phil 210

kill me now hahahahha

TFL argument

any collection of premises together with a conclusion

atomic sentence

every sentence letter with or without connectives is a sentence

inductive

begins with some specificable bare elements and then presents ways to guarantee indefinitely more elements by compounding previously established ones

scope of a connective in a sentence

the subsentence for which that connective is the main logicall operator

ABC

placeholders for ordinary sentences

fancy ABC

placeholders for placeholders, part of meta language

commutative

truth value for A and B is always the same truth value as B and A— same for A or B, A←→B, not A→B because you cannot swap antecedent and consequence without changing sentence meaning

Biconditional truth values

both true or both false

conjunction truth values

only true if both are true

disjunction truth values

only true if at least one is true

conditional truth values

true if A is false or B is true

complex sentence

when a connective helps build a sentence

unique readability

A → (B → C) as opposed to A → B → C

validity

an argument is invalid only if the premises are true and conclusion is false

necessary truth / tautology

true in every case and valuation

TFL equivalence

their truth values agree in every valuation— none with opposite truth tables

TFL entailment

restates validity, every valuation either makes premises false or conclusion true

jointly satisfiable

some valuation makes all true. unsatisfiable— no valuation makes all true

contingent

neither tautology nor contradiction, satisfiable but not necessarily true

predicates

properties and relations, distinguished by n-arity. lowercase. all relations are predicates but not all predicates are relations

names

individual things

proper name

some specific thing

object-variables

FOL, x, y, x

quantifiers

express something about the property

assertoric sentence

H(g) as opposed to H(x), capable of beign true or false

FOL equivalence

2 formulas which are true or false in exactly the same interpretations and with the same variable assignments

FOL term

a potential name- any name a or any variable x

necessary falsehood / contradiction

false in every case / valuation

hypothetical syllogism

A → B

B → C

Therefore A→C

Fallacy of the Undistributed Middle

A → B
C → B

Therefore A →C

Denying the conjunct

-(A and B)

-B

Therefore A

Affirming the consequent

A → B

B

Therefore A

Affirming the Disjunct

A or B

A

Therefore -B

Denying the antecedent

A → B

-A

Therefore -B

Modus ponens

A → B

A

Therefore B

Modus tollens

A → B

-B

Therefore -A

Soundness

guarantees that derivable statements are true in all models

completeness

guarantees that if a statement is true in all models, then it is derivable (provable) in the system.