Combining Texts

All the ideas for 'Philosophical Fragments', 'What Numbers Are' and ''

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8 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

11211

If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

11210

Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]

11212

The sense of a connective comes from primitively obvious rules of inference [Rumfitt]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17813

Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17812

Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]

7. Existence / A. Nature of Existence / 5. Reason for Existence

16007

I assume existence, rather than reasoning towards it [Kierkegaard]

10. Modality / A. Necessity / 2. Nature of Necessity

16013

Nothing necessary can come into existence, since it already 'is' [Kierkegaard]

19. Language / F. Communication / 3. Denial

11214

We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]