I · Anatomy
Argument
argumentum · ‘that which is brought forward in proof’
An argument is reasoning made portable. Premises, a conclusion, and the move that joins them. What follows is the standard vocabulary, together with the two principal ways an argument can be appraised.
The parts
Anatomy
Every argument resolves into three components. The first two are propositions; the third is the relation that holds between them.
- Premise
- a proposition offered in support of a conclusion.
- Conclusion
- the proposition the premises are offered to support.
- Inferential move
- the relation between premises and conclusion.
Premises are the inputs of an argument. They may be asserted, assumed for the sake of argument, or derived from a prior step. An argument with no premises has nothing for the conclusion to follow from.
An argument has exactly one final conclusion. Intermediate steps in a longer chain are sub-conclusions — each is itself supported by earlier premises.
Where the premises end and the conclusion begins, an inferential move connects them. The move is governed by a rule — explicit (in formal reasoning) or implicit (in everyday reasoning). The rule is what makes the inference legitimate, if it is.
Canonical example · the Socratic syllogism
- P₁.
- All men are mortal.
- P₂.
- Socrates is a man.
- ∴
- Socrates is mortal.
The appraisal
Validity, soundness, cogency
An argument has two questions to answer: does the conclusion follow from the premises, and are the premises true? The answers compose into the three standards below.
- Validity
- a structural property — premises true ⇒ conclusion true.
- Soundness
- validity plus true premises.
- Cogency
- the inductive analogue of soundness.
Validity is a relation between premises and conclusion: if it is impossible for the premises to be true and the conclusion false, the argument is valid. Validity says nothing about whether the premises are actually true. "All cats are reptiles; Felix is a cat; therefore Felix is a reptile" is valid.
An argument is sound when it is valid and all its premises are true. Soundness is the standard that deductive arguments aspire to. Validity is purely structural; soundness adds the question of fit with the world.
Inductive arguments cannot be valid in the deductive sense — their premises do not entail their conclusions. They are evaluated by cogency: are the premises true, and do they raise the probability of the conclusion to an appropriate degree? Cogency is graded; validity is binary.
Validity is settled by structure alone — see formal logic. Whether the premises are true is the further question that soundness and cogency depend on; that question lives in truth.
The unstated step
Enthymeme
An enthymeme is an argument with a premise suppressed — left tacit because the speaker takes it for granted. Aristotle named the form in the Rhetoric; medieval logicians made it routine. Most everyday arguments are enthymemes.
The example given in the textbooks is Hume's sunrise: “The sun has risen on every observed morning, so it will rise tomorrow.” The argument as stated has one premise and a leap. The suppressed premise — that observed regularities project — is what carries the conclusion. Make it explicit and the argument is deductively valid.
The enthymeme is therefore not a separate kind of argument. It is an argument whose form is masked by rhetorical economy. A long-standing thesis is that every inductive inference is an enthymeme whose suppressed premise is some principle of projectibility — see the publication Induction Reduced.
The richer anatomy
The Toulmin model
Stephen Toulmin's The Uses of Argument (1958) proposed that real arguments — in law, ethics, ordinary discourse — are not adequately described by the premise/conclusion pair. Six components are needed.
- Claim
- The position being advanced. (= conclusion in the bare model.)
- Data (grounds)
- The facts cited in support. (= premises.)
- Warrant
- The general principle that licenses the move from data to claim. (Often the suppressed premise of an enthymeme.)
- Backing
- Whatever justifies the warrant — the body of evidence, tradition, or theory that stands behind it.
- Qualifier
- The strength with which the claim is advanced: presumably, certainly, in most cases.
- Rebuttal
- The conditions under which the claim would not hold — exceptions the arguer is willing to admit.
The Toulmin model is most useful where the bare model is silent: in disagreement, in qualified claims, in arguments whose force depends on a warrant that the parties disagree about. It is informal in method and applies across modes.
Lineage
Where this vocabulary comes from
The premise/conclusion structure descends from Aristotle's Prior Analytics (c. 350 BC), where the syllogism was first systematised. Validity as a structural property is already in Aristotle, though the explicit syntactic characterisation belongs to Frege and the formal-logic tradition of the late nineteenth century.
Soundness and cogency are modern terminological refinements. The enthymeme is named in Aristotle's Rhetoric. The Toulmin model belongs to The Uses of Argument (Cambridge University Press, 1958), and remains the standard alternative to the bare model in informal-logic curricula.