Combining Texts

All the ideas for 'fragments/reports', 'A Mathematical Introduction to Logic (2nd)' and 'Metaphysics of Morals I: Doctrine of Right'

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45 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Because there is only one human reason, there can only be one true philosophy from principles [Kant]
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]
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]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
We are equipped with the a priori intuitions needed for the concept of right [Kant]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
A power-based state of nature may not be unjust, but there is no justice without competent judges [Kant]
24. Political Theory / C. Ruling a State / 2. Leaders / a. Autocracy
Monarchs have the highest power; autocrats have complete power [Kant]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
Hereditary nobility has not been earned, and probably won't be earned [Kant]
24. Political Theory / D. Ideologies / 6. Liberalism / d. Liberal freedom
Actions are right if the maxim respects universal mutual freedoms [Kant]
24. Political Theory / D. Ideologies / 12. Feminism
Women have no role in politics [Kant]
25. Social Practice / B. Equalities / 3. Legal equality
Equality is not being bound in ways you cannot bind others [Kant]
25. Social Practice / C. Rights / 3. Alienating rights
In the contract people lose their rights, but immediately regain them, in the new commonwealth [Kant]
25. Social Practice / C. Rights / 4. Property rights
If someone has largely made something, then they own it [Kant]
25. Social Practice / D. Justice / 1. Basis of justice
Human life is pointless without justice [Kant]
25. Social Practice / D. Justice / 3. Punishment / a. Right to punish
Justice asserts the death penalty for murder, from a priori laws [Kant]
25. Social Practice / E. Policies / 2. Religion in Society
The church has a political role, by offering a supreme power over people [Kant]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]