Combining Philosophers

All the ideas for Michael Burke, Gordon Graham and E.J. Lemmon

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74 ideas

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
That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon]
That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon]
If A and B are 'interderivable' from one another we may write A -||- B [Lemmon]
We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon]
The sign |- may be read as 'therefore' [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]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon]
Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon]
A 'well-formed formula' follows the rules for variables, , →, ∧, ∨, and ↔ [Lemmon]
'Contrary' propositions are never both true, so that (A∧B) is a tautology [Lemmon]
A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [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]
A wff is 'contingent' if produces at least one T and at least one F [Lemmon]
A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon]
The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon]
A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / c. Derivation rules of PL
∨I: Given either A or B separately, we may derive A∨B [Lemmon]
DN: Given A, we may derive A [Lemmon]
CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon]
∧I: Given A and B, we may derive A∧B [Lemmon]
∧E: Given A∧B, we may derive either A or B separately [Lemmon]
∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon]
RAA: If assuming A will prove B∧B, then derive A [Lemmon]
MTT: Given B and A→B, we derive A [Lemmon]
A: we may assume any proposition at any stage [Lemmon]
MPP: Given A and A→B, we may derive B [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]
De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon]
We can change conjunctions into negated conditionals with P→Q -||- (P → Q) [Lemmon]
The Distributive Laws can rearrange a pair of conjunctions or disjunctions [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]
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
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]
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]
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]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley]
The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman]
Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley]
Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
'Subjectivism' is an extension of relativism from the social group to the individual [Graham]
22. Metaethics / B. The Good / 1. Goodness / g. Consequentialism
Negative consequences are very hard (and possibly impossible) to assess [Graham]
22. Metaethics / B. The Good / 1. Goodness / i. Moral luck
We can't criticise people because of unforeseeable consequences [Graham]
22. Metaethics / C. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
The chain of consequences may not be the same as the chain of responsibility [Graham]
23. Ethics / A. Egoism / 1. Ethical Egoism
Egoism submits to desires, but cannot help form them [Graham]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / h. Right feelings
Rescue operations need spontaneous benevolence, not careful thought [Graham]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
'What if everybody did that?' rather misses the point as an objection to cheating [Graham]
23. Ethics / F. Existentialism / 1. Existentialism
It is more plausible to say people can choose between values, than that they can create them [Graham]
23. Ethics / F. Existentialism / 2. Nihilism
Life is only absurd if you expected an explanation and none turns up [Graham]
23. Ethics / F. Existentialism / 5. Existence-Essence
Existentialism may transcend our nature, unlike eudaimonism [Graham]
23. Ethics / F. Existentialism / 6. Authentic Self
A standard problem for existentialism is the 'sincere Nazi' [Graham]
23. Ethics / F. Existentialism / 7. Existential Action
The key to existentialism: the way you make choices is more important than what you choose [Graham]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
The great religions are much more concerned with the religious life than with ethics [Graham]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Western religion saves us from death; Eastern religion saves us from immortality [Graham]