Logic and Reasoning Flashcards

Flashcards for reviewing key concepts in logic and reasoning.

Hypothetico-Deductive Method

A method in science and everyday reasoning where a hypothesis is tested by deducing an observational prediction and determining if it is borne out.

Auxiliary Hypotheses

Implicit assumptions needed for a conclusion when testing a hypothesis. Examples include proper testing conditions and theoretical background knowledge.

Alternative Hypotheses

A rival hypothesis that could also explain the same observational prediction as the main hypothesis.

Prior Probability

The probability that a hypothesis is true before considering any test of that hypothesis.

Crucial Experiment (experimentum crucis)

A test that favors one of two competing hypotheses and definitively rules out the other.

AD HOC Revision

An arbitrary change made solely to save a hypothesis from unfavorable experimental results, without independent testability or new predictions.

Conditional Arguments

A compound sentence where the truth of one clause (the consequent) is conditional on the truth of the other (the antecedent).

Antecedent

The part of a conditional statement that follows "if"; expresses a condition that must be met.

Consequent

The part of a conditional statement that follows "then"; expresses the outcome if the antecedent is true.

Truth Functional Connective

The truth of the conditional is determined by the truth of its component sentences.

Modus Ponens

Affirming the Antecedent: If P then Q, P, Therefore Q

Modus Tollens

Denying the Consequent: If P then Q, Not Q, Therefore not P

Fallacy of Affirming the Consequent

Premises can be true and yet conclusion false. If P then Q, Q, Therefore, P

Fallacy of Denying the Antecedent

Premises can be true and yet conclusion false. If P then Q, Not P, Therefore, not Q

Disjunctive Syllogism

P or Q, Not P, Therefore, Q

Hypothetical Syllogism

If P then Q, If Q then R, Therefore, If P then R

Constructive Dilemma

P or R, If P then Q, If R then S, Therefore, Q or S

Destructive Dilemma

If P then Q, If R then S, Not Q or not S, Therefore, not P or not R

De Morgan’s law

~(p * q) = ~p v ~q, ~(p v q) = ~p * ~q, p * q = ~(~p v ~q), p v q = ~(~p * ~q)

Tautology

A structure which is always logically true–it has all truths in the truth table.

Self-Contradictions

A structure which is always logically false–it has all falses in the truth table.

Corresponding Conditional

Has as its antecedent the conjunction of all the premises and as its consequent the conclusion.

A

Every S is a P (Affirmative Universal Generalization)

E

No S is a P (Negative Universal Generalization)

I

Some S is a P (Affirmative Particular Generalization)

O

Some S is not P (Negative Particular Generalization)

Contradictory

If one True the other is False.

Contrary

Both sentences cannot be True, but both can be False.

Subcontrary

Could both be True, but cannot both be False.

Existential Import

Assuming that [SiP & SoP] have true things and some things don’t exist.

Quality

Whether the sentence is “affirmative” (A & I) or “negative” (E & O).

Complement

The complement of a class is the class of all things that are not the original class.

Obversion

Process that produces a logically equivalent sentence; can be used for AEIO. eg. Change quality of sentence and Change predicate term, P, to its complement, non-P

Contraposition

Process that produces a logically equivalent sentence; can be used for A & O only. Switch subject and predicate terms (P ←→ S) and Change both S & P to their complement (eg. S ←→ nonS)

Conversion

Process that produces a logically equivalent sentence; can be used for E & I only. Switch S and P

Categorical Syllogism

3 terms occur. The “middle term” (“M”) occurs once in each premise; the “end terms” appear once in a premise.

Fallacy of Distributed Middle

M distribution repeats.

Distribution

What the sentence is trying to say about every member in a class.

Quasi-Syllogism

Has one universal categorical premise and a second premise that is a singular sentence.

Relational Logic

Validity of arguments depends on formal properties of relationships.

Transitive Properties

if a stands in a particular relation to b, and b stands in that same relation to c, then a also stands in that relation to c.

Intransitive

if a stands in a particular relation to b, and b stands in that same relation to c, a cannot stand in the relation to c–it is ruled out.

Nontransitive

if a stands in a particular relation to b, and b stands in that same relation to c, then it is an open question whether a stands in that relation c (it either could or could not).

Symmetric

if a stands in a particular relation to b, then b also stands in that same relation to a.

Asymmetric

if a stands in a particular relation to b, then b cannot stand in that relation to a.

Nonsymmetric

if a stands in a particular relation to b, then it is an open question whether b stands in that relation to a.

Reflexive

a relationship a thing does have to itself.

Irreflexive

a relationship that a thing cannot have to itself.

Nonreflexive

an individual may or may not bear such a relation to itself.