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
Why regard standard mathematics as truths, rather than as interesting fictions?
Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true
Abstractions can form useful counterparts to concrete statements
Mathematics is only empirical as regards which theory is useful
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