PHI 210 Final Exam Vocabulary Study Guide

Comprehensive vocabulary flashcards covering vagueness, inductive logic, inductive paradoxes, and the lottery paradox for the PHI 210 final exam.

Sorites Paradox

Also known as the Paradox of the Heaps, it is a paradox of vagueness that arises from predicates without sharp boundaries.

Vague predicate

A predicate that admits of borderline cases and lacks a sharp boundary between its application and non-application.

Borderline case

A case where it is unclear whether a vague predicate applies or does not apply.

Principle of excluded middle

The logical principle stating that for every proposition, either that proposition or its negation is true.

Principle of bivalence

The principle that every statement has exactly one of two truth-values: true or false.

Indeterminate (indefinite)

A status in three-valued propositional logic where a statement is neither definitively true nor definitively false.

Universal generalization

A statement that claims a certain property applies to every member of a specific class or set.

Statistical generalization

An inductive argument that generalizes a property from a sample group to a larger population based on probability.

Method of agreement

A method of induction used to identify a cause by looking for a single common factor present in all occurrences of a phenomenon.

Method of disagreement

An inductive method used to identify a cause by comparing cases where the phenomenon occurs with cases where it does not, looking for a differentiating factor.

Method of concomitant variation

An inductive method that identifies a causal relationship by observing how changes in one factor correlate with changes in another.

Method of residue

An inductive method that identifies a cause by subtracting the effects of known causes from a total phenomenon.

The Raven Paradox

An inductive paradox, also known as Hempel's Paradox, regarding what constitutes evidence for a universal generalization.

Nicod’s Criterion

The principle that a universal generalization is confirmed by its positive instances.

Equivalence Criterion

The logical principle that if two statements are logically equivalent, then anything that confirms one also confirms the other.

Accidental generalization

A true generalization that does not express a law of nature and is not considered law-like.

Grue

A predicate introduced by Nelson Goodman to illustrate the New Riddle of Induction, commonly defined as an object that is green if observed before a certain time and blue if observed after.

Bleen

A companion predicate to grue, typically defining objects that are blue if observed before a certain time and green if observed after.

Discontinuity objection

An objection to Goodman's Goodman's Paradox focusing on the temporal or spatial breaks in the definitions of predicates like grue.

Integration-with-science objection

An objection to Goodman's paradox arguing that law-like generalizations must integrate with established scientific theories.

JTB analysis of knowledge

The traditional philosophical definition of knowledge as justified true belief.

Gettier cases

Thought experiments that provide counterexamples to the JTB analysis by showing cases of justified true belief that do not intuitively count as knowledge.

Closure Principle

The principle that if a person knows $P$, and knows that $P$ implies $Q$, then that person also knows $Q$.

Conjunction Principle

The principle that if one is justified in believing $P$ and justified in believing $Q$, then one is also justified in believing the conjunction $P ext{ and } Q$.

Wang's Paradox

A sorites-style paradox applied to numbers: 0 is a small number; if n is small, then n+1 is small; therefore every number is small. It highlights how vague predicates like "small" resist sharp numerical boundaries.

Sharp Boundary

A precise cutoff point that separates the things a predicate applies to from those it does not. Vague predicates are said to lack sharp boundaries — there is no single grain of sand whose removal turns a heap into a non-heap.

Truth Value

The semantic status assigned to a proposition — classically either true or false. In three-valued and intuitionist logics, a third value (e.g., indeterminate) may be admitted to handle borderline cases.

Proof

A finite sequence of statements in which each line is either a premise or follows from earlier lines by a valid inference rule, culminating in the conclusion. Proofs establish that a conclusion is guaranteed by the logical system.

Inference Rule

A syntactic rule that licenses moving from one or more statements (premises) to a new statement (conclusion). Examples include modus ponens ("If P then Q; P; therefore Q") and conjunction introduction.

Existential Generalization

A statement asserting that at least one member of a domain has a certain property (e.g., "Some ravens are black," symbolized ∃x Rx). Contrast with a universal generalization, which makes a claim about all members.

Immediate vs. Distant Causes

An immediate cause is the cause that directly and proximately produces an effect (the last link in the causal chain). A distant cause is an earlier, more indirect cause that sets the causal chain in motion but does not act directly on the effect.

Explicit vs. Implicit Causal Sentences

An explicit causal sentence uses a causal connective overtly (e.g., "The spark caused the fire"). An implicit causal sentence conveys causation without a causal term (e.g., "The spark ignited the fire" — the verb implies causation).

Singular vs. General Causal Sentences

A singular causal sentence concerns a specific causal relationship between particular events (e.g., "This match caused this fire"). A general causal sentence expresses a causal regularity across types of events (e.g., "Smoking causes cancer").

Comparative Causal Sentences

Sentences that express causation in terms of degree or relative contribution (e.g., "Fertilizer A causes more growth than fertilizer B"). They compare the causal strength or efficacy of two or more factors.

Joint Method

One of Mill's Methods combining the Method of Agreement and Method of Disagreement: the suspected cause is present in all cases where the effect occurs, and absent in all cases where it does not. Convergence of both methods strengthens the causal inference.

Inductive Paradoxes

Puzzles that reveal internal tensions in principles of inductive reasoning. The two main ones in this course are the Raven Paradox (Hempel's paradox about confirmation) and Goodman's Paradox (the "grue" problem about projectibility of predicates).

Positive vs. Negative Instance

A positive instance of a universal generalization "All Fs are G" is an object that is both F and G (confirming evidence). A negative instance is an object that is F but not G (disconfirming evidence). Non-F objects are neither positive nor negative instances — though the Raven Paradox complicates this.

Prediction

In the context of confirmation theory, a statement about an as-yet-unobserved case that is derived from a hypothesis. Successful predictions are taken to confirm the hypothesis that generated them.

Confirmation

The evidential relation in which an observation supports or raises the probability of a hypothesis. A key question is what counts as a confirming instance — a question at the heart of both the Raven Paradox and Goodman's Paradox.

Law-like Generalization

A generalization that supports counterfactual conditionals and is projectable to unobserved cases (e.g., "All copper conducts electricity"). Contrasted with accidental generalizations, which happen to be true but lack nomological (law-like) force.

Enumerative Inductive Argument

An argument that moves from observed instances to a universal (or statistical) generalization: "All observed Fs have been G; therefore, all Fs are G." The strength of the argument depends on the number, variety, and representativeness of the observed cases.

Color

In Goodman's framework, a term like "green" or "blue" whose extension is determined by straightforward physical properties (e.g., wavelength). Color predicates are projectible — we can reasonably use them in inductive generalizations.

Grulor

A Goodman-style predicate analogous to "grue," applied to a different domain (e.g., sound or shape) to illustrate that the grue problem is general. It is defined by a time-indexed disjunction, making it non-projectible for the same reasons as "grue."

Complexity Objection

An objection to Goodman's "grue" predicate arguing that "grue" is more complex than "green" (since its definition requires reference to a time and a disjunction), and that simpler predicates should be preferred for inductive projection. Goodman challenges whether complexity alone can do the required work.

Integration-with-Science Objection

An objection to "grue" arguing that it fails to mesh with the established vocabulary and laws of science (e.g., physics explains color in terms of wavelength, not "grulength"). Projectible predicates are those that integrate smoothly into our best scientific theories.

Wavelength

The physical property — the length of a light wave — that grounds our ordinary color predicates. "Green" picks out objects reflecting light of a certain wavelength range, which is why "green" is scientifically integrated and projectible.

Lavewength

A Goodman-style analogue of "wavelength," defined by a time-indexed disjunction (like "grue" is to "green"). It illustrates that even apparently physical-sounding predicates can be constructed to be non-projectible, challenging the idea that scientific vocabulary alone solves Goodman's problem.

Principle of Certainty

The epistemic principle that knowledge requires certainty — you only know P if you are certain that P. Applied to the Lottery Paradox: since you cannot be certain your ticket will lose, you cannot know it will lose, even with very high probability.

Principle of High Probability

The principle that a belief is justified (or counts as knowledge) if its probability is sufficiently high — even if not certain. This seems intuitively reasonable but leads to the Lottery Paradox: it would license "knowing" your ticket loses, yet also "knowing" some ticket will win.

HIV Paradox

A paradox structurally similar to the Lottery Paradox: if high probability suffices for justification, then a patient with a positive HIV test (even a very accurate one) could be said to "know" they have HIV — but also, given base rates, might "know" they don't. It exposes tensions in applying the Principle of High Probability to medical reasoning.