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All the ideas for 'Axiomatic Theories of Truth (2005 ver)', 'On the Genealogy of Morals' and 'Axiomatic Theories of Truth'

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84 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
The main aim of philosophy must be to determine the order of rank among values [Nietzsche]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Analysis rests on natural language, but its ideal is a framework which revises language [Halbach]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
Scientific knowledge is nothing without a prior philosophical 'faith' [Nietzsche]
2. Reason / A. Nature of Reason / 5. Objectivity
Objectivity is not disinterestedness (impossible), but the ability to switch perspectives [Nietzsche]
2. Reason / D. Definition / 2. Aims of Definition
An explicit definition enables the elimination of what is defined [Halbach]
2. Reason / D. Definition / 3. Types of Definition
Only that which has no history is definable [Nietzsche]
2. Reason / E. Argument / 3. Analogy
Don't trust analogies; they are no more than a guideline [Halbach]
3. Truth / A. Truth Problems / 1. Truth
Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach]
Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach]
3. Truth / A. Truth Problems / 2. Defining Truth
Any definition of truth requires a metalanguage [Halbach]
Truth definitions don't produce a good theory, because they go beyond your current language [Halbach]
Traditional definitions of truth often make it more obscure, rather than less [Halbach]
If people have big doubts about truth, a definition might give it more credibility [Halbach]
3. Truth / A. Truth Problems / 3. Value of Truth
Psychologists should be brave and proud, and prefer truth to desires, even when it is ugly [Nietzsche]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach]
Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach]
3. Truth / F. Semantic Truth / 2. Semantic Truth
Disquotational truth theories are short of deductive power [Halbach]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach]
CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach]
Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach]
If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach]
Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach]
The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach]
To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach]
Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach]
Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach]
Truth axioms need a base theory, because that is where truth issues arise [Halbach]
We know a complete axiomatisation of truth is not feasible [Halbach]
A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG]
The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach]
Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach]
Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach]
3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach]
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach]
The KF is much stronger deductively than FS, which relies on classical truth [Halbach]
The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Some say deflationism is axioms which are conservative over the base theory [Halbach]
Deflationists say truth merely serves to express infinite conjunctions [Halbach]
Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach]
The main problem for deflationists is they can express generalisations, but not prove them [Halbach]
Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach]
Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach]
4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach]
In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
To prove the consistency of set theory, we must go beyond set theory [Halbach]
Every attempt at formal rigour uses some set theory [Halbach]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach]
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
A theory is some formulae and all of their consequences [Halbach]
5. Theory of Logic / K. Features of Logics / 3. Soundness
You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach]
Normally we only endorse a theory if we believe it to be sound [Halbach]
Soundness must involve truth; the soundness of PA certainly needs it [Halbach]
5. Theory of Logic / L. Paradox / 1. Paradox
Many new paradoxes may await us when we study interactions between frameworks [Halbach]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
The compactness theorem can prove nonstandard models of PA [Halbach]
The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
To reduce PA to ZF, we represent the non-negative integers with von Neumann ordinals [Halbach]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Set theory was liberated early from types, and recent truth-theories are exploring type-free [Halbach]
7. Existence / C. Structure of Existence / 2. Reduction
That Peano arithmetic is interpretable in ZF set theory is taken by philosophers as a reduction [Halbach]
10. Modality / A. Necessity / 2. Nature of Necessity
Maybe necessity is a predicate, not the usual operator, to make it more like truth [Halbach]
11. Knowledge Aims / A. Knowledge / 5. Aiming at Truth
Philosophers have never asked why there is a will to truth in the first place [Nietzsche]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
Forgetfulness is a strong positive ability, not mental laziness [Nietzsche]
13. Knowledge Criteria / E. Relativism / 1. Relativism
There is only 'perspective' seeing and knowing, and so the best objectivity is multiple points of view [Nietzsche]
16. Persons / F. Free Will / 5. Against Free Will
Philosophers invented "free will" so that our virtues would be permanently interesting to the gods [Nietzsche]
18. Thought / A. Modes of Thought / 1. Thought
People who think in words are orators rather than thinkers, and think about facts instead of thinking facts [Nietzsche]
19. Language / D. Propositions / 4. Mental Propositions
We need propositions to ascribe the same beliefs to people with different languages [Halbach]
20. Action / A. Definition of Action / 1. Action Theory
It is a delusion to separate the man from the deed, like the flash from the lightning [Nietzsche]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / h. Against ethics
We must question the very value of moral values [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / f. Übermensch
The concept of 'good' was created by aristocrats to describe their own actions [Nietzsche]
A strong rounded person soon forgets enemies, misfortunes, and even misdeeds [Nietzsche]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / g. Will to power
All animals strive for the ideal conditions to express their power, and hate any hindrances [Nietzsche]
23. Ethics / A. Egoism / 1. Ethical Egoism
Only the decline of aristocratic morality led to concerns about "egoism" [Nietzsche]
Nietzsche rejects impersonal morality, and asserts the idea of living well [Nietzsche, by Nagel]
23. Ethics / B. Contract Ethics / 1. Contractarianism
Basic justice is the negotiation of agreement among equals, and the imposition of agreement [Nietzsche]
A masterful and violent person need have nothing to do with contracts [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
Plato, Spinoza and Kant are very different, but united in their low estimation of pity [Nietzsche]
23. Ethics / D. Deontological Ethics / 2. Duty
Guilt and obligation originated in the relationship of buying and selling, credit and debt [Nietzsche]
23. Ethics / F. Existentialism / 1. Existentialism
If we say birds of prey could become lambs, that makes them responsible for being birds of prey [Nietzsche]
23. Ethics / F. Existentialism / 2. Nihilism
Modern nihilism is now feeling tired of mankind [Nietzsche]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Old tribes always felt an obligation to the earlier generations, and the founders [Nietzsche]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / b. Natural authority
The state begins with brutal conquest of a disorganised people, not with a 'contract' [Nietzsche]
25. Social Practice / D. Justice / 3. Punishment / d. Reform of offenders
Punishment makes people harder, more alienated, and hostile [Nietzsche]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
The truly great haters in world history have always been priests [Nietzsche]