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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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9757
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A person viewed as an agent makes no sense without its own future [Korsgaard]
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Full Idea:
In forming a particular plan of life, you need to identify with your future in order to be what you are even now. When the person is viewed as an agent, no clear content can be given to the idea of a merely present self.
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From:
Christine M. Korsgaard (Intro to 'Creating the Kingdom of Ends' [1996], §2)
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A reaction:
I certainly like the notion that we should treat persons primarily as agents, since I take personhood to be more like a process than an existent entity. If a large brick is about to hit you, you actually have no future, though you think you have.
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9760
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Self-concern may be a source of pain, or a lack of self-respect, or a failure of responsibility [Korsgaard]
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Full Idea:
For utilitarians, self-concern causes needless pain; for Kantians, it evinces a lack of respect for one's own humanity; for the religious moralist, it is a failure of responsibility for what has been placed in one's special care.
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From:
Christine M. Korsgaard (Intro to 'Creating the Kingdom of Ends' [1996], §5)
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A reaction:
Worryingly, given my heathenish views, I find the third one the most congenial. If we don't take responsibility for our own selves (e.g. for having a great talent), then no one (even parents) will take responsibility for anything.
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9761
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Personal concern for one's own self widens out into concern for the impersonal [Korsgaard]
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Full Idea:
The personal concern which begins with one's life in a particular body finds its place in ever-widening spheres of agency and enterprise, developing finally into a personal concern for the impersonal.
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From:
Christine M. Korsgaard (Intro to 'Creating the Kingdom of Ends' [1996], §5)
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A reaction:
I am very struck by this nice thought, which comes from a very committed Kantian. It seems to me to capture the modern orthodoxy in ethical thinking - that concern for one's self, rather than altruism, is central, but altruism should follow from it.
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