Combining Texts

All the ideas for 'Philosophical Logic', 'Against the Physicists (two books)' and 'The Putney Debates'

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49 ideas

4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
15413 With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
15415 The temporal Barcan formulas fix what exists, which seems absurd [Burgess]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
15430 Is classical logic a part of intuitionist logic, or vice versa? [Burgess]
15431 It is still unsettled whether standard intuitionist logic is complete [Burgess]
4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
15429 Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
15404 Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
15405 Classical logic neglects the non-mathematical, such as temporality or modality [Burgess]
15427 The Cut Rule expresses the classical idea that entailment is transitive [Burgess]
15421 Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess]
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
15403 Philosophical logic is a branch of logic, and is now centred in computer science [Burgess]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
15407 Formalising arguments favours lots of connectives; proving things favours having very few [Burgess]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / e. or
15424 Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
15409 All occurrences of variables in atomic formulas are free [Burgess]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
15414 The denotation of a definite description is flexible, rather than rigid [Burgess]
5. Theory of Logic / H. Proof Systems / 1. Proof Systems
15406 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess]
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
15425 The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess]
15426 We can build one expanding sequence, instead of a chain of deductions [Burgess]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
15408 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
15418 Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
15412 Models leave out meaning, and just focus on truth values [Burgess]
15411 We only need to study mathematical models, since all other models are isomorphic to these [Burgess]
15416 We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
15428 The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
22744 Parts are not parts if their whole is nothing more than the parts [Sext.Empiricus]
10. Modality / A. Necessity / 4. De re / De dicto modality
15420 De re modality seems to apply to objects a concept intended for sentences [Burgess]
10. Modality / A. Necessity / 6. Logical Necessity
15419 General consensus is S5 for logical modality of validity, and S4 for proof [Burgess]
15417 Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess]
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
15422 Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess]
15423 It is doubtful whether the negation of a conditional has any clear meaning [Burgess]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
22748 Some say motion is perceived by sense, but others say it is by intellect [Sext.Empiricus]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
22746 If we try to conceive of a line with no breadth, it ceases to exist, and so has no length [Sext.Empiricus]
17. Mind and Body / D. Property Dualism / 4. Emergentism
22741 The incorporeal is not in the nature of body, and so could not emerge from it [Sext.Empiricus]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
23215 Even the poorest have a life to lead, and so should consent to who governs them [-]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
22747 A man walking backwards on a forwards-moving ship is moving in a fixed place [Sext.Empiricus]
27. Natural Reality / D. Time / 2. Passage of Time / c. Tenses and time
22749 Time doesn't end with the Universe, because tensed statements about destruction remain true [Sext.Empiricus]
27. Natural Reality / D. Time / 3. Parts of Time / c. Intervals
22750 Time is divisible, into past, present and future [Sext.Empiricus]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
22742 Socrates either dies when he exists (before his death) or when he doesn't (after his death) [Sext.Empiricus]
22751 If the present is just the limit of the past or the future, it can't exist because they don't exist [Sext.Empiricus]
28. God / A. Divine Nature / 2. Divine Nature
22730 All men agree that God is blessed, imperishable, happy and good [Sext.Empiricus]
22739 God must suffer to understand suffering [Sext.Empiricus]
28. God / A. Divine Nature / 3. Divine Perfections
22738 The Divine must lack the virtues of continence and fortitude, because they are not needed [Sext.Empiricus]
28. God / B. Proving God / 1. Proof of God
22734 God is defended by agreement, order, absurdity of denying God, and refutations [Sext.Empiricus]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
22736 God's sensations imply change, and hence perishing, which is absurd, so there is no such God [Sext.Empiricus]
22740 God without virtue is absurd, but God's virtues will be better than God [Sext.Empiricus]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
22735 The original substance lacked motion or shape, and was given these by a cause [Sext.Empiricus]
28. God / C. Attitudes to God / 4. God Reflects Humanity
22732 The perfections of God were extrapolations from mankind [Sext.Empiricus]
28. God / C. Attitudes to God / 5. Atheism
22728 Gods were invented as watchers of people's secret actions [Sext.Empiricus]
22737 An incorporeal God could do nothing, and a bodily god would perish, so there is no God [Sext.Empiricus]
29. Religion / A. Polytheistic Religion / 1. Animism
22731 It is mad to think that what is useful to us, like lakes and rivers, are gods [Sext.Empiricus]