, effects and spatio-temporal locations [Mellor/Oliver]