Combining Philosophers

All the ideas for Archimedes, Kent Bach and Gerhard Gentzen

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31 ideas

4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
10455 Free logic at least allows empty names, but struggles to express non-existence [Bach]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
11022 Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10454 In first-order we can't just assert existence, and it is very hard to deny something's existence [Bach]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11065 The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
11023 The logical connectives are 'defined' by their introduction rules [Gentzen]
11213 Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
5. Theory of Logic / E. Structures of Logic / 3. Constants in Logic
10453 In logic constants play the role of proper names [Bach]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
10452 Proper names can be non-referential - even predicate as well as attributive uses [Bach]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
10456 Millian names struggle with existence, empty names, identities and attitude ascription [Bach]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / a. Descriptions
10440 An object can be described without being referred to [Bach]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
10444 Definite descriptions can be used to refer, but are not semantically referential [Bach]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
13832 Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10067 Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
12900 How could 'S knows he has hands' not have a fixed content? [Bach]
12901 If contextualism is right, knowledge sentences are baffling out of their context [Bach]
12902 Sceptics aren't changing the meaning of 'know', but claiming knowing is tougher than we think [Bach]
19. Language / B. Reference / 1. Reference theories
10446 Fictional reference is different inside and outside the fiction [Bach]
10447 We can refer to fictional entities if they are abstract objects [Bach]
10443 You 'allude to', not 'refer to', an individual if you keep their identity vague [Bach]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
10439 What refers: indefinite or definite or demonstrative descriptions, names, indexicals, demonstratives? [Bach]
10441 If we can refer to things which change, we can't be obliged to single out their properties [Bach]
10442 We can think of an individual without have a uniquely characterizing description [Bach]
10445 It can't be real reference if it could refer to some other thing that satisfies the description [Bach]
10457 Since most expressions can be used non-referentially, none of them are inherently referential [Bach]
10463 Just alluding to or describing an object is not the same as referring to it [Bach]
19. Language / B. Reference / 5. Speaker's Reference
10459 Context does not create reference; it is just something speakers can exploit [Bach]
10460 'That duck' may not refer to the most obvious one in the group [Bach]
10461 What a pronoun like 'he' refers back to is usually a matter of speaker's intentions [Bach]
10462 Information comes from knowing who is speaking, not just from interpretation of the utterance [Bach]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
10458 People slide from contextual variability all the way to contextual determination [Bach]