Combining Philosophers

All the ideas for Anaxarchus, Heraclitus and M Fitting/R Mendelsohn

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81 ideas

1. Philosophy / A. Wisdom / 2. Wise People
421 Men who love wisdom must be inquirers into very many things indeed [Heraclitus]
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
1491 Everyone has the potential for self-knowledge and sound thinking [Heraclitus]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
5863 Reason is eternal, but men are foolish [Heraclitus]
2. Reason / A. Nature of Reason / 2. Logos
414 Logos is common to all, but most people live as if they have a private understanding [Heraclitus]
2. Reason / B. Laws of Thought / 5. Opposites
425 A thing can have opposing tensions but be in harmony, like a lyre [Heraclitus]
416 Beautiful harmony comes from things that are in opposition to one another [Heraclitus]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
9738 Each line of a truth table is a model [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / a. Symbols of ML
9727 Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn]
9726 We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn]
9737 The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn]
13136 The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / b. Terminology of ML
9734 Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn]
9736 A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn]
13727 A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn]
9735 A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn]
9741 Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / c. Derivation rules of ML
13137 Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn]
13140 Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn]
13138 Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn]
13143 Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn]
13142 Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn]
13141 Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn]
13139 Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn]
13144 T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn]
13148 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn]
13147 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn]
13146 B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn]
13145 D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn]
13149 S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn]
9740 If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn]
9739 If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / b. System K
9742 The system K has no accessibility conditions [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
13114 □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn]
9743 The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
9744 The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / e. System K4
9746 The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
9745 The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
9747 The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
9748 System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
9404 Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 5. Epistemic Logic
13111 Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn]
13112 In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
13113 F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
13729 The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn]
13728 The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
1312 If everything is and isn't then everything is true, and a midway between true and false makes everything false [Aristotle on Heraclitus]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
9725 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
15658 The hidden harmony is stronger than the visible [Heraclitus]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
13782 Everything gives way, and nothing stands fast [Heraclitus]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
11853 A mixed drink separates if it is not stirred [Heraclitus]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
11091 You can bathe in the same river twice, but not in the same river stage [Quine on Heraclitus]
427 It is not possible to step twice into the same river [Heraclitus]
9. Objects / E. Objects over Time / 13. No Identity over Time
2064 If flux is continuous, then lack of change can't be a property, so everything changes in every possible way [Plato on Heraclitus]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
13730 The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
13725 □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn]
13731 Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
13726 Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
430 Senses are no use if the soul is corrupt [Heraclitus]
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
1500 When we sleep, reason closes down as the senses do [Heraclitus, by Sext.Empiricus]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
13. Knowledge Criteria / E. Relativism / 1. Relativism
417 Donkeys prefer chaff to gold [Heraclitus]
426 Sea water is life-giving for fish, but not for people [Heraclitus]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
431 Health, feeding and rest are only made good by disease, hunger and weariness [Heraclitus]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / e. Ethical cognitivism
429 To God (though not to humans) all things are beautiful and good and just [Heraclitus]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / h. Against ethics
12294 Good and evil are the same thing [Heraclitus, by Aristotle]
22. Metaethics / B. Value / 1. Nature of Value / e. Means and ends
419 If one does not hope, one will not find the unhoped-for, since nothing leads to it [Heraclitus]
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
415 If happiness is bodily pleasure, then oxen are happy when they have vetch to eat [Heraclitus]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
5155 It is hard to fight against emotion, but harder still to fight against pleasure [Heraclitus]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
433 For man character is destiny [Heraclitus]
25. Social Practice / D. Justice / 2. The Law / b. Rule of law
422 The people should fight for the law as if for their city-wall [Heraclitus]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
614 Heraclitus said sometimes everything becomes fire [Heraclitus, by Aristotle]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
424 Reason tells us that all things are one [Heraclitus]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
17539 The sayings of Heraclitus are still correct, if we replace 'fire' with 'energy' [Heraclitus, by Heisenberg]
5096 Heraclitus says that at some time everything becomes fire [Heraclitus, by Aristotle]
3054 Heraclitus said fire could be transformed to create the other lower elements [Heraclitus, by Diog. Laertius]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
15660 Logos is the source of everything, and my theories separate and explain each nature [Heraclitus]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
12269 All things are in a state of motion [Heraclitus, by Aristotle]
27. Natural Reality / E. Cosmology / 2. Eternal Universe
420 The cosmos is eternal not created, and is an ever-living and changing fire [Heraclitus]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
1499 Heraclitus says intelligence draws on divine reason [Heraclitus, by Sext.Empiricus]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
15659 Purifying yourself with blood is as crazy as using mud to wash off mud [Heraclitus]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
1501 In their ignorance people pray to statues, which is like talking to a house [Heraclitus]