Combining Texts

All the ideas for 'Axiomatic Theories of Truth (2013 ver)', 'Philosophy of Nature (Encylopedia II)' and 'Philosophy without Intuitions'

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14 ideas

1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual

22077	Metaphysics is the lattice which makes incoming material intelligible [Hegel]
	Full Idea: Metaphysics means nothing other than the range of general determinations of thought, the diamond lattice, as it were, into which we bring all material and thereby first make it intelligible.
	From: Georg W.F.Hegel (Philosophy of Nature (Encylopedia II) [1817], §3), quoted by Stephen Houlgate - Hegel p.95
	A reaction: This sounds to me like a perfect summary of Kant's transcendental view. Metaphysics is the a priori deconstruction of our conceptual scheme. But for Kant it is fixed, and for Hegel it is dynamic.

2. Reason / E. Argument / 7. Thought Experiments

20183	So-called 'though experiments' are just philosophers observing features of the world [Cappelen]
	Full Idea: What are called 'thought experiments' in philosophy are in effect just philosophers drawing our attention to interesting features of the world.
	From: Herman Cappelen (Philosophy without Intuitions [2012], 11.3)
	A reaction: Thought experiments are said to rely (perhaps excessively) on 'intuition', but Cappelen says intuition is irrelevant, because we are merely making judgements. It think they ARE experiments, if one feature varies while the rest is held steady.

3. Truth / A. Truth Problems / 2. Defining Truth

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.

3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth

19128	If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh]
	Full Idea: If axioms are formulated for a language (such as set theory) that lacks names for all objects, then they require the use of a satisfaction relation rather than a unary truth predicate.
	From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.3)
	A reaction: I take it this is an important idea for understanding why Tarski developed his account of truth based on satisfaction.

3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth

19120	Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh]
	Full Idea: Semantic approaches to truth usually necessitate the use of a metalanguage that is more powerful than the object-language for which it provides a semantics. It is usually taken to include set theory.
	From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1)
	A reaction: This is a motivation for developing an axiomatic account of truth, that moves it into the object language.

3. Truth / F. Semantic Truth / 2. Semantic Truth

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.

3. Truth / G. Axiomatic Truth / 1. Axiomatic 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?

3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms

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.

3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms

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]

8. Modes of Existence / B. Properties / 12. Denial of Properties

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.

8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta

19122	Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh]
	Full Idea: The reduction of second-order theories (of properties or sets) to axiomatic theories of truth is a form of reductive nominalism, replacing existence assumptions (e.g. comprehension axioms) by innocuous assumptions about the truth predicate.
	From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1)
	A reaction: I'm currently thinking that axiomatic theories of truth are the most exciting development in contemporary philosophy. See Halbach and Horsten.

12. Knowledge Sources / E. Direct Knowledge / 2. Intuition

20182	The word 'intuitive' often plays not role at all in arguments, and can be removed [Cappelen]
	Full Idea: Careful study of uses of 'intuitive' will reveal that it often plays no significant argumentative role, and that removal will improve overall argumentative transparency.
	From: Herman Cappelen (Philosophy without Intuitions [2012], 04.1)
	A reaction: This is a key part of Cappelen's argument that 'intuition' is a rather empty concept, and that philosophers do not really rely on it. In effect, he is consigning it to mere rhetoric. He gives lots of examples in support.

24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution

21756	All revolutions result from spirit changing its categories, to achieve a deeper understanding [Hegel]
	Full Idea: All revolutions ...originate solely from the fact that spirit, in order to understand and comprehend itself with a view to possessing itself, has changed its categories, comprehending itself more truly, more deeply, more intimately in unity with itself.
	From: Georg W.F.Hegel (Philosophy of Nature (Encylopedia II) [1817], §246), quoted by Stephen Houlgate - An Introduction to Hegel 01
	A reaction: Some Hegelian waffle here, but it focuses on what seems important, which is how societal thinking has shifted, so that what was previously tolerated now triggers a revolution.