Combining Philosophers
Ideas for Anaxarchus, Mark Colyvan and Willard Quine
expand these ideas
|
start again
|
choose
another area for these philosophers
display all the ideas for this combination of philosophers
54 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
9020
|
My logical grammar has sentences by predication, then negation, conjunction, and existential quantification [Quine]
|
13010
|
In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine]
|
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
9028
|
Maybe logical truth reflects reality, but in different ways in different languages [Quine]
|
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
9002
|
Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine]
|
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13639
|
Quine says higher-order items are intensional, and lack a clearly defined identity relation [Quine, by Shapiro]
|
8789
|
Various strategies try to deal with the ontological commitments of second-order logic [Hale/Wright on Quine]
|
10014
|
Quine rejects second-order logic, saying that predicates refer to multiple objects [Quine, by Hodes]
|
10828
|
Quantifying over predicates is treating them as names of entities [Quine]
|
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13681
|
Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider]
|
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
12219
|
Whether a modal claim is true depends on how the object is described [Quine, by Fine,K]
|
22437
|
Logical languages are rooted in ordinary language, and that connection must be kept [Quine]
|
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
10064
|
Quine quickly dismisses If-thenism [Quine, by Musgrave]
|
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
20296
|
Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey]
|
8998
|
Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine]
|
8999
|
Logic isn't conventional, because logic is needed to infer logic from conventions [Quine]
|
9000
|
If a convention cannot be communicated until after its adoption, what is its role? [Quine]
|
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
19043
|
Bivalence applies not just to sentences, but that general terms are true or false of each object [Quine]
|
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
9024
|
Excluded middle has three different definitions [Quine]
|
17924
|
Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]
|
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
10012
|
Quantification theory can still be proved complete if we add identity [Quine]
|
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
22434
|
Reduction to logical forms first simplifies idioms and grammar, then finds a single reading of it [Quine]
|
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13829
|
If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine]
|
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
12221
|
'Corner quotes' (quasi-quotation) designate 'whatever these terms designate' [Quine]
|
1618
|
We study bound variables not to know reality, but to know what reality language asserts [Quine]
|
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
21698
|
All relations, apart from ancestrals, can be reduced to simpler logic [Quine]
|
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
8453
|
If we had to name objects to make existence claims, we couldn't discuss all the real numbers [Quine]
|
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
10925
|
Failure of substitutivity shows that a personal name is not purely referential [Quine]
|
5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
19321
|
We might do without names, by converting them into predicates [Quine, by Kirkham]
|
8455
|
Canonical notation needs quantification, variables and predicates, but not names [Quine, by Orenstein]
|
8456
|
Quine extended Russell's defining away of definite descriptions, to also define away names [Quine, by Orenstein]
|
9204
|
Quine's arguments fail because he naively conflates names with descriptions [Fine,K on Quine]
|
9016
|
Names are not essential, because naming can be turned into predication [Quine]
|
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
1611
|
Names can be converted to descriptions, and Russell showed how to eliminate those [Quine]
|
5. Theory of Logic / G. Quantification / 1. Quantification
10926
|
Quantifying into referentially opaque contexts often produces nonsense [Quine]
|
10922
|
Objects are the values of variables, so a referentially opaque context cannot be quantified into [Quine]
|
10311
|
No sense can be made of quantification into opaque contexts [Quine, by Hale]
|
10538
|
Finite quantification can be eliminated in favour of disjunction and conjunction [Quine, by Dummett]
|
9015
|
Universal quantification is widespread, but it is definable in terms of existential quantification [Quine]
|
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
10793
|
Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal [Quine, by Marcus (Barcan)]
|
10801
|
Either reference really matters, or we don't need to replace it with substitutions [Quine]
|
21642
|
If quantification is all substitutional, there is no ontology [Quine]
|
9025
|
You can't base quantification on substituting names for variables, if the irrationals cannot all be named [Quine]
|
9026
|
Some quantifications could be false substitutionally and true objectually, because of nameless objects [Quine]
|
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10705
|
Putting a predicate letter in a quantifier is to make it the name of an entity [Quine]
|
5. Theory of Logic / G. Quantification / 6. Plural Quantification
12798
|
Plurals can in principle be paraphrased away altogether [Quine]
|
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9027
|
A sentence is logically true if all sentences with that grammatical structure are true [Quine]
|
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17929
|
Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]
|
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17930
|
Axioms are 'categorical' if all of their models are isomorphic [Colyvan]
|
5. Theory of Logic / L. Paradox / 3. Antinomies
21691
|
Antinomies contradict accepted ways of reasoning, and demand revisions [Quine]
|
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
21690
|
Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on [Quine]
|
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
9003
|
Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine]
|
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
21689
|
A barber shaves only those who do not shave themselves. So does he shave himself? [Quine]
|
21694
|
Membership conditions which involve membership and non-membership are paradoxical [Quine]
|
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
21692
|
If we write it as '"this sentence is false" is false', there is no paradox [Quine]
|