Language & Definition

This is Unit Two of Logic: Language and Definition. Unit One gave you the skeleton of an argument. This unit deals with what happens before any of that machinery can run, because an argument made of slippery words cannot be tested at all — it can only be argued about. Words fail in a small number of specific ways, and each has a name and a fix. A word can carry an attitude alongside its content. It can hold several meanings. It can hold one meaning with no clear edge. And a definition offered to settle any of that can itself be built badly, in ways this unit will let you grade. The unit closes on a genuinely useful skill: telling a disagreement about the world from a disagreement about a word, when the second one feels exactly like the first from inside it. By the end you will be able to do five things. One: separate what a word reports from what it makes you feel, before you evaluate anything. Two: tell ambiguity from vagueness, and say which one a given term has. Three: name the five kinds of definition, and say what each one can be graded on. Four: test a definition for letting the wrong things in, shutting the right things out, and leaning on itself. Five: recognise a verbal dispute and dissolve it, without pretending anyone won.

Start with something a word does that has nothing to do with information. Alongside whatever it reports, a word can carry an attitude — approval or contempt, built right into the vocabulary. Arguments run on the reporting part, so the first move is separating the two.

The two jobs a word does at once.

Logic 041 Cognitive vs. Emotive Meaning

Call someone careful with money thrifty and you approve; call the same behaviour cheap and you sneer. Identical conduct, opposite verdicts, delivered by word choice alone.

A term can fail in two quite different ways, and confusing them leads to the wrong repair. One kind of failure means the word has several distinct senses. The other means it has one sense that never resolves at the edges. Different faults, different fixes.

The first fault.

Logic 042 Ambiguity

Riverside, or financial institution — surrounding sentences normally settle which. The damage happens when the sense quietly changes partway through an argument.

It can live in the word or in the grammar.

Logic 043 Lexical vs. Syntactic Ambiguity

Consider the sentence about flying planes being dangerous. Nothing is wrong with any individual word; the sentence structure itself permits two readings, and that has its own fallacy waiting later.

The second fault.

Logic 044 Vagueness

Six foot four is tall and nobody argues. Five foot nine is where the word stops working — and no discovery settles it, because there is nothing there to discover.

Telling the two apart.

Logic 045 Ambiguity vs. Vagueness

Weight or illumination is a choice between two clean senses. Wealth is one sense with no line in it. A term can manage both faults at once — consider what "fast" does.

Before grading definitions, two pieces of vocabulary. Every term has two aspects that can come apart, and every definition has two halves that do different work.

The two aspects of a term.

Logic 046 Intension and Extension

One side is the set of conditions a thing must satisfy; the other is everything that actually satisfies them. A word can collect nothing at all and still state its conditions perfectly — think of unicorns.

The two halves of the sentence.

Logic 047 Definiendum and Definiens

One half names the word under discussion; the other half is the wording put forward to explain it. That second half is language talking about language, which is exactly why it can be graded.

Five kinds, and the useful thing is not the list but the question that goes with it: what would it even mean for this definition to be wrong? The answer changes completely from one kind to the next, and one of the five is not really a definition at all.

The first kind.

Logic 048 Stipulative Definitions

A study announcing what counts as a heavy user is not reporting anything, so it cannot be mistaken. It can still be pointless, loaded, or abandoned halfway through the argument.

The second reports.

Logic 049 Lexical Definitions

Because it claims something about usage, it can be right or wrong. Reference books record how people speak rather than ruling on it, so appealing to one settles less than people imagine.

The third draws a line.

Logic 050 Precising Definitions

Ordinary usage has no threshold for blindness; a statute needs one, so it names an acuity. Where that threshold sits was chosen, and can be defended or attacked — never discovered.

The fourth carries a theory.

Logic 051 Theoretical Definitions

Explaining heat by molecular motion is physics wearing a definition's clothing. These live and die with the science behind them, as the phlogiston account of burning did.

And the fifth is not really a definition.

Logic 052 Persuasive Definitions

Define taxation as forcible confiscation and the debate has been decided before anyone speaks. The test: would accepting this wording alone settle the live dispute? Then it is doing argument's work without argument's labour.

Now the construction techniques. One is far stronger than the others and takes the grading in the next topic seriously. Two more are genuinely useful inside their range and badly overreached outside it.

The strongest technique.

Logic 053 Definition by Genus and Difference

Put the thing in a category, then say what marks it off from everything else in that category. Ice goes in the category of water, marked off by being frozen. That is the whole move.

Pointing, and listing.

Logic 054 Ostensive and Enumerative Definitions

One shows an example; the other names the members. Pointing is wildly underspecified — gesture at a rabbit and nothing tells your listener whether you meant the animal, the species, or the fur.

Defining by procedure.

Logic 055 Operational Definitions

One mineral counts as harder when it marks the other. Precise where the procedure runs, and silent everywhere else — which is the whole limitation.

Two standard failures. The first comes in a matched pair, and the pairing matters, because repairing one half is the most reliable way to produce the other.

The matched pair.

Logic 056 Too Broad, Too Narrow

Define a bird as an animal that flies and bats walk straight in while penguins are turned away. One wording, both failures at once — so always run both checks.

The second failure.

Logic 057 Circular Definitions

Explaining a logician as someone who does logic helps nobody who needed the explanation. The loop can also run through two definitions instead of one, where it is far harder to see.

Grading a definition in order, and the order matters because the first step decides which of the later tests even apply. One kind of definition is exempt from the broad-and-narrow tests entirely, and knowing why is the point of the procedure.

Watch three get graded.

Logic 058 Evaluating a Definition

Name the kind first. Then hunt for things it wrongly admits — furniture with four legs includes tables. Then things it wrongly excludes, then loops, then wording doing argumentative work. A definition announcing a usage cannot be too broad, because it never claimed to report one.

The unit's most useful idea, and the reason it comes last: a great many disagreements are not about the world at all. They feel exactly like the ones that are, and there is a clean test for telling.

The distinction, and the test.

Logic 059 Verbal vs. Factual Disputes

Whether a hot dog counts as a sandwich turns on a word; whether the freezer is below zero turns on the freezer. The tell is agreement — when both sides already accept every fact, the fight is over vocabulary.

The unit closes on a disagreement people actually have. Two people argue over whether graffiti counts as art. Establish that they agree on everything that happened, and then find what is left.

The capstone. One dispute, taken apart.

Logic 060 Capstone: Dissolving a Verbal Dispute

First confirm they agree on the facts: who painted, with what, when, and whether permission was given. Then separate the part turning on a word from the part where they genuinely differ. Dissolving a dispute is not the same as declaring a winner.

Five things you can now do. You can separate what a word reports from the attitude it carries, and strip the charge before you evaluate anything — thrifty and cheap describe one behaviour. You can tell ambiguity from vagueness: several crisp senses against one sense with no edge, and you know a single word can suffer both. You can name the five kinds of definition and say what wrong would mean for each — a stipulation cannot be mistaken, a report can, and a persuasive one is a verdict in disguise. You can grade a definition: what it wrongly admits, what it wrongly excludes, whether it loops, and whether its wording is doing argument's work. And you can spot a dispute that is really about a word — both sides agreeing on every fact is the tell — and dissolve it without pretending anyone was refuted.