Combining Philosophers

All the ideas for Peter B. Lewis, Saunders MacLane and Hartry Field

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47 ideas

2. Reason / F. Fallacies / 4. Circularity
Maybe reasonableness requires circular justifications - that is one coherentist view [Field,H]
3. Truth / A. Truth Problems / 4. Uses of Truth
The notion of truth is to help us make use of the utterances of others [Field,H]
3. Truth / A. Truth Problems / 9. Rejecting Truth
In the early 1930s many philosophers thought truth was not scientific [Field,H]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Tarski reduced truth to reference or denotation [Field,H, by Hart,WD]
Tarski really explained truth in terms of denoting, predicating and satisfied functions [Field,H]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
Tarski just reduced truth to some other undefined semantic notions [Field,H]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
Tarski gives us the account of truth needed to build a group of true sentences in a model [Field,H]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Model theory is unusual in restricting the range of the quantifiers [Field,H]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
If mathematical theories conflict, it may just be that they have different subject matter [Field,H]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
In Field's version of science, space-time points replace real numbers [Field,H, by Szabó]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H]
6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro]
Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H]
Hilbert explains geometry, by non-numerical facts about space [Field,H]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Mathematics is only empirical as regards which theory is useful [Field,H]
Abstractions can form useful counterparts to concrete statements [Field,H]
Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true [Field,H]
Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H]
7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
You can reduce ontological commitment by expanding the logic [Field,H]
8. Modes of Existence / B. Properties / 12. Denial of Properties
Field presumes properties can be eliminated from science [Field,H, by Szabó]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
Fichte, Schelling and Hegel rejected transcendental idealism [Lewis,PB]
Fichte, Hegel and Schelling developed versions of Absolute Idealism [Lewis,PB]
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible [Field,H]
12. Knowledge Sources / A. A Priori Knowledge / 7. A Priori from Convention
We treat basic rules as if they were indefeasible and a priori, with no interest in counter-evidence [Field,H]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes [Field,H]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
Believing nothing, or only logical truths, is very reliable, but we want a lot more than that [Field,H]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
People vary in their epistemological standards, and none of them is 'correct' [Field,H]
14. Science / C. Induction / 1. Induction
If we only use induction to assess induction, it is empirically indefeasible, and hence a priori [Field,H]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Beneath every extrinsic explanation there is an intrinsic explanation [Field,H]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
'Valence' and 'gene' had to be reduced to show their compatibility with physicalism [Field,H]
18. Thought / E. Abstraction / 4. Abstracta by Example
'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H]
19. Language / B. Reference / 1. Reference theories
'Partial reference' is when the subject thinks two objects are one object [Field,H, by Recanati]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Field says reference is a causal physical relation between mental states and objects [Field,H, by Putnam]
26. Natural Theory / C. Causation / 1. Causation
Explain single events by general rules, or vice versa, or probability explains both, or they are unconnected [Field,H]
26. Natural Theory / C. Causation / 5. Direction of causation
Physical laws are largely time-symmetric, so they make a poor basis for directional causation [Field,H]
Identifying cause and effect is not just conventional; we explain later events by earlier ones [Field,H]
The only reason for adding the notion of 'cause' to fundamental physics is directionality [Field,H]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
In theories of fields, space-time points or regions are causal agents [Field,H]
27. Natural Reality / C. Space-Time / 1. Space / d. Substantival space
Both philosophy and physics now make substantivalism more attractive [Field,H]
27. Natural Reality / C. Space-Time / 1. Space / e. Relational space
Relational space is problematic if you take the idea of a field seriously [Field,H]