Combining Texts

All the ideas for 'fragments/reports', 'Questions on Aristotle's Physics' and 'Principles of Arithmetic, by a new method'

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17 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
PA concerns any entities which satisfy the axioms [Peano, by Bostock]
Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
7. Existence / A. Nature of Existence / 1. Nature of Existence
Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
Without magnitude a thing would retain its parts, but they would have no location [Buridan]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
A thing is (less properly) the same over time if each part is succeeded by another [Buridan]
14. Science / A. Basis of Science / 2. Demonstration
Induction is not demonstration, because not all of the instances can be observed [Buridan]
14. Science / C. Induction / 2. Aims of Induction
Science is based on induction, for general truths about fire, rhubarb and magnets [Buridan]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander]
The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander]
Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius]
Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander]
27. Natural Reality / E. Cosmology / 2. Eternal Universe
The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius]