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All the ideas for 'Philosophy of Arithmetic', 'Non-Monotonic Logic' and 'works'

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43 ideas

2. Reason / E. Argument / 1. Argument
You can 'rebut' an argument's conclusion, or 'undercut' its premises [Antonelli]
3. Truth / A. Truth Problems / 6. Verisimilitude
Truth does not admit of more and less [Frege]
4. Formal Logic / E. Nonclassical Logics / 1. Nonclassical Logics
We infer that other objects are like some exceptional object, if they share some of its properties [Antonelli]
4. Formal Logic / E. Nonclassical Logics / 12. Non-Monotonic Logic
Reasoning may be defeated by new premises, or by finding out more about the given ones [Antonelli]
Should we accept Floating Conclusions, derived from two arguments in conflict? [Antonelli]
Weakest Link Principle: prefer the argument whose weakest link is the stronger [Antonelli]
Non-monotonic core: Reflexivity, Cut, Cautious Monotonicity, Left Logical Equivalence, Right Weakening [Antonelli]
We can rank a formula by the level of surprise if it were to hold [Antonelli]
People don't actually use classical logic, but may actually use non-monotonic logic [Antonelli]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Frege did not think of himself as working with sets [Frege, by Hart,WD]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The null set is indefensible, because it collects nothing [Frege, by Burge]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Frege, by Benardete,JA]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Frege frequently expressed a contempt for language [Frege, by Dummett]
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
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 / 7. Predicates in Logic
For Frege, predicates are names of functions that map objects onto the True and False [Frege, by McGinn]
Frege gives a functional account of predication so that we can dispense with predicates [Frege, by Benardete,JA]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Frege always, and fatally, neglected the domain of quantification [Dummett on Frege]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Basic truths of logic are not proved, but seen as true when they are understood [Frege, by Burge]
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
In classical logic the relation |= has Monotony built into its definition [Antonelli]
Cautious Monotony ignores proved additions; Rational Monotony fails if the addition's negation is proved [Antonelli]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Multiplicity in general is just one and one and one, etc. [Husserl]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content [Benardete,JA on Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Frege aimed to discover the logical foundations which justify arithmetical judgements [Frege, by Burge]
Eventually Frege tried to found arithmetic in geometry instead of in logic [Frege, by Friend]
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
Frege's logic showed that there is no concept of being [Frege, by Scruton]
9. Objects / F. Identity among Objects / 5. Self-Identity
Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x' [Frege, by Benardete,JA]
11. Knowledge Aims / A. Knowledge / 2. Understanding
To understand a thought, understand its inferential connections to other thoughts [Frege, by Burge]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Frege's concept of 'self-evident' makes no reference to minds [Frege, by Burge]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
An apriori truth is grounded in generality, which is universal quantification [Frege, by Burge]
14. Science / B. Scientific Theories / 1. Scientific Theory
The building blocks contain the whole contents of a discipline [Frege]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Husserl identifies a positive mental act of unification, and a negative mental act for differences [Husserl, by Frege]
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
We clarify concepts (e.g. numbers) by determining their psychological origin [Husserl, by Velarde-Mayol]
18. Thought / E. Abstraction / 8. Abstractionism Critique
Frege said concepts were abstract entities, not mental entities [Frege, by Putnam]
Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl]
Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
A thought is not psychological, but a condition of the world that makes a sentence true [Frege, by Miller,A]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Frege's 'sense' is the strict and literal meaning, stripped of tone [Frege, by Miller,A]
'Sense' solves the problems of bearerless names, substitution in beliefs, and informativeness [Frege, by Miller,A]
19. Language / E. Analyticity / 1. Analytic Propositions
'P or not-p' seems to be analytic, but does not fit Kant's account, lacking clear subject or predicate [Frege, by Weiner]
19. Language / E. Analyticity / 2. Analytic Truths
Analytic truths are those that can be demonstrated using only logic and definitions [Frege, by Miller,A]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
Frege put forward an ontological argument for the existence of numbers [Frege, by Benardete,JA]