Combining Texts

All the ideas for 'reports', 'The Sophist' and 'What are Sets and What are they For?'

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43 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
1798 He studied philosophy by suspending his judgement on everything [Pyrrho, by Diog. Laertius]
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
1642 We must fight fiercely for knowledge, understanding and intelligence [Plato]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
1645 The desire to split everything into its parts is unpleasant and unphilosophical [Plato]
2. Reason / A. Nature of Reason / 9. Limits of Reason
1800 Sceptics say reason is only an instrument, because reason can only be attacked with reason [Pyrrho, by Diog. Laertius]
2. Reason / C. Styles of Reason / 1. Dialectic
1644 Dialectic should only be taught to those who already philosophise well [Plato]
287 Good analysis involves dividing things into appropriate forms without confusion [Plato]
2. Reason / C. Styles of Reason / 2. Elenchus
20478 In discussion a person's opinions are shown to be in conflict, leading to calm self-criticism [Plato]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
14240 The empty set is something, not nothing! [Oliver/Smiley]
14241 We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
14242 Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
14243 The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
14237 We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
14245 Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
14246 If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
14247 Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
11278 What does 'that which is not' refer to? [Plato]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
1643 If statements about non-existence are logically puzzling, so are statements about existence [Plato]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
7022 To be is to have a capacity, to act on other things, or to receive actions [Plato]
7. Existence / D. Theories of Reality / 6. Physicalism
1641 Some alarming thinkers think that only things which you can touch exist [Plato]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
10784 Whenever there's speech it has to be about something [Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
16122 Good thinkers spot forms spread through things, or included within some larger form [Plato]
10422 The not-beautiful is part of the beautiful, though opposed to it, and is just as real [Plato]
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
15855 If we see everything as separate, we can then give no account of it [Plato]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
1637 A soul without understanding is ugly [Plato]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
6595 If we need a criterion of truth, we need to know whether it is the correct criterion [Pyrrho, by Fogelin]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
6593 The Pyrrhonians attacked the dogmas of professors, not ordinary people [Pyrrho, by Fogelin]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
6592 Academics said that Pyrrhonians were guilty of 'negative dogmatism' [Pyrrho, by Fogelin]
13. Knowledge Criteria / E. Relativism / 1. Relativism
1805 Judgements vary according to local culture and law (Mode 5) [Pyrrho, by Diog. Laertius]
1807 Perception varies with viewing distance and angle (Mode 7) [Pyrrho, by Diog. Laertius]
1810 Perception and judgement depend on comparison (Mode 10) [Pyrrho, by Diog. Laertius]
1802 Individuals vary in responses and feelings (Mode 2) [Pyrrho, by Diog. Laertius]
1801 Animals vary in their feelings and judgements (Mode 1) [Pyrrho, by Diog. Laertius]
1804 Perception varies with madness or disease (Mode 4) [Pyrrho, by Diog. Laertius]
1808 Perception of things depends on their size or quantity (Mode 8) [Pyrrho, by Diog. Laertius]
1806 Perception of objects depends on surrounding conditions (Mode 6) [Pyrrho, by Diog. Laertius]
1809 Perception is affected by expectations (Mode 9) [Pyrrho, by Diog. Laertius]
1803 Objects vary according to which sense perceives them (Mode 3) [Pyrrho, by Diog. Laertius]
23. Ethics / A. Egoism / 1. Ethical Egoism
1636 Wickedness is an illness of the soul [Plato]
25. Social Practice / E. Policies / 5. Education / c. Teaching
1638 Didactic education is hard work and achieves little [Plato]
26. Natural Theory / C. Causation / 7. Eliminating causation
3062 There are no causes, because they are relative, and alike things can't cause one another [Pyrrho, by Diog. Laertius]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
3063 Motion can't move where it is, and can't move where it isn't, so it can't exist [Pyrrho, by Diog. Laertius]