Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Negation' and 'Maths as a Science of Patterns'

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23 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
18781 Inconsistency doesn't prevent us reasoning about some system [Mares]
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]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
18789 Intuitionist logic looks best as natural deduction [Mares]
18790 Intuitionism as natural deduction has no rule for negation [Mares]
4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
18787 Three-valued logic is useful for a theory of presupposition [Mares]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
18793 Material implication (and classical logic) considers nothing but truth values for implications [Mares]
18784 In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
18786 Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares]
18780 Standard disjunction and negation force us to accept the principle of bivalence [Mares]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
18782 The connectives are studied either through model theory or through proof theory [Mares]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
18783 Many-valued logics lack a natural deduction system [Mares]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
18792 Situation semantics for logics: not possible worlds, but information in situations [Mares]
5. Theory of Logic / K. Features of Logics / 2. Consistency
18785 Consistency is semantic, but non-contradiction is syntactic [Mares]
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 / 10. Constructivism / b. Intuitionism
18788 For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares]
19. Language / C. Assigning Meanings / 2. Semantics
18791 In 'situation semantics' our main concepts are abstracted from situations [Mares]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]