Validity and Truth
Validity and Truth
An argument has two separate places it can fail. Its premises can be false, or its conclusion can fail to follow from them. Those are different failures, and they take different repairs. The pages in this section are about the second one. A page here asks whether the reasoning holds, and it takes the premises as given unless something specific overturns them.
That division decides how these pages are read. Elsewhere in this knowledge base a claim is usually a practice: a study method, or a way of arranging a room. The honest question about a practice is whether it works for a given person, since methods vary by temperament and circumstance. An inference does not vary by temperament. Either the conclusion follows or it does not, and the answer is the same for everyone who reads the argument. So a page here carries no advice about whether the reasoning suits you.
Core takeaways
- An argument can fail in two places: a false premise, or a conclusion that does not follow. These pages examine the second one.
- A premise stands unless a reader can check something that overturns it. The burden sits on the overturning rather than on the confirming.
- A number on one of these pages is almost always a premise inside an argument. Its accuracy is a separate question from whether the conclusion drawn from it follows.
- Reasoning breaks structurally in eight recurring ways, from definitional contradiction to historical counterexample.
- Nine page forms recur, from the defense inventory to the primer, and each one has a way it fails.
- A page here can show that an argument works, or where it breaks. It cannot show that a position is false.
Why the premises are left standing
Stopping to litigate every premise breaks the thing being examined. You cannot test whether a conclusion follows from its premises while you are also pulling those premises apart. So the working rule is that a premise stands unless it is actively overturned by something a reader can check, and the burden sits on the overturning rather than on the confirming.
This is a reading discipline, not a claim that the premises are all true. A conclusion can follow perfectly from premises that turn out to be wrong. An argument that fails on validity is finished regardless of whether its premises were sound. Keeping the two questions apart is what makes either of them answerable.
What a number is doing here
Statistics behave differently here than they do on a technique page. There, a number is evidence for a practice: this method produced that result. Here a number is almost always a premise inside an argument. Its accuracy is a separate question from whether the conclusion drawn from it follows. A figure can be exactly right and license nothing.
The eight ways reasoning breaks
Arguments fail structurally in a small number of ways, and the same few recur across every subject.
Definitional contradiction. The conclusion requires a word to carry two incompatible meanings at once, so the argument cannot be stated without contradicting itself.
Equivocation. A word shifts meaning between the premise and the conclusion. The argument looks valid because the word looks constant.
Precondition failure. A general result is invoked in a situation where the conditions the result depends on are absent. The result is real; the case doesn’t qualify for it.
Correlation offered as causation. Two things occur together and one is treated as producing the other, with no account of direction and no confound ruled out.
Category error. A question of one kind is answered with a method suited to another: an empirical instrument applied to a question that isn’t empirical, or the reverse.
Question-begging. A premise assumes the very thing the conclusion asserts, so the argument moves in a circle and establishes nothing it did not start with.
Reversibility. The argument’s form works equally well against the position advancing it. An explanation that discredits any belief by naming a motive discredits its own.
Historical counterexample. A general claim about how things go is answered with a case where they went otherwise, which caps the claim’s scope rather than refuting it outright.
This list supplies the names. On the pages themselves the break is written out step by step, so the reader watches it happen. A sentence announcing that an argument commits an equivocation asks the reader to take it on trust. An argument shown equivocating can be checked.
The nine shapes an argument page takes
Nine forms recur. Each one does a particular job, and the job decides the shape.
Defense inventory. Take a contested position, enumerate every common defense of it, evaluate each, say which survive. Fails when only the weak defenses are enumerated.
The article. Objections first: three or four arguments against the position, each at full strength. Then a counter-authority, then the position, then a reply to each objection. The oldest of these forms, and the only one where stating the opposition well is structurally unavoidable rather than a matter of good intentions.
Criterion ranking. Order a class of things by one explicitly stated standard, with the standard held apart from your agreement with the items. Fails when the criterion drifts partway down the list.
The puzzle. Pose a case the reader can answer, let their answer surface the concept, name it through the case, enumerate why people get it wrong, and close on a test that discriminates. Fails when the concept is named before the case lands, which spends the case for nothing.
Phenomenon and mechanism. Start from something the reader has already noticed, then supply the causal account. Fails when the mechanism doesn’t actually predict the phenomenon it was built to explain.
Retrospective verdict. What something promised, what it did, and the verdict. Fails when the verdict doesn’t follow from the record just laid out.
Causal chain. How a present condition was produced, each link compounding into the next. Fails on a link that is asserted rather than shown.
Internal critique. Address people who share your goal, credit what they achieved, then show where the shared method failed them. Fails when the credit reads as setup.
The primer. Establish one term in a specific sense so a later argument can proceed. Not an argument itself, which is why it is the shortest of the nine.
What every form has to do
The scope limit comes first. Narrow the claim before defending it, not afterward as a retreat. A reader who knows what is being asserted can weigh it. A reader who finds out at the end has been reading the wrong argument.
State the opposition to a standard, not to a feeling. The test is whether someone holding the position would recognise it and prefer your phrasing to their own. Anything weaker produces an argument against a position nobody holds.
Concede what is earned, and only that. A piece where nothing survives has stopped tracking its material. A concession invented for balance has stopped tracking it too.
Make abstractions checkable. A worked case with real quantities lets a reader test the reasoning themselves rather than take it. The case shows the reasoning working; it does not instruct the reader.
Say what the argument establishes and what it does not. An inference that holds establishes exactly its conclusion and nothing adjacent to it.
What a page here can and cannot settle
A page in this section can show that an argument works, or that it breaks and where. It can show that a defense is weaker than its reputation, or stronger. It cannot show that a position is false. A position can survive every argument currently made for it and still be wrong, and a bad argument for a true claim leaves the claim exactly where it was.
That limit is worth holding onto, because it is what the method buys. An assessment of reasoning is checkable by anyone who can follow the reasoning: no citation, no appeal to who holds what. What the method costs is the ability to settle the question. It never offered that.
How to practice this
- Take an argument you accept and split it into premises and conclusion. Then ask whether the conclusion would still follow if a premise were false. The two questions have different answers.
- Find a number inside an argument you accept. Treat it as a premise rather than as evidence. Notice whether the conclusion follows even when the figure is exactly right.
- Pick a word that appears in both a premise and the conclusion. Check whether it carries the same meaning in both places. A shift there is an equivocation.
- Turn an argument’s form back on the position advancing it. If it works equally well against that position, the argument is reversible.
- Write the strongest version of a position you disagree with. Show it to someone who holds that position. They should prefer your phrasing to their own.
- Before defending a claim you wrote, state its scope limit first. Notice whether you were about to defend something wider than you meant.
Related pages
- Positions: what the owner of these pages actually holds, kept off this page so the method stays a method.
- Worldviews & the Political Order: the map of pages this method governs.
- Racial Egalitarianism - The Disparity Inference: a number as a premise inside an argument, and what it does not license.
- Moral Language as Leverage: an argument used as an instrument is not thereby false; validity and motive stay separate.
Open questions
If a page here cannot settle whether a position is true, what would make the split between the method page and a separate positions note fail?
Sources
The claim, grounds, and warrant analysis is Stephen Toulmin, The Uses of Argument (1958). The warrant is the usually unstated assumption licensing the step from one to the other. The standard for stating an opposing position is Rapoport’s rules as set out by Daniel Dennett in Intuition Pumps and Other Tools for Thinking (2013): re-express the target’s position so clearly and fairly that they would thank you for the phrasing. The objections-first form is the medieval articulus, most fully worked in the Summa Theologiae, where producing the objections was the students’ task and each had to be a valid argument resting on a recognized authority.