Combining Texts

All the ideas for 'Philosophy of Mathematics', 'Zettel' and 'On the Heavens'

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19 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
A philosopher is outside any community of ideas [Wittgenstein]
2. Reason / A. Nature of Reason / 9. Limits of Reason
A very hungry man cannot choose between equidistant piles of food [Aristotle]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
'This sentence is false' sends us in a looping search for its proposition [Wittgenstein, by Fogelin]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
Causes of beliefs are irrelevant to their contents [Wittgenstein]
22. Metaethics / B. Value / 2. Values / b. Successful function
Each thing that has a function is for the sake of that function [Aristotle]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
An unworn sandal is in vain, but nothing in nature is in vain [Aristotle]
There has to be some goal, and not just movement to infinity [Aristotle]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
Aether moves in circles and is imperishable; the four elements perish, and move in straight lines [Aristotle, by Gill,ML]
An element is what bodies are analysed into, and won't itself divide into something else [Aristotle]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
If the more you raise some earth the faster it moves, why does the whole earth not move? [Aristotle]
27. Natural Reality / C. Space / 1. Void
Void is a kind of place, so it can't explain place [Aristotle]
27. Natural Reality / E. Cosmology / 1. Cosmology
The Earth must be spherical, because it casts a convex shadow on the moon [Aristotle]
The earth must be round and of limited size, because moving north or south makes different stars visible [Aristotle]
27. Natural Reality / E. Cosmology / 3. The Beginning
Everyone agrees that the world had a beginning, but thinkers disagree over whether it will end [Aristotle]
27. Natural Reality / E. Cosmology / 10. Multiverse
It seems possible that there exists a limited number of other worlds apart from this one [Aristotle]