Combining Texts

All the ideas for 'works', 'Maths as a Science of Patterns' and 'Summa totius logicae'

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25 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction
9108 From an impossibility anything follows [William of Ockham]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
9107 A proposition is true if its subject and predicate stand for the same thing [William of Ockham]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
16300 Ockham had an early axiomatic account of truth [William of Ockham, by Halbach]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
6299 Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
5. Theory of Logic / G. Quantification / 1. Quantification
9106 The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
6304 Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
6300 Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
6303 Sets are positions in patterns [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
6302 Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
6295 There are too many mathematical objects for them all to be mental or physical [Resnik]
6296 Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
6301 Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
9113 Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham]
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
9110 The words 'thing' and 'to be' assert the same idea, as a noun and as a verb [William of Ockham]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
15388 Universals are single things, and only universal in what they signify [William of Ockham]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
9109 If essence and existence were two things, one could exist without the other, which is impossible [William of Ockham]
12. Knowledge Sources / B. Perception / 1. Perception
22167 Our images of bodies are not produced by the bodies, but by our own minds [Augustine, by Aquinas]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
22117 Our minds grasp reality by direct illumination (rather than abstraction from experience) [Augustine, by Matthews]
19. Language / D. Propositions / 4. Mental Propositions
9105 Some concepts for propositions exist only in the mind, and in no language [William of Ockham]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
22118 Augustine created the modern concept of the will [Augustine, by Matthews]
22. Metaethics / B. Value / 2. Values / g. Love
4348 Love, and do what you will [Augustine]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
7821 Pagans produced three hundred definitions of the highest good [Augustine, by Grayling]
23. Ethics / D. Deontological Ethics / 2. Duty
22119 Augustine said (unusually) that 'ought' does not imply 'can' [Augustine, by Matthews]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
22116 Augustine identified Donatism, Pelagianism and Manicheism as the main heresies [Augustine, by Matthews]
29. Religion / D. Religious Issues / 3. Problem of Evil / b. Human Evil
19338 Augustine said evil does not really exist, and evil is a limitation in goodness [Augustine, by Perkins]