Combining Texts

All the ideas for 'Concerning the Author', 'fragments/reports' and 'Alfred Tarski: life and logic'

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27 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
1542 Diogenes of Apollonia was the last natural scientist [Diogenes of Apollonia, by Simplicius]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
14767 The demonstrations of the metaphysicians are all moonshine [Peirce]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
14764 I am saturated with the spirit of physical science [Peirce]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10147 The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman]
10148 Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman]
10149 Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman]
10150 The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman]
10146 Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10158 A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
10162 Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10159 Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
10160 Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10161 If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 7. Decidability
10156 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]
10155 Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
489 Each thing must be in some way unique [Diogenes of Apollonia]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
14768 Infallibility in science is just a joke [Peirce]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
483 Start a thesis with something undisputable [Diogenes of Apollonia]
12. Knowledge Sources / B. Perception / 6. Inference in Perception
1544 Perception must be an internal matter, because we can fail to perceive when we are preoccupied [Diogenes of Apollonia, by Theophrastus]
12. Knowledge Sources / D. Empiricism / 2. Associationism
14765 Association of ideas is the best philosophical idea of the prescientific age [Peirce]
14. Science / B. Scientific Theories / 1. Scientific Theory
14766 Duns Scotus offers perhaps the best logic and metaphysics for modern physical science [Peirce]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
24042 The older Diogenes said the soul is air, made of the smallest particles [Diogenes of Apollonia]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
5995 Diogenes of Apollonia offered the first teleological account of cosmology [Diogenes of Apollonia, by Robinson,TM]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
484 Everything is ultimately a variation of one underlying thing [Diogenes of Apollonia]
488 Air is divine, because it is in and around everything, and arranges everything [Diogenes of Apollonia]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
486 Plants and animals can only come into existence if something fixes their species [Diogenes of Apollonia]
485 Things must retain their essential nature during change, or mixing would be impossible [Diogenes of Apollonia]