Ideas of Hartry Field, by Theme

[American, fl. 1992, Professor at University of Southern California, and then New York University.]

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2. Reason / F. Fallacies / 4. Circularity
Maybe reasonableness requires circular justifications - that is one coherentist view
3. Truth / A. Truth Problems / 4. Uses of Truth
The notion of truth is to help us make use of the utterances of others
3. Truth / A. Truth Problems / 9. Rejecting Truth
In the early 1930s many philosophers thought truth was not scientific
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Tarski reduced truth to reference or denotation
Tarski really explained truth in terms of denoting, predicating and satisfied functions
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
Tarski just reduced truth to some other undefined semantic notions
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
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Logical consequence is defined by the impossibility of P and q
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
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Model theory is unusual in restricting the range of the quantifiers
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
If mathematical theories conflict, it may just be that they have different subject matter
6. Mathematics / A. Nature of Mathematics / 3. Numbers / a. Numbers
In Field's version of science, space-time points replace real numbers
6. Mathematics / B. Foundations for Mathematics / 2. Axioms for Geometry
Hilbert's geometry is interesting because it captures Euclid without using real numbers
'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space
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
6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
Nominalists try to only refer to physical objects, or language, or mental constructions
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
The application of mathematics only needs its possibility, not its truth
Hilbert explains geometry, by non-numerical facts about space
Field needs a semantical notion of second-order consequence, and that needs sets
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
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Abstractions can form useful counterparts to concrete statements
Mathematics is only empirical as regards which theory is useful
Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true
Why regard standard mathematics as truths, rather than as interesting fictions?
7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
You can reduce ontological commitment by expanding the logic
8. Modes of Existence / B. Properties / 12. Denial of Properties
Field presumes properties can be eliminated from science
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
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
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
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
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
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
People vary in their epistemological standards, and none of them is 'correct'
14. Science / C. Induction / 1. Induction
If we only use induction to assess induction, it is empirically indefeasible, and hence a priori
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Beneath every extrinsic explanation there is an intrinsic explanation
17. Mind and Body / E. Physicalism / 2. Reduction of Mind
'Valence' and 'gene' had to be reduced to show their compatibility with physicalism
18. Thought / D. Concepts / 6. Abstract Concepts / d. Abstracta by example
'Abstract' is unclear, but numbers, functions and sets are clearly abstract
19. Language / D. Theories of Reference / 3. Direct Reference / b. Causal reference
Field says reference is a causal physical relation between mental states and objects
26. Natural Theory / B. Concepts of Nature / 3. Space / b. Points in space
In theories of fields, space-time points or regions are causal agents
26. Natural Theory / B. Concepts of Nature / 3. Space / c. Substantival space
Both philosophy and physics now make substantivalism more attractive
26. Natural Theory / B. Concepts of Nature / 3. Space / d. Relational space
Relational space is problematic if you take the idea of a field seriously
26. Natural Theory / C. Causation / 1. Causation / a. Causation
Explain single events by general rules, or vice versa, or probability explains both, or they are unconnected
26. Natural Theory / C. Causation / 1. Causation / e. Direction of causation
Physical laws are largely time-symmetric, so they make a poor basis for directional causation
Identifying cause and effect is not just conventional; we explain later events by earlier ones
The only reason for adding the notion of 'cause' to fundamental physics is directionality