Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'On the Heavens' and 'First-order Logic, 2nd-order, Completeness'

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23 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
19740 A very hungry man cannot choose between equidistant piles of food [Aristotle]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10751 Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
10757 Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
10759 There are at least seven possible systems of semantics for second-order logic [Rossberg]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10753 Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
10752 Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10754 In proof-theory, logical form is shown by the logical constants [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10756 A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10758 If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10761 Completeness can always be achieved by cunning model-design [Rossberg]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10755 A deductive system is only incomplete with respect to a formal semantics [Rossberg]
22. Metaethics / B. Value / 2. Values / b. Successful function
398 Each thing that has a function is for the sake of that function [Aristotle]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
394 An unworn sandal is in vain, but nothing in nature is in vain [Aristotle]
396 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
16102 Aether moves in circles and is imperishable; the four elements perish, and move in straight lines [Aristotle, by Gill,ML]
17463 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
399 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
20918 Void is a kind of place, so it can't explain place [Aristotle]
27. Natural Reality / E. Cosmology / 1. Cosmology
403 The earth must be round and of limited size, because moving north or south makes different stars visible [Aristotle]
402 The Earth must be spherical, because it casts a convex shadow on the moon [Aristotle]
27. Natural Reality / E. Cosmology / 3. The Beginning
1498 Everyone agrees that the world had a beginning, but thinkers disagree over whether it will end [Aristotle]
27. Natural Reality / E. Cosmology / 10. Multiverse
395 It seems possible that there exists a limited number of other worlds apart from this one [Aristotle]