Combining Texts

All the ideas for 'A Short History of Ethics', 'Essays on Intellectual Powers 2: Senses' and 'Logic for Philosophy'

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66 ideas

1. Philosophy / B. History of Ideas / 4. Early European Thought
8013 In the Reformation, morality became unconditional but irrational, individually autonomous, and secular [MacIntyre]
1. Philosophy / B. History of Ideas / 5. Later European Thought
8021 The Levellers and the Diggers mark a turning point in the history of morality [MacIntyre]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
13689 'Theorems' are formulas provable from no premises at all [Sider]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
13705 Truth tables assume truth functionality, and are just pictures of truth functions [Sider]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
13706 Intuitively, deontic accessibility seems not to be reflexive, but to be serial [Sider]
13710 In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary [Sider]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
13711 System B introduces iterated modalities [Sider]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
13708 S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid [Sider]
4. Formal Logic / D. Modal Logic ML / 5. Epistemic Logic
13712 Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K) [Sider]
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
13714 We can treat modal worlds as different times [Sider]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
13720 Converse Barcan Formula: □∀αφ→∀α□φ [Sider]
13718 The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider]
13723 System B is needed to prove the Barcan Formula [Sider]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
13715 You can employ intuitionist logic without intuitionism about mathematics [Sider]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13678 The most popular account of logical consequence is the semantic or model-theoretic one [Sider]
13679 Maybe logical consequence is more a matter of provability than of truth-preservation [Sider]
13682 Maybe logical consequence is impossibility of the premises being true and the consequent false [Sider]
13680 Maybe logical consequence is a primitive notion [Sider]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
13722 A 'theorem' is an axiom, or the last line of a legitimate proof [Sider]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13696 When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity [Sider]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
13700 A 'total' function must always produce an output for a given domain [Sider]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
13703 λ can treat 'is cold and hungry' as a single predicate [Sider]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
13688 Good axioms should be indisputable logical truths [Sider]
13687 No assumptions in axiomatic proofs, so no conditional proof or reductio [Sider]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
13690 Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider]
13691 Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
13685 Natural deduction helpfully allows reasoning with assumptions [Sider]
5. Theory of Logic / H. Proof Systems / 6. Sequent Calculi
13686 We can build proofs just from conclusions, rather than from plain formulae [Sider]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
13697 Valuations in PC assign truth values to formulas relative to variable assignments [Sider]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
13684 The semantical notion of a logical truth is validity, being true in all interpretations [Sider]
13704 It is hard to say which are the logical truths in modal logic, especially for iterated modal operators [Sider]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
13724 In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider]
5. Theory of Logic / K. Features of Logics / 4. Completeness
13698 In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13699 Compactness surprisingly says that no contradictions can emerge when the set goes infinite [Sider]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
13701 A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically [Sider]
7. Existence / A. Nature of Existence / 1. Nature of Existence
23634 Accepting the existence of anything presupposes the notion of existence [Reid]
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
13692 A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation [Sider]
13695 Supervaluational logic is classical, except when it adds the 'Definitely' operator [Sider]
13693 A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification [Sider]
13694 We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings [Sider]
8. Modes of Existence / A. Relations / 1. Nature of Relations
13683 A relation is a feature of multiple objects taken together [Sider]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
13702 The identity of indiscernibles is necessarily true, if being a member of some set counts as a property [Sider]
10. Modality / A. Necessity / 3. Types of Necessity
13721 'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist [Sider]
10. Modality / A. Necessity / 5. Metaphysical Necessity
13707 Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider]
10. Modality / A. Necessity / 6. Logical Necessity
13709 Logical truths must be necessary if anything is [Sider]
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
13716 'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true [Sider]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
13717 Transworld identity is not a problem in de dicto sentences, which needn't identify an individual [Sider]
10. Modality / E. Possible worlds / 3. Transworld Objects / e. Possible Objects
13719 Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
23635 Truths are self-evident to sensible persons who understand them clearly without prejudice [Reid]
12. Knowledge Sources / B. Perception / 1. Perception
7631 Sensation is not committed to any external object, but perception is [Reid]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / c. Primary qualities
23637 Primary qualities are the object of mathematics [Reid]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
23638 Secondary qualities conjure up, and are confused with, the sensations which produce them [Reid]
12. Knowledge Sources / B. Perception / 5. Interpretation
23639 It is unclear whether a toothache is in the mind or in the tooth, but the word has a single meaning [Reid]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
6492 Reid is seen as the main direct realist of the eighteenth century [Reid, by Robinson,H]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
23641 People dislike believing without evidence, and try to avoid it [Reid]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
23642 If non-rational evidence reaches us, it is reason which then makes use of it [Reid]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
8006 When Aristotle speaks of soul he means something like personality [MacIntyre]
18. Thought / E. Abstraction / 2. Abstracta by Selection
23640 Only mature minds can distinguish the qualities of a body [Reid]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
8002 Sophists don't distinguish a person outside one social order from someone outside all order [MacIntyre]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
8012 The value/fact logical gulf is misleading, because social facts involve values [MacIntyre]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
8005 'Happiness' is a bad translation of 'eudaimonia', which includes both behaving and faring well [MacIntyre]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
8001 'Dikaiosune' is justice, but also fairness and personal integrity [MacIntyre]
23. Ethics / D. Deontological Ethics / 2. Duty
8023 My duties depend on my identity, which depends on my social relations [MacIntyre]
24. Political Theory / A. Basis of a State / 3. Natural Values / a. Natural freedom
8022 I am naturally free if I am not tied to anyone by a contract [MacIntyre]
25. Social Practice / C. Rights / 1. Basis of Rights
8031 Fans of natural rights or laws can't agree on what the actual rights or laws are [MacIntyre]
29. Religion / B. Monotheistic Religion / 5. Bible
8008 The Bible is a story about God in which humans are incidental characters [MacIntyre]