Combining Philosophers

All the ideas for Timon, Anaxagoras and Michal Walicki

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43 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
17749 Post proved the consistency of propositional logic in 1921 [Walicki]
17765 Propositional language can only relate statements as the same or as different [Walicki]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
17764 Boolean connectives are interpreted as functions on the set {1,0} [Walicki]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
17752 The empty set is useful for defining sets by properties, when the members are not yet known [Walicki]
17753 The empty set avoids having to take special precautions in case members vanish [Walicki]
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
17759 Ordinals play the central role in set theory, providing the model of well-ordering [Walicki]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
17741 To determine the patterns in logic, one must identify its 'building blocks' [Walicki]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
17747 A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17748 The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17761 A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
17763 Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17758 Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki]
17755 Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]
17756 The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki]
17760 Two infinite ordinals can represent a single infinite cardinal [Walicki]
17757 Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
21382 Things get smaller without end [Anaxagoras]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
17762 In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17754 Inductive proof depends on the choice of the ordering [Walicki]
7. Existence / A. Nature of Existence / 1. Nature of Existence
481 Nothing is created or destroyed; there is only mixing and separation [Anaxagoras]
7. Existence / A. Nature of Existence / 3. Being / f. Primary being
21822 Anaxagoras's concept of supreme Mind has a simple First and a multiple One [Anaxagoras, by Plotinus]
7. Existence / C. Structure of Existence / 6. Fundamentals / a. Fundamental reality
17995 Basic is the potentially perceptible, then comes the contrary qualities, and finally the 'elements' [Anaxagoras]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
12. Knowledge Sources / B. Perception / 1. Perception
20802 Snow is not white, and doesn't even appear white, because it is made of black water [Anaxagoras, by Cicero]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
13257 The senses are too feeble to determine the truth [Anaxagoras]
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
22761 We reveal unreliability in the senses when we cannot discriminate a slow change of colour [Anaxagoras, by Sext.Empiricus]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
2975 That honey is sweet I do not affirm, but I agree that it appears so [Timon]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
13256 Nous is unlimited, self-ruling and pure; it is the finest thing, with great discernment and strength [Anaxagoras]
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
13784 Mind is self-ruling, pure, ordering and ubiquitous [Anaxagoras, by Plato]
16. Persons / F. Free Will / 1. Nature of Free Will
5118 Anaxagoras says mind remains pure, and so is not affected by what it changes [Anaxagoras, by Aristotle]
23. Ethics / C. Virtue Theory / 3. Virtues / g. Contemplation
18231 Anaxagoras said a person would choose to be born to contemplate the ordered heavens [Anaxagoras]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
631 For Anaxagoras the Good Mind has no opposite, and causes all movement, for a higher reason [Anaxagoras, by Aristotle]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
22727 Mind creates the world from a mixture of pure substances [Anaxagoras, by ]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
550 Anaxagoras said that the number of principles was infinite [Anaxagoras, by Aristotle]
21383 The ultimate constituents of reality are the homoeomeries [Anaxagoras, by Vlastos]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
13208 Anaxagoreans regard the homoeomeries as elements, which compose earth, air, fire and water [Anaxagoras, by Aristotle]
26. Natural Theory / C. Causation / 1. Causation
367 Anaxagoras says mind produces order and causes everything [Anaxagoras, by Plato]
27. Natural Reality / G. Biology / 1. Biology
21381 Germs contain microscopic organs, which become visible as they grow [Anaxagoras]
28. God / A. Divine Nature / 1. God
22726 When things were unified, Mind set them in order [Anaxagoras]
2629 Anaxagoras was the first to say that the universe is directed by an intelligence [Anaxagoras, by Cicero]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
480 Past, present and future, and the movements of the heavens, were arranged by Mind [Anaxagoras]
28. God / C. Attitudes to God / 5. Atheism
5956 Anaxagoras was charged with impiety for calling the sun a lump of stone [Anaxagoras, by Plutarch]
7488 Anaxagoras was the first recorded atheist [Anaxagoras, by Watson]