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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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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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7322
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Constitutive scepticism is about facts, and epistemological scepticism about our ability to know them [Miller,A]
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Full Idea:
We should distinguish 'constitutive scepticism' (about the existence of certain sorts of facts) from the traditional 'epistemological scepticism' (which concedes that the sort of fact in question exists, but questions our right to claim knowledge of it).
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From:
Alexander Miller (Philosophy of Language [1998], 4.7)
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A reaction:
I would be inclined to call the first type 'ontological scepticism'. Miller is discussing Quine's scepticism about meaning. Atheists fall into the first group, and agnostics into the second. An important, and nicely simple, distinction.
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7325
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Dispositions say what we will do, not what we ought to do, so can't explain normativity [Miller,A]
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Full Idea:
Dispositional facts are facts about what we will do, not about what we ought to do, and as such cannot capture the normativity of meaning.
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From:
Alexander Miller (Philosophy of Language [1998], 6.2)
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A reaction:
Miller is discussing language, but this raises a nice question for all behaviourist accounts of mental events. Perhaps there is a disposition to behave in a guilty way if you do something you think you shouldn't do. (Er, isn't 'guilt' a mental event?)
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7324
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Explain meaning by propositional attitudes, or vice versa, or together? [Miller,A]
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Full Idea:
Grice wants to explain linguistic meaning in terms of the content of propositional attitudes, Dummett has championed the view that propositional attitudes must be explained by linguistic meaning, while Davidson says they must be explained together.
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From:
Alexander Miller (Philosophy of Language [1998], 6.1)
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A reaction:
A useful map. My intuition says propositional attitudes come first, for evolutionary reasons. We are animals first, and speakers second. Thought precedes language. A highly social animal flourishes if it can communicate.
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7328
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The principle of charity is holistic, saying we must hold most of someone's system of beliefs to be true [Miller,A]
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Full Idea:
Properly construed, the principle of charity is a holistic constraint applying, not to individual beliefs, but rather to systems of belief: we must interpret a speaker so that most of the beliefs in his system are, by our lights, true.
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From:
Alexander Miller (Philosophy of Language [1998], 8.7)
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A reaction:
This is a lot more plausible than applying the principle to individual sentences, particularly if you are in the company of habitual ironists or constitutional liars.
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7903
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The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
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Full Idea:
The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
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From:
Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
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A reaction:
What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
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