Combining Philosophers

Ideas for Xenocrates, Plotinus and Gottlob Frege

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50 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
7728 Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner]
16881 The laws of logic are boundless, so we want the few whose power contains the others [Frege]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
7622 In 1879 Frege developed second order logic [Frege, by Putnam]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
9179 Frege frequently expressed a contempt for language [Frege, by Dummett]
16867 Logic not only proves things, but also reveals logical relations between them [Frege]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
16863 Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege]
16862 The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege]
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
13473 Frege thinks there is an independent logical order of the truths, which we must try to discover [Frege, by Hart,WD]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
4975 A thought can be split in many ways, so that different parts appear as subject or predicate [Frege]
7729 Frege replaced Aristotle's subject/predicate form with function/argument form [Frege, by Weiner]
8645 Convert "Jupiter has four moons" into "the number of Jupiter's moons is four" [Frege]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
8490 First-level functions have objects as arguments; second-level functions take functions as arguments [Frege]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
8492 Relations are functions with two arguments [Frege]
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
3319 Frege gives a functional account of predication so that we can dispense with predicates [Frege, by Benardete,JA]
6076 For Frege, predicates are names of functions that map objects onto the True and False [Frege, by McGinn]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
16891 Despite Gödel, Frege's epistemic ordering of all the truths is still plausible [Frege, by Burge]
16906 The primitive simples of arithmetic are the essence, determining the subject, and its boundaries [Frege, by Jeshion]
16865 'Theorems' are both proved, and used in proofs [Frege]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
8447 In 'Etna is higher than Vesuvius' the whole of Etna, including all the lava, can't be the reference [Frege]
18772 We can treat designation by a few words as a proper name [Frege]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
10424 A Fregean proper name has a sense determining an object, instead of a concept [Frege, by Sainsbury]
18773 People may have different senses for 'Aristotle', like 'pupil of Plato' or 'teacher of Alexander' [Frege]
8448 Any object can have many different names, each with a distinct sense [Frege]
14075 Proper name in modal contexts refer obliquely, to their usual sense [Frege, by Gibbard]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
4978 The meaning of a proper name is the designated object [Frege]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
10510 Frege ascribes reference to incomplete expressions, as well as to singular terms [Frege, by Hale]
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
18937 If sentences have a 'sense', empty name sentences can be understood that way [Frege, by Sawyer]
18940 It is a weakness of natural languages to contain non-denoting names [Frege]
18939 In a logically perfect language every well-formed proper name designates an object [Frege]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
13733 Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
5. Theory of Logic / G. Quantification / 1. Quantification
9950 A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
9991 For Frege the variable ranges over all objects [Frege, by Tait]
10536 Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege]
9871 Frege always, and fatally, neglected the domain of quantification [Dummett on Frege]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
7730 Frege introduced quantifiers for generality [Frege, by Weiner]
7742 Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
9874 Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
14236 Each horse doesn't fall under the concept 'horse that draws the carriage', because all four are needed [Oliver/Smiley on Frege]
5. Theory of Logic / H. Proof Systems / 1. Proof Systems
13824 Proof theory began with Frege's definition of derivability [Frege, by Prawitz]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
13609 Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
16884 Basic truths of logic are not proved, but seen as true when they are understood [Frege, by Burge]
5. Theory of Logic / I. Semantics of Logic / 6. Intensionalism
9462 Frege is intensionalist about reference, as it is determined by sense; identity of objects comes first [Frege, by Jacquette]
18936 Frege moved from extensional to intensional semantics when he added the idea of 'sense' [Frege, by Sawyer]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
22294 We can show that a concept is consistent by producing something which falls under it [Frege]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17624 To understand axioms you must grasp their logical power and priority [Frege, by Burge]
16866 Tracing inference backwards closes in on a small set of axioms and postulates [Frege]
16868 The essence of mathematics is the kernel of primitive truths on which it rests [Frege]
16870 Axioms are truths which cannot be doubted, and for which no proof is needed [Frege]
16871 A truth can be an axiom in one system and not in another [Frege]
16886 The truth of an axiom must be independently recognisable [Frege]