Combining Philosophers

All the ideas for Engelbretsen,G/Sayward,C, Ian Hacking and Michael Martin

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30 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
7454 Gassendi is the first great empiricist philosopher [Hacking]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
6855 Interesting philosophers hardly every give you explicitly valid arguments [Martin,M]
2. Reason / D. Definition / 3. Types of Definition
13838 A decent modern definition should always imply a semantics [Hacking]
2. Reason / E. Argument / 1. Argument
6856 Valid arguments can be rejected by challenging the premises or presuppositions [Martin,M]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
13913 The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward]
13914 Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
13915 Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward]
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
13916 Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
13833 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
13834 Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking]
13835 Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
13845 The various logics are abstractions made from terms like 'if...then' in English [Hacking]
13850 In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13840 First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
13844 A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
13849 Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13842 Second-order completeness seems to need intensional entities and possible worlds [Hacking]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
13851 Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13837 With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13839 Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843 If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
13852 Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward]
10. Modality / B. Possibility / 6. Probability
7447 Probability was fully explained between 1654 and 1812 [Hacking]
7448 Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence) [Hacking]
7449 Epistemological probability based either on logical implications or coherent judgments [Hacking]
12. Knowledge Sources / B. Perception / 1. Perception
6857 An error theory of perception says our experience is not as it seems to be [Martin,M]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
7450 In the medieval view, only deduction counted as true evidence [Hacking]
7451 Formerly evidence came from people; the new idea was that things provided evidence [Hacking]
14. Science / A. Basis of Science / 3. Experiment
7452 An experiment is a test, or an adventure, or a diagnosis, or a dissection [Hacking, by PG]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
7459 Follow maths for necessary truths, and jurisprudence for contingent truths [Hacking]