Combining Philosophers

All the ideas for Philolaus, Nicholas P. White and Dag Prawitz

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15 ideas

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

13831

Logic is based on transitions between sentences [Prawitz]

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

13827

Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz]

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

13825

Natural deduction introduction rules may represent 'definitions' of logical connectives [Prawitz]

5. Theory of Logic / H. Proof Systems / 4. Natural Deduction

13823

In natural deduction, inferences are atomic steps involving just one logical constant [Prawitz]

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

13826

Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz]

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]

9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification

472	No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus]

20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will

22511

Some reasonings are stronger than we are [Philolaus]

26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature

1518	Everything must involve numbers, or it couldn't be thought about or known [Philolaus]

1519	Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus]

473	There is no falsehood in harmony and number, only in irrational things [Philolaus]

26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited

469	Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited [Philolaus]

26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical

476	Self-created numbers make the universe stable [Philolaus]

27. Natural Reality / E. Cosmology / 1. Cosmology

1787	Philolaus was the first person to say the earth moves in a circle [Philolaus, by Diog. Laertius]