Ideas of Hartry Field, by Theme
[American, fl. 1992, Professor at University of Southern California, and then New York University.]
green numbers give full details 
back to list of philosophers 
expand these ideas
2. Reason / F. Fallacies / 4. Circularity
9161

Maybe reasonableness requires circular justifications  that is one coherentist view

3. Truth / A. Truth Problems / 4. Uses of Truth
10825

The notion of truth is to help us make use of the utterances of others

3. Truth / A. Truth Problems / 9. Rejecting Truth
10820

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
10818

Tarski really explained truth in terms of denoting, predicating and satisfied functions

13499

Tarski reduced truth to reference or denotation [Hart,WD]

3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
10817

Tarski just reduced truth to some other undefined semantic notions

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
9570

In Field's Platonist view, set theory is false because it asserts existence for nonexistent things [Chihara]

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10260

Logical consequence is defined by the impossibility of P and ¬q [Shapiro]

5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
10819

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
10827

Model theory is unusual in restricting the range of the quantifiers

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
9226

If mathematical theories conflict, it may just be that they have different subject matter

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
8958

In Field's version of science, spacetime points replace real numbers [Szabó]

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
18221

'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
8757

The Indispensability Argument is the only serious ground for the existence of mathematical entities

6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
18212

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
10261

The application of mathematics only needs its possibility, not its truth [Shapiro]

18218

Hilbert explains geometry, by nonnumerical facts about space

9623

Field needs a semantical notion of secondorder consequence, and that needs sets [Brown,JR]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
18215

It seems impossible to explain the idea that the conclusion is contained in the premises

6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
18216

Abstractions can form useful counterparts to concrete statements

18214

Mathematics is only empirical as regards which theory is useful

18210

Why regard standard mathematics as truths, rather than as interesting fictions?

8714

Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true

7. Existence / D. Theories of Reality / 10. Ontological Commitment / a. Ontological commitment
18211

You can reduce ontological commitment by expanding the logic

8. Modes of Existence / B. Properties / 12. Denial of Properties
8959

Field presumes properties can be eliminated from science [Szabó]

9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
18213

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
9160

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
9164

We treat basic rules as if they were indefeasible and a priori, with no interest in counterevidence

13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
9165

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. Antireliabilism
9162

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
9166

People vary in their epistemological standards, and none of them is 'correct'

14. Science / C. Induction / 1. Induction
9163

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
18222

Beneath every extrinsic explanation there is an intrinsic explanation

17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
10826

'Valence' and 'gene' had to be reduced to show their compatibility with physicalism

18. Thought / E. Abstraction / 4. Abstracta by Example
9917

'Abstract' is unclear, but numbers, functions and sets are clearly abstract

19. Language / B. Reference / 3. Direct Reference / b. Causal reference
7615

Field says reference is a causal physical relation between mental states and objects [Putnam]

26. Natural Theory / C. Causation / 1. Causation
8404

Explain single events by general rules, or vice versa, or probability explains both, or they are unconnected

26. Natural Theory / C. Causation / 5. Direction of causation
8401

Physical laws are largely timesymmetric, so they make a poor basis for directional causation

8400

Identifying cause and effect is not just conventional; we explain later events by earlier ones

8402

The only reason for adding the notion of 'cause' to fundamental physics is directionality

27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
18223

In theories of fields, spacetime points or regions are causal agents

27. Natural Reality / C. SpaceTime / 1. Space / d. Substantival space
18220

Both philosophy and physics now make substantivalism more attractive

27. Natural Reality / C. SpaceTime / 1. Space / e. Relational space
18219

Relational space is problematic if you take the idea of a field seriously
