Combining Philosophers

All the ideas for Empedocles, Michal Walicki and Mark Jago

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42 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 / E. Nonclassical Logics / 7. Paraconsistency
15382 Paraconsistent reasoning can just mean responding sensibly to inconsistencies [Jago]
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
17763 Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
17761 A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17757 Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
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]
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 / 5. Reason for Existence
458 Nothing could come out of nothing, and existence could never completely cease [Empedocles]
7. Existence / B. Change in Existence / 1. Nature of Change
5112 Empedocles says things are at rest, unless love unites them, or hatred splits them [Empedocles, by Aristotle]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
13209 There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle]
9. Objects / E. Objects over Time / 10. Beginning of an Object
457 Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
462 One vision is produced by both eyes [Empedocles]
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
22765 Wisdom and thought are shared by all things [Empedocles]
18. Thought / A. Modes of Thought / 1. Thought
1524 For Empedocles thinking is almost identical to perception [Empedocles, by Theophrastus]
22. Metaethics / B. Value / 2. Values / j. Evil
552 Empedocles said good and evil were the basic principles [Empedocles, by Aristotle]
26. Natural Theory / A. Speculations on Nature / 1. Nature
589 'Nature' is just a word invented by people [Empedocles]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
21823 The principle of 'Friendship' in Empedocles is the One, and is bodiless [Empedocles, by Plotinus]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
2680 Empedocles said that there are four material elements, and two further creative elements [Empedocles, by Aristotle]
6002 Empedocles says bone is water, fire and earth in ratio 2:4:2 [Empedocles, by Inwood]
13207 Fire, Water, Air and Earth are elements, being simple as well as homoeomerous [Empedocles, by Aristotle]
13218 The elements combine in coming-to-be, but how do the elements themselves come-to-be? [Aristotle on Empedocles]
459 All change is unity through love or division through hate [Empedocles]
13225 Love and Strife only explain movement if their effects are distinctive [Aristotle on Empedocles]
460 If the one Being ever diminishes it would no longer exist, and what could ever increase it? [Empedocles]
27. Natural Reality / G. Biology / 3. Evolution
5090 Maybe bodies are designed by accident, and the creatures that don't work are destroyed [Empedocles, by Aristotle]
28. God / A. Divine Nature / 2. Divine Nature
461 God is a pure, solitary, and eternal sphere [Empedocles]
466 God is pure mind permeating the universe [Empedocles]
28. God / A. Divine Nature / 4. Divine Contradictions
1719 In Empedocles' theory God is ignorant because, unlike humans, he doesn't know one of the elements (strife) [Aristotle on Empedocles]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
1522 It is wretched not to want to think clearly about the gods [Empedocles]