The Hypothetico-Deductive Method and Deductive Reasoning

Hypothetico-Deductive Method

Testing hypotheses through observational predictions.

Auxiliary Hypotheses

Implicit assumptions supporting the main hypothesis.

Proper Testing Conditions

Assumptions about functioning instruments and materials.

Theoretical Background Knowledge

Assumptions regarding the correctness of existing knowledge.

Alternative Hypotheses

Competing hypotheses explaining the same prediction.

Prior Probability

Initial likelihood of a hypothesis being true.

Confirmation Arguments

Inductive reasoning supporting a hypothesis's validity.

Falsificationism

Popper's method emphasizing disconfirmation over confirmation.

Modus Tollens

Logical form: If P, then Q; not Q, therefore not P.

Corroborating Evidence

Evidence from serious attempts to falsify a theory.

Inductive Argument

Reasoning from specific instances to general conclusions.

Deductive Argument

Reasoning from general premises to specific conclusions.

Valid Deductive Argument

Conclusion logically follows from premises.

Incompatible Hypotheses

Hypotheses that cannot both be true simultaneously.

Scientific Method

Systematic approach to inquiry and hypothesis testing.

Risky Predictions

Predictions that challenge existing theories significantly.

Ad Hoc Assumptions

Adjustments made to theories to avoid falsification.

Causal Explanation

Explanation accounting for observed phenomena.

Theory Prohibition

A theory's ability to restrict possible outcomes.

Francis Bacon

Philosopher known for scientific method development.

Crucial Experiment

Test favoring one hypothesis over another.

Ad Hoc Revision

Change made to save a hypothesis from refutation.

Main Hypothesis Revision

Modification without new predictions is ad hoc.

Auxiliary Hypothesis Revision

Change not independently testable is ad hoc.

Deductive Reasoning

Logical process of deriving conclusions from premises.

Conditional Argument

Argument containing sentences with conditional relationships.

Antecedent

First clause in a conditional sentence.

Consequent

Second clause in a conditional sentence.

Material Conditional

Truth determined by component sentences' truth values.

Modus Ponens

Valid form: If P then Q; P; therefore Q.

Modus Tollens

Valid form: If P then Q; not Q; therefore not P.

Fallacy of Affirming Consequent

Invalid: If P then Q; Q; therefore P.

Fallacy of Denying Antecedent

Invalid: If P then Q; not P; therefore not Q.

Disjunctive Syllogism

Valid: P or Q; not P; therefore Q.

Hypothetical Syllogism

Valid: If P then Q; If Q then R; therefore If P then R.

Constructive Dilemma

Valid: P or R; If P then Q; If R then S; therefore Q or S.

Material Biconditional

True when both P and Q share truth values.

Truth Functional Connective

Connective determining truth based on component sentences.

Truth Table

Table showing truth values of logical expressions.

Causal Relationships

Connections where one event influences another.

Logical Relationships

Connections based on logical implications.

Punctuation in English

Used to eliminate ambiguity in sentences.

Parentheses in Logic

Used to disambiguate logical expressions.

Main Connective

Indicates the primary logical relationship in a sentence.

Disjunction

Logical operation represented by 'v' (or).

De Morgan's Laws

Rules for transforming logical expressions.

Tautology

A sentence true by its logical form.

Self-Contradiction

A sentence false by its logical structure.

Contingent Sentence

Truth depends on the truth of components.

Corresponding Conditional

Conditional formed from premises and conclusion.

Categorical Syllogism

Argument with two premises involving categorical sentences.

Affirmative Universal Generalization

Every S is a P (type A).

Negative Universal Generalization

No S is a P (type E).

Affirmative Particular Generalization

Some S is a P (type I).

Negative Particular Generalization

Some S is not P (type O).

Square of Opposition

Diagram showing relationships between categorical sentences.

Contradictory Sentences

Negation of one implies truth of the other.

Contrary Sentences

Both cannot be true, but can be false.

Subcontrary Sentences

Both can be true, but cannot be false.

Existential Import

Implication of existence in categorical sentences.

Quality of Sentences

A & I are affirmative; E & O are negative.

Complement of a Class

All things not in the original class.

Truth Table

Tool for determining logical validity.

Obversion

Produces logically equivalent sentences via quality change.

Contraposition

Switches S and P, changes both to complements.

Conversion

Switches S and P for E & I sentences.

Venn Diagram

Pictorial representation of subject and predicate classes.

Shaded Region

Indicates an empty area in Venn diagrams.

Categorical Syllogism

Deductive argument with two premises and a conclusion.

Middle Term (M)

Occurs once in each premise of syllogism.

Floating X

Indeterminate region for X in Venn diagrams.

Truth Function

Validity based on connections in sentential logic.

Transitive Relation

If A relates to B and B to C, then A to C.

Intransitive Relation

If A relates to B and B to C, then A cannot relate to C.

Nontransitive Relation

Open question if A relates to C through B.

Symmetric Relation

If A relates to B, then B relates to A.

Asymmetric Relation

If A relates to B, then B cannot relate to A.

Nonsymmetric Relation

Open question if B relates to A when A relates to B.

Reflexive Relation

A relationship a thing has to itself.

Irreflexive Relation

A relationship a thing cannot have to itself.

Nonreflexive Relation

An individual may or may not relate to itself.

Universal Quantifier

Symbolized as (x), means 'for any x'.

Universal Affirmative

'All S are P' read as 'If S then P'.

Universal Negative

'No S are P' read as 'If S then not P'.

Existential Quantifier

Symbolized as (∃x), meaning 'there exists some x'.

I-type Sentence

Interpreted as 'Some S are P'.

O-type Sentence

Interpreted as 'Some S are not P'.

Relational Predicate

Involves two variables, x and y.

Individual Constants

Lowercase letters a, b, c for specific entities.

Reflexive Relation

Expressed as (x) xRx, meaning x relates to itself.

Irreflexive Relation

Expressed as (x) ~xRx, meaning x does not relate to itself.

Symmetric Relation

If xRy then yRx, meaning relation is mutual.

Asymmetric Relation

If xRy then ~yRx, meaning one-way relation.

Nonsymmetric Relation

If xRy then yRx, but not vice versa.

Transitive Relation

If xRy and yRz, then xRz holds.

Intransitive Relation

If xRy and yRz, then ~xRz holds.

Nontransitive Relation

Neither transitive nor intransitive properties hold.

Distributed Term

Refers to every member of a class.

A-type Sentence

'Every S is a P', subject term distributed.

E-type Sentence

'No S is a P', both terms distributed.