Meaning

Core idea

Before logic can evaluate an argument, the sentences in the argument have to mean something definite. That sounds trivial. It is not. Ordinary language is shot through with ambiguity, vagueness, incomplete expressions, idiosyncratic jargon, and metaphor — every one of which can wreck an inference that would otherwise be valid. The same words can pick out different things in different contexts, two different expressions can pick out the same thing, and some expressions seem to refer only when you know what the speaker has in mind.

The philosophical machinery this topic introduces — sense vs reference, ambiguity vs vagueness, and the discipline of definition — is the bridge from natural-language prose to the formal symbolism that begins in the topic on categorical logic. Every later technique (truth tables, syllogisms, quantifiers) assumes that the sentences being analysed have a fixed, unambiguous meaning. This is the topic that earns that assumption.

Why it matters

The bridge to formal logic

You cannot symbolize what you cannot pin down. If a key term in an argument is ambiguous, the argument may appear valid in one reading and invalid in another — and the speaker can slide between the readings to dodge objections. Most of the informal fallacies catalogued in the next topic are, at root, exploitations of meaning-instability.

Why precision is not pedantry

Asking "what exactly do you mean by X?" is the single most powerful move in real-world argument. It is not nitpicking; it is the operation that surfaces the hidden disagreement.

Mental model

Three ways meaning goes wrong

Most meaning problems in ordinary language fall into three buckets. Ambiguity is one expression with multiple distinct meanings (bank = financial institution or river edge). Vagueness is one expression with one meaning but a fuzzy boundary (tall, bald, happy — how many hairs do you have to lose to be bald?). Incompleteness is an expression that does not specify its full reference (the pub — which pub?).

Copy sourceZoom

Sense and reference — Frege's distinction

Two expressions can pick out the same object yet differ in meaning. The classic case: the morning star and the evening star both refer to Venus, but ancient astronomers did not know they referred to the same thing. The discovery the morning star is the evening star was informative. If meaning were only reference, this identity would be trivial (like Venus is Venus). It is not. So an expression must have both a reference (the thing it points to in the world) and a sense (the mode of presentation, the route by which it points).

Copy sourceZoom

The discipline of definition

A definition assigns a precise meaning to a term. Several kinds exist, each suited to different goals. Lexical definitions report ordinary usage; stipulative definitions invent a new term or fix a technical meaning; precising definitions narrow a vague term for a specific context; theoretical definitions tie a term to a broader explanatory framework. Whichever kind you offer, the same five criteria of a good definition apply.

Copy sourceZoom

Practical application

When an argument turns on a key term, run the term through four diagnostic questions before evaluating the inference:

1. Is the term ambiguous? Does it have two or more distinct meanings? If so, which one is the speaker using? Force a paraphrase.
2. Is the term vague? Does it have a fuzzy boundary? If so, where is the threshold being placed, and is the speaker shifting it between premises?
3. Is the reference complete? Has the speaker specified the domain — "every X" of what kind, in what context?
4. Has the speaker offered a definition? If so, does it meet the five criteria? If not, can you reverse-engineer the working definition from how the speaker uses the term?

This four-pass discipline catches the meaning-shifting that lets bad arguments survive. Many political debates are not really disagreements about facts — they are disagreements about which definition of a contested term (freedom, fairness, democracy) should anchor the rest of the argument.

Example

A workplace conversation:

• Alice: "Our team isn't productive enough."
• Bob: "Productivity has been up 18% quarter over quarter."
• Alice: "I don't mean output. I mean the team isn't producing the right things."

Alice's first sentence used productive ambiguously. Bob picked the natural reading — output per unit time — and produced a fact that refutes the claim under that reading. Alice's second sentence revealed she meant something else: alignment of output with priorities. That is not productivity; it is prioritization.

Now apply the four diagnostic passes:

• Ambiguous? Yes — productive is doing two jobs (volume vs alignment).
• Vague? Also yes, even under Alice's intended reading: how much misalignment counts as "not enough"?
• Complete? No — "not enough" for what goal, on whose standard?
• Defined? No definition offered. Both speakers assumed their own reading.

The fix is not to argue harder about whether the team is "productive". It is to ask Alice to replace the word with the definition she actually means: "the team is shipping a lot, but I am worried we are not shipping the highest-priority items." That sentence is checkable. The original one was not.

Most workplace conflict has this structure — different parties hearing the same word in different senses and arguing past each other for an hour before the ambiguity surfaces. The discipline of definition is what shortens the loop.

Related lessons