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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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20653
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Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
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Full Idea:
There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles.
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From:
report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro'
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A reaction:
I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture?
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5888
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Souls are born, since they are sensitive and inherited, so they must perish [Panaetius, by Cicero]
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Full Idea:
Panaetius says that whatever is born must perish, and souls are clearly born, as shown by the resemblance of children to their parents in disposition as well as body; also, anything sensible of pain is susceptible to sickness, and hence perishes.
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From:
report of Panaetius (fragments/reports [c.145 BCE]) by M. Tullius Cicero - Tusculan Disputations I.xxxii
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A reaction:
These seem to be rather good arguments. If we actually observe what someone's soul is like (through character) it seems rooted in a family and culture, and it certainly seems susceptible to disease. An empirical approach.
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