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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 Field says reference is a causal physical relation between mental states and objects
p.90 Tarski reduced truth to reference or denotation
p.368 Tarski really explained truth in terms of denoting, predicating and satisfied functions
0 p.365 Tarski just reduced truth to some other undefined semantic notions
1 p.369 Tarski gives us the account of truth needed to build a group of true sentences in a model
3 p.375 In the early 1930s many philosophers thought truth was not scientific
5 p.388 The notion of truth is to help us make use of the utterances of others
5 p.391 'Valence' and 'gene' had to be reduced to show their compatibility with physicalism
n 5 p.394 Model theory is unusual in restricting the range of the quantifiers
1980 Science without Numbers
p.36 In Field's version of science, space-time points replace real numbers
p.36 Field presumes properties can be eliminated from science
p.222 Logical consequence is defined by the impossibility of P and q
p.223 The application of mathematics only needs its possibility, not its truth
p.318 In Field's Platonist view, set theory is false because it asserts existence for non-existent things
Prelim p.1 Nominalists try to only refer to physical objects, or language, or mental constructions
1 p.9 Abstract objects are only applicable to the world if they are impure, and connect to the physical
1 p.15 Mathematics is only empirical as regards which theory is useful
1 p.16 It seems impossible to explain the idea that the conclusion is contained in the premises
3 p.24 Abstractions can form useful counterparts to concrete statements
3 p.25 Hilbert's geometry is interesting because it captures Euclid without using real numbers
3 p.27 Hilbert explains geometry, by non-numerical facts about space
4 p.35 Relational space is problematic if you take the idea of a field seriously
4 p.35 Both philosophy and physics now make substantivalism more attractive
5 p.42 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space
5 p.44 Beneath every extrinsic explanation there is an intrinsic explanation
Ch.4 p.54 Field needs a semantical notion of second-order consequence, and that needs sets
n 23 p.114 In theories of fields, space-time points or regions are causal agents
p.1 p.13 'Abstract' is unclear, but numbers, functions and sets are clearly abstract
p.5 p.227 The Indispensability Argument is the only serious ground for the existence of mathematical entities
p.ix p.-6 You can reduce ontological commitment by expanding the logic
p.viii p.-7 Why regard standard mathematics as truths, rather than as interesting fictions?
1989 Realism, Mathematics and Modality
1.1.1 p.3 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 Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible
2 p.122 Maybe reasonableness requires circular justifications - that is one coherentist view
3 p.125 Believing nothing, or only logical truths, is very reliable, but we want a lot more than that
4 p.133 If we only use induction to assess induction, it is empirically indefeasible, and hence a priori
4 p.136 We treat basic rules as if they were indefeasible and a priori, with no interest in counter-evidence
5 p.138 Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes
5 p.140 People vary in their epistemological standards, and none of them is 'correct'
2003 Causation in a Physical World
1 p.436 Physical laws are largely time-symmetric, so they make a poor basis for directional causation
1 p.436 Identifying cause and effect is not just conventional; we explain later events by earlier ones
1 p.438 The only reason for adding the notion of 'cause' to fundamental physics is directionality
2 p.443 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 If mathematical theories conflict, it may just be that they have different subject matter