Combining Texts

All the ideas for 'The Tragedy of Reason', 'The Semantic Conception of Truth' and 'Mathematics and Philosophy: grand and little'

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46 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
You have to be a Platonist to debate about reality, so every philosopher is a Platonist [Roochnik]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
Philosophy aims to satisfy the chief human desire - the articulation of beauty itself [Roochnik]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Philosophy aims to reveal the grandeur of mathematics [Badiou]
1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
Some say metaphysics is a highly generalised empirical study of objects [Tarski]
1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
Disputes that fail to use precise scientific terminology are all meaningless [Tarski]
2. Reason / A. Nature of Reason / 2. Logos
'Logos' ranges from thought/reasoning, to words, to rational structures outside thought [Roochnik]
In the seventeenth century the only acceptable form of logos was technical knowledge [Roochnik]
The hallmark of a person with logos is that they give reasons why one opinion is superior to another [Roochnik]
Logos cannot refute the relativist, and so must admit that it too is a matter of desire (for truth and agreement) [Roochnik]
Human desire has an ordered structure, with logos at the pinnacle [Roochnik]
Logos is not unconditionally good, but good if there is another person willing to engage with it [Roochnik]
2. Reason / A. Nature of Reason / 4. Aims of Reason
We prefer reason or poetry according to whether basics are intelligible or not [Roochnik]
2. Reason / A. Nature of Reason / 8. Naturalising Reason
Modern science, by aiming for clarity about the external world, has abandoned rationality in the human world [Roochnik]
2. Reason / A. Nature of Reason / 9. Limits of Reason
Unfortunately for reason, argument can't be used to establish the value of argument [Roochnik]
Attempts to suspend all presuppositions are hopeless, because a common ground must be agreed for the process [Roochnik]
2. Reason / D. Definition / 1. Definitions
For a definition we need the words or concepts used, the rules, and the structure of the language [Tarski]
3. Truth / A. Truth Problems / 2. Defining Truth
Definitions of truth should not introduce a new version of the concept, but capture the old one [Tarski]
A definition of truth should be materially adequate and formally correct [Tarski]
A rigorous definition of truth is only possible in an exactly specified language [Tarski]
We may eventually need to split the word 'true' into several less ambiguous terms [Tarski]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
It is convenient to attach 'true' to sentences, and hence the language must be specified [Tarski]
In the classical concept of truth, 'snow is white' is true if snow is white [Tarski]
Scheme (T) is not a definition of truth [Tarski]
Each interpreted T-sentence is a partial definition of truth; the whole definition is their conjunction [Tarski]
Use 'true' so that all T-sentences can be asserted, and the definition will then be 'adequate' [Tarski]
We don't give conditions for asserting 'snow is white'; just that assertion implies 'snow is white' is true [Tarski]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
The best truth definition involves other semantic notions, like satisfaction (relating terms and objects) [Tarski]
Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects [Tarski]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
We can't use a semantically closed language, or ditch our logic, so a meta-language is needed [Tarski]
The metalanguage must contain the object language, logic, and defined semantics [Tarski]
3. Truth / F. Semantic Truth / 2. Semantic Truth
If listing equivalences is a reduction of truth, witchcraft is just a list of witch-victim pairs [Field,H on Tarski]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
We need an undefined term 'true' in the meta-language, specified by axioms [Tarski]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
Truth can't be eliminated from universal claims, or from particular unspecified claims [Tarski]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Semantics is a very modest discipline which solves no real problems [Tarski]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Truth tables give prior conditions for logic, but are outside the system, and not definitions [Tarski]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) [Tarski]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
The Liar makes us assert a false sentence, so it must be taken seriously [Tarski]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
In mathematics, if a problem can be formulated, it will eventually be solved [Badiou]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Mathematics shows that thinking is not confined to the finite [Badiou]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
Mathematics inscribes being as such [Badiou]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
It is of the essence of being to appear [Badiou]
7. Existence / D. Theories of Reality / 3. Reality
Reality can be viewed neutrally, or as an object of desire [Roochnik]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
Relativism is a disease which destroys the possibility of rational debate [Roochnik]
19. Language / F. Communication / 1. Rhetoric
If relativism is the correct account of human values, then rhetoric is more important than reasoning [Roochnik]
Reasoning aims not at the understanding of objects, but at the desire to give beautiful speeches [Roochnik]
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
All great poetry is engaged in rivalry with mathematics [Badiou]