Combining Texts

All the ideas for 'works', 'A Mathematical Introduction to Logic (2nd)' and 'The Tragedy of Reason'

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48 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]
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]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Until the 1960s the only semantics was truth-tables [Enderton]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
'dom R' indicates the 'domain' of objects having a relation [Enderton]
'fld R' indicates the 'field' of all objects in the relation [Enderton]
'ran R' indicates the 'range' of objects being related to [Enderton]
We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton]
'F(x)' is the unique value which F assumes for a value of x [Enderton]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton]
A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton]
The 'powerset' of a set is all the subsets of a given set [Enderton]
Two sets are 'disjoint' iff their intersection is empty [Enderton]
A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton]
A 'relation' is a set of ordered pairs [Enderton]
A 'function' is a relation in which each object is related to just one other object [Enderton]
A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton]
A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton]
A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton]
A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton]
A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton]
We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
A logical truth or tautology is a logical consequence of the empty set [Enderton]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton]
5. Theory of Logic / K. Features of Logics / 3. Soundness
A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton]
5. Theory of Logic / K. Features of Logics / 4. Completeness
A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton]
5. Theory of Logic / K. Features of Logics / 6. Compactness
Proof in finite subsets is sufficient for proof in an infinite set [Enderton]
5. Theory of Logic / K. Features of Logics / 7. Decidability
Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
For a reasonable language, the set of valid wff's can always be enumerated [Enderton]
7. Existence / D. Theories of Reality / 3. Reality
Reality can be viewed neutrally, or as an object of desire [Roochnik]
10. Modality / B. Possibility / 8. Conditionals / f. Pragmatics of conditionals
Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton]
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]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
Philosophers are the forefathers of heretics [Tertullian]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
I believe because it is absurd [Tertullian]