Combining Texts

All the ideas for 'fragments/reports', 'Primary Truths' and 'Logical Consequence'

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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]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
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]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
An a priori proof is independent of experience [Leibniz]
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]