|
19125
|
If we define truth, we can eliminate it [Halbach/Leigh]
|
|
Full Idea:
If truth can be explicitly defined, it can be eliminated.
|
|
From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3)
|
|
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.
|
|
19127
|
The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh]
|
|
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.
|
|
From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.2)
|
|
A reaction:
They are weak because they can't prove completeness. This idea give two reasons for looking for a better theory of truth.
|
|
19124
|
A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh]
|
|
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.
|
|
From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.2)
|
|
A reaction:
This seems like a big attraction of axiomatic theories of truth for students of metamathematics.
|
|
19126
|
If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh]
|
|
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'.
|
|
From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3)
|
|
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?
|
|
19129
|
The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh]
|
|
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), …
|
|
From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.3)
|
|
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.
|
|
19130
|
KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh]
|
|
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.
|
|
From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.4)
|
|
A reaction:
[summary, which I hope is correct! Stanford is not wholly clear]
|
|
19121
|
We can reduce properties to true formulas [Halbach/Leigh]
|
|
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.
|
|
From:
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1)
|
|
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.
|
|
8430
|
Causal statements are used to explain, to predict, to control, to attribute responsibility, and in theories [Kim]
|
|
Full Idea:
The function of causal statements is 1) to explain events, 2) for predictive usefulness, 3) to help control events, 4) with agents, to attribute moral responsibility, 5) in physical theory. We should judge causal theories by how they account for these.
|
|
From:
Jaegwon Kim (Causes and Counterfactuals [1973], p.207)
|
|
A reaction:
He suggests that Lewis's counterfactual theory won't do well on this test. I think the first one is what matters. Philosophy aims to understand, and that is achieved through explanation. Regularity and counterfactual theories explain very little.
|
|
8429
|
Counterfactuals can express four other relations between events, apart from causation [Kim]
|
|
Full Idea:
Counterfactuals can express 'analytical' dependency, or the fact that one event is part of another, or an action done by doing another, or (most interestingly) an event can determine another without causally determining it.
|
|
From:
Jaegwon Kim (Causes and Counterfactuals [1973], p.205)
|
|
A reaction:
[Kim gives example of each case] Counterfactuals can even express a relation that involves no dependency. Or they might just involve redescription, as in 'If Scott were still alive, then the author of "Waverley" would be too'.
|
|
4781
|
Many counterfactual truths do not imply causation ('if yesterday wasn't Monday, it isn't Tuesday') [Kim, by Psillos]
|
|
Full Idea:
Kim gives a range of examples of counterfactual dependence without causation, as: 'if yesterday wasn't Monday, today wouldn't be Tuesday', and 'if my sister had not given birth, I would not be an uncle'.
|
|
From:
report of Jaegwon Kim (Causes and Counterfactuals [1973]) by Stathis Psillos - Causation and Explanation §3.3
|
|
A reaction:
This is aimed at David Lewis. The objection seems like commonsense. "If you blink, the cat gets it". Causal claims involve counterfactuals, but they are not definitive of what causation is.
|