The three classical constraints on a formed sentence.
Status: Working notes Faith & Logic Published August 29, 2026 Updated October 5, 2026
If First Principles named why an argument must stop somewhere, this page names the three stops that belong to the sentence itself. The later name is the laws of thought: identity, non-contradiction, and excluded middle. Aristotle did not print that trio as a table of contents. He argued non-contradiction as the firmest principle. Identity and excluded middle sit beside it in the later list. This page treats the three together because that is how they are now named. It does not pretend Moses or Paul printed the list.
A law here is not a statute and not a mood. It is a constraint: if you violate it, you no longer have a testable claim. You have noise, a change of subject, or an unfinished sentence.
Formulation. A thing is what it is. A is A. In a given sense and context, the term must keep its meaning long enough to be tested.
Identity is not the claim that nothing changes. A man may be a carpenter in one respect and Messiah in another. Identity forbids using one spelling as if it were one term when the sense has moved.
Common mistake. Treating a tautology (A is A) as empty. The law is empty only if you never use words. The moment a word must survive from premise to conclusion, identity is doing work.
Nearby errors. Equivocation: the same letters, two senses, counted as one term. Four-Term Fallacy: the same leak inside a syllogism that may only carry three terms.
Formulation. The same thing cannot at the same time belong and not belong to the same thing in the same respect. Not both A and not-A. Aristotle, Metaphysics IV (Gamma) 1005b19–20. He calls this the firmest principle. It operates at more than one level: what can be, what can be believed, and what a sentence can mean.
You cannot deny it without using it. The man who says “contradictions are fine” has said that this claim, and not its denial, is the one he wants heard.
Common mistake. Dropping “in the same respect.” Without that clause, ordinary distinctions look like contradictions, and real contradictions hide inside a fog of “it’s complicated.”
Calculation. If P and not-P are asserted in the same sense, the conjunction has probability 0. No extra emphasis raises that number.
Metaphor. A scale that reads both eight pounds and not eight pounds at once is not a second kind of weight. It is a broken scale.
Nearby tool. Reductio grants a claim, follows only what it requires, and asks whether P and not-P appear. The method has its own page. The law it leans on lives here.
Formulation. For a well-formed claim, either it holds or its denial holds. A or not-A. Later Latin: tertium non datur — no third is given.