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Ideas of Hartry Field, by Text

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

1972 Tarski's Theory of Truth
p.45 7615 Field says reference is a causal physical relation between mental states and objects [Putnam]
p.90 13499 Tarski reduced truth to reference or denotation [Hart,WD]
p.368 10818 Tarski really explained truth in terms of denoting, predicating and satisfied functions
§0 p.365 10817 Tarski just reduced truth to some other undefined semantic notions
§1 p.369 10819 Tarski gives us the account of truth needed to build a group of true sentences in a model
§3 p.375 10820 In the early 1930s many philosophers thought truth was not scientific
§5 p.388 10825 The notion of truth is to help us make use of the utterances of others
§5 p.391 10826 'Valence' and 'gene' had to be reduced to show their compatibility with physicalism
n 5 p.394 10827 Model theory is unusual in restricting the range of the quantifiers
1973 Theory Change and the Indeterminacy of Reference
p.30 22244 'Partial reference' is when the subject thinks two objects are one object [Recanati]
1980 Science without Numbers
p.36 8958 In Field's version of science, space-time points replace real numbers [Szabó]
p.36 8959 Field presumes properties can be eliminated from science [Szabó]
p.222 10260 Logical consequence is defined by the impossibility of P and ¬q [Shapiro]
p.223 10261 The application of mathematics only needs its possibility, not its truth [Shapiro]
p.318 9570 In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Chihara]
Prelim p.1 18212 Nominalists try to only refer to physical objects, or language, or mental constructions
1 p.9 18213 Abstract objects are only applicable to the world if they are impure, and connect to the physical
1 p.15 18214 Mathematics is only empirical as regards which theory is useful
1 p.16 18215 It seems impossible to explain the idea that the conclusion is contained in the premises
3 p.24 18216 Abstractions can form useful counterparts to concrete statements
3 p.27 18218 Hilbert explains geometry, by non-numerical facts about space
4 p.35 18220 Both philosophy and physics now make substantivalism more attractive
4 p.35 18219 Relational space is problematic if you take the idea of a field seriously
5 p.42 18221 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space
5 p.44 18222 Beneath every extrinsic explanation there is an intrinsic explanation
Ch.4 p.54 9623 Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR]
n 23 p.114 18223 In theories of fields, space-time points or regions are causal agents
p.1 p.13 9917 'Abstract' is unclear, but numbers, functions and sets are clearly abstract
p.5 p.227 8757 The Indispensability Argument is the only serious ground for the existence of mathematical entities
p.ix p.-6 18211 You can reduce ontological commitment by expanding the logic
p.viii p.-7 18210 Why regard standard mathematics as truths, rather than as interesting fictions?
1989 Realism, Mathematics and Modality
1.1.1 p.3 8714 Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true
2000 Apriority as an Evaluative Notion
1 p.120 9160 Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible
2 p.122 9161 Maybe reasonableness requires circular justifications - that is one coherentist view
3 p.125 9162 Believing nothing, or only logical truths, is very reliable, but we want a lot more than that
4 p.133 9163 If we only use induction to assess induction, it is empirically indefeasible, and hence a priori
4 p.136 9164 We treat basic rules as if they were indefeasible and a priori, with no interest in counter-evidence
5 p.138 9165 Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes
5 p.140 9166 People vary in their epistemological standards, and none of them is 'correct'
2003 Causation in a Physical World
1 p.436 8400 Identifying cause and effect is not just conventional; we explain later events by earlier ones
1 p.436 8401 Physical laws are largely time-symmetric, so they make a poor basis for directional causation
1 p.438 8402 The only reason for adding the notion of 'cause' to fundamental physics is directionality
2 p.443 8404 Explain single events by general rules, or vice versa, or probability explains both, or they are unconnected
2005 Recent Debates on the A Priori
7 p.82 9226 If mathematical theories conflict, it may just be that they have different subject matter