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All the ideas for 'Mahaprajnaparamitashastra', 'LOT 2' and 'Beginning Logic'

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94 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Who cares what 'philosophy' is? Most pre-1950 thought doesn't now count as philosophy [Fodor]
1. Philosophy / F. Analytic Philosophy / 3. Analysis of Preconditions
Definitions often give necessary but not sufficient conditions for an extension [Fodor]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
'Contradictory' propositions always differ in truth-value [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL
We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon]
That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon]
We write the 'negation' of P (not-P) as ¬ [Lemmon]
We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P) [Lemmon]
If A and B are 'interderivable' from one another we may write A -||- B [Lemmon]
That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon]
The sign |- may be read as 'therefore' [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon]
The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon]
A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon]
A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon]
'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon]
Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon]
A wff is 'contingent' if produces at least one T and at least one F [Lemmon]
'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon]
A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon]
A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon]
A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / c. Derivation rules of PL
∧I: Given A and B, we may derive A∧B [Lemmon]
CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon]
MPP: Given A and A→B, we may derive B [Lemmon]
RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon]
MTT: Given ¬B and A→B, we derive ¬A [Lemmon]
∨I: Given either A or B separately, we may derive A∨B [Lemmon]
∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon]
DN: Given A, we may derive ¬¬A [Lemmon]
A: we may assume any proposition at any stage [Lemmon]
∧E: Given A∧B, we may derive either A or B separately [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
'Modus tollendo ponens' (MTP) says ¬P, P ∨ Q |- Q [Lemmon]
'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon]
We can change conditionals into negated conjunctions with P→Q -||- ¬(P ∧ ¬Q) [Lemmon]
We can change conditionals into disjunctions with P→Q -||- ¬P ∨ Q [Lemmon]
De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon]
The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon]
We can change conjunctions into negated conditionals with P→Q -||- ¬(P → ¬Q) [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Truth-tables are good for showing invalidity [Lemmon]
A truth-table test is entirely mechanical, but this won't work for more complex logic [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 4. Soundness of PL
If any of the nine rules of propositional logic are applied to tautologies, the result is a tautology [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 5. Completeness of PL
Propositional logic is complete, since all of its tautologous sequents are derivable [Lemmon]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / a. Symbols of PC
Write '(∀x)(...)' to mean 'take any x: then...', and '(∃x)(...)' to mean 'there is an x such that....' [Lemmon]
'Gm' says m has property G, and 'Pmn' says m has relation P to n [Lemmon]
The 'symbols' are bracket, connective, term, variable, predicate letter, reverse-E [Lemmon]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / b. Terminology of PC
Our notation uses 'predicate-letters' (for 'properties'), 'variables', 'proper names', 'connectives' and 'quantifiers' [Lemmon]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / c. Derivations rules of PC
Universal Elimination (UE) lets us infer that an object has F, from all things having F [Lemmon]
With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro [Lemmon]
UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon]
Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon]
Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀
If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / e. Existential quantifier ∃
'Some Frenchmen are generous' is rendered by (∃x)(Fx→Gx), and not with the conditional → [Lemmon]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
A truth-table, not inferential role, defines 'and' [Fodor]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
Names in thought afford a primitive way to bring John before the mind [Fodor]
'Paderewski' has two names in mentalese, for his pianist file and his politician file [Fodor]
5. Theory of Logic / K. Features of Logics / 2. Consistency
P-and-Q gets its truth from the truth of P and truth of Q, but consistency isn't like that [Fodor]
10. Modality / B. Possibility / 1. Possibility
There's statistical, logical, nomological, conceptual and metaphysical possibility [Fodor]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
Some beliefs are only inferred when needed, like 'Shakespeare had not telephone' [Fodor]
11. Knowledge Aims / A. Knowledge / 6. Knowing How
Knowing that must come before knowing how [Fodor]
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
Pragmatism is the worst idea ever [Fodor]
15. Nature of Minds / A. Nature of Mind / 1. Mind / c. Features of mind
Mental states have causal powers [Fodor]
15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
The different types of resemblance don't resemble one another [Fodor]
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
In the Representational view, concepts play the key linking role [Fodor]
17. Mind and Body / E. Mind as Physical / 4. Connectionism
Only the labels of nodes have semantic content in connectionism, and they play no role [Fodor]
18. Thought / A. Modes of Thought / 1. Thought
Associative thinking avoids syntax, but can't preserve sense, reference or truth [Fodor]
Connectionism gives no account of how constituents make complex concepts [Fodor]
18. Thought / B. Mechanics of Thought / 4. Language of Thought
Ambiguities in English are the classic reason for claiming that we don't think in English [Fodor]
18. Thought / B. Mechanics of Thought / 5. Mental Files
Mental representations name things in the world, but also files in our memory [Fodor]
We think in file names [Fodor]
18. Thought / B. Mechanics of Thought / 6. Artificial Thought / a. Artificial Intelligence
Frame Problem: how to eliminate most beliefs as irrelevant, without searching them? [Fodor]
18. Thought / C. Content / 5. Twin Earth
If concept content is reference, then my Twin and I are referring to the same stuff [Fodor]
18. Thought / D. Concepts / 2. Origin of Concepts / a. Origin of concepts
Nobody knows how concepts are acquired [Fodor]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
We have an innate capacity to form a concept, once we have grasped the stereotype [Fodor]
18. Thought / D. Concepts / 3. Ontology of Concepts / a. Concepts as representations
Having a concept isn't a pragmatic matter, but being able to think about the concept [Fodor]
Concepts have two sides; they are files that face thought, and also face subject-matter [Fodor]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
Cartesians put concept individuation before concept possession [Fodor]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
Frege's puzzles suggest to many that concepts have sense as well as reference [Fodor]
If concepts have sense, we can't see the connection to their causal powers [Fodor]
Belief in 'senses' may explain intentionality, but not mental processes [Fodor]
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
You can't think 'brown dog' without thinking 'brown' and 'dog' [Fodor]
18. Thought / D. Concepts / 4. Structure of Concepts / d. Concepts as prototypes
Maybe stereotypes are a stage in concept acquisition (rather than a by-product) [Fodor]
One stereotype might be a paradigm for two difference concepts [Fodor]
18. Thought / D. Concepts / 4. Structure of Concepts / g. Conceptual atomism
For the referential view of thought, the content of a concept is just its reference [Fodor]
Compositionality requires that concepts be atomic [Fodor]
18. Thought / E. Abstraction / 2. Abstracta by Selection
Abstractionism claims that instances provide criteria for what is shared [Fodor]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
'Inferential-role semantics' says meaning is determined by role in inference [Fodor]
19. Language / B. Reference / 1. Reference theories
Co-referring terms differ if they have different causal powers [Fodor]
We refer to individuals and to properties, and we use singular terms and predicates [Fodor]
19. Language / C. Assigning Meanings / 2. Semantics
Semantics (esp. referential semantics) allows inferences from utterances to the world [Fodor]
Semantics relates to the world, so it is never just psychological [Fodor]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
Before you can plan action, you must decide on the truth of your estimate of success [Fodor]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]