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5438
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Hermeneutics of tradition is sympathetic, hermeneutics of suspicion is hostile [Ricoeur, by Mautner]
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Full Idea:
Ricoeur distinguishes a hermeneutics of tradition (e.g. Gadamar), which interprets sympathetically looking for hidden messages, and a hermeneutics of suspicion (e.g. Nietzsche, Freud) which sees hidden drives and interests.
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From:
report of Paul Ricoeur (works [1970]) by Thomas Mautner - Penguin Dictionary of Philosophy p.249
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A reaction:
Obviously the answer is somewhere between the two. Nietzsche's suspicion can be wonderful, but Freud's can seem silly (e.g. on Leonardo). On the whole I am on the 'tradition' side, because great thinkers can rise above their culture (on a good day).
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19125
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If we define truth, we can eliminate it [Halbach/Leigh]
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Full Idea:
If truth can be explicitly defined, it can be eliminated.
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3)
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A reaction:
That we could just say p corresponds to the facts, or p coheres with our accepted beliefs, or p is the aim of our enquiries, and never mention the word 'true'. Definition is a strategy for reduction or elimination.
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19127
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The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh]
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Full Idea:
Although the theory is materially adequate, Tarski thought that the T-sentences are deductively too weak. …Also it seems that the T-sentences are not conservative, because they prove in PA that 0=0 and ¬0=0 are different, so at least two objects exist.
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.2)
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A reaction:
They are weak because they can't prove completeness. This idea give two reasons for looking for a better theory of truth.
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19124
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A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh]
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Full Idea:
If a natural theory of truth is added to Peano Arithmetic, it is not necessary to add explicity global reflection principles to assert soundness, as the truth theory proves them. Truth theories thus prove soundess, and allows its expression.
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.2)
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A reaction:
This seems like a big attraction of axiomatic theories of truth for students of metamathematics.
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19126
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If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh]
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Full Idea:
If truth does not have any explanatory force, as some deflationists claim, the axioms of truth should not allow us to prove any new theorems that do not involve the truth predicate. That is, a deflationary axiomatisation of truth should be 'conservative'.
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3)
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A reaction:
So does truth have 'explanatory force'? These guys are interested in explaining theorems of arithmetic, but I'm more interested in real life. People do daft things because they have daft beliefs. Logic should be neutral, but truth has values?
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19129
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The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh]
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Full Idea:
It is a virtue of the Friedman-Sheard axiomatisation that it is thoroughly classical in its logic. Its drawback is that it is ω-inconsistent. That is, it proves &exists;x¬φ(x), but proves also φ(0), φ(1), φ(2), …
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.3)
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A reaction:
It seems the theory is complete (and presumably sound), yet not fully consistent. FS also proves the finite levels of Tarski's hierarchy, but not the transfinite levels.
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19130
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KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh]
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Full Idea:
KF is formulated in classical logic, but describes a non-classical notion of truth. It allow truth-value gluts, making some sentences (such as the Liar) both true and not-true. Some authors add an axiom ruling out such gluts.
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.4)
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A reaction:
[summary, which I hope is correct! Stanford is not wholly clear]
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6304
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Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
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Full Idea:
Mathematical realism is the doctrine that mathematical objects exist, that much contemporary mathematics is true, and that the existence and truth in question is independent of our constructions, beliefs and proofs.
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From:
Michael D. Resnik (Maths as a Science of Patterns [1997], Three.12.9)
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A reaction:
As thus defined, I would call myself a mathematical realist, but everyone must hesitate a little at the word 'exist' and ask, how does it exist? What is it 'made of'? To say that it exists in the way that patterns exist strikes me as very helpful.
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6301
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Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
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Full Idea:
Of the equivalence relationships which occur between patterns, congruence is the strongest, equivalence the next, and mutual occurrence the weakest. None of these is identity, which would require the same position.
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From:
Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.3)
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A reaction:
This gives some indication of how an account of mathematics as a science of patterns might be built up. Presumably the recognition of these 'degrees of strength' cannot be straightforward observation, but will need an a priori component?
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19121
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We can reduce properties to true formulas [Halbach/Leigh]
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Full Idea:
One might say that 'x is a poor philosopher' is true of Tom instead of saying that Tom has the property of being a poor philosopher. We quantify over formulas instead of over definable properties, and thus reduce properties to truth.
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From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1)
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A reaction:
[compressed] This stuff is difficult (because the axioms are complex and hard to compare), but I am excited (yes!) about this idea. Their point is that you need a truth predicate within the object language for this, which disquotational truth forbids.
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