Logic Meme Explained: How Logic Became Formal, From Aristotle’s Syllogism to Truth Tables

Last updated: October 21, 2026

The first logic meme on this page uses the “Scroll of Truth” format: after 15 years of searching, an explorer finds the scroll in a cave, reads it, and throws it away, because the truth turns out to be a truth table for “if P then Q” and “if Q then R”. Logic really did turn truth into tables. Aristotle wrote the earliest formal study of logic we have, according to the Stanford Encyclopedia of Philosophy, but the familiar truth table is usually dated to 1921, when it appeared in Ludwig Wittgenstein’s Tractatus and, independently, in a paper by the American logician Emil Post, more than 2,000 years after Aristotle’s Prior Analytics.

Every cell on the scroll is correct. It lists all eight combinations of true and false for P, Q and R and checks when “P implies Q” and “Q implies R” hold together. Add a column for “P implies R” and it comes out true in all four rows where both conditionals hold, which is exactly why the chain from P to Q to R is a valid argument form. The scroll stops one column short of its own punchline, and the explorer, who wanted the truth, got a table of it.

Aristotle’s Syllogism: Logic as Terms, Not Sentences

Aristotle founded formal logic as the logic of terms: the syllogism links “all”, “some” and “no” statements through a shared middle term, and it has no truth tables at all.

In the Prior Analytics Aristotle defines a syllogism as discourse in which, certain things being stated, something else “follows of necessity from their being so” (Jenkinson translation). His model case is simple: if A is said of all B and B of all C, then A must be said of all C. Medieval teachers later gave the valid forms Latin nicknames, and this one became “Barbara”: its three vowels mark both premises and the conclusion as universal affirmatives (New Catholic Encyclopedia). As the SEP notes, he treated every assertion as a subject and a predicate, joined by affirmation or denial, and made no attempt at a logic of whole sentences linked by “and”, “or” and “if”. A truth table needs exactly that, so calling truth tables “Aristotle’s logic” credits him with something he did not invent, though his laws of thought are built into every row.

Those rules are what later textbooks call the laws of thought. Britannica lists three: the law of contradiction, the law of excluded middle and the principle of identity. In Metaphysics IV Aristotle states the first as the claim that the same attribute “cannot at the same time belong and not belong” to the same subject in the same respect, and adds that “there cannot be an intermediate between contradictories”, which is the excluded middle. He then made trouble for himself in On Interpretation 9 with the sea battle: is “there will be a sea battle tomorrow” already true or false today? The SEP notes that his answer, an apparent exception for statements about the future, is still widely disputed.

Chrysippus and the Stoics Built Propositional Logic

The logic of “if”, “and” and “or”, now called propositional logic, comes from the Stoics, above all Chrysippus of Soli in the third century BC.

The SEP entry on ancient logic calls Chrysippus “the second great logician in the history of logic” and credits the Stoics with a propositional logic built from statements that are either true or false. They listed five “indemonstrable” argument forms, such as: from “if the first, then the second” and “the first”, infer “the second”. Diogenes Laërtius reports that people said if the gods took to dialectic, they would use no other system than that of Chrysippus (Hicks translation). Of Chrysippus’ logical works, the SEP says, only two badly damaged papyri survive, so most of Stoic logic reaches us secondhand, through Diogenes and the sceptic Sextus Empiricus.

The meme’s “P implies Q” column has a Greek ancestor as well. Philo of Megara, according to the SEP, held that a conditional is false only when its antecedent is true and its consequent false. That rule fills the column, including the rows where a false P makes “if P then Q” true regardless. Chrysippus rejected it and demanded a real connection: a conditional holds only if the opposite of the consequent clashes with the antecedent. Modern classical logic adopted Philo’s rule as the material conditional, which is why “if the moon is cheese, then 2 + 2 = 5” counts as true.

Boole’s Laws of Thought: Logic Becomes Algebra

George Boole turned logic into algebra in The Mathematical Analysis of Logic (1847) and An Investigation of the Laws of Thought (1854), with variables that take only the values 0 and 1.

Boole never went to university and taught himself languages and advanced mathematics before becoming, in 1849, professor of mathematics in Cork, Ireland, according to the SEP entry on Boole. In The Laws of Thought (full text on Project Gutenberg) he proposed an algebra in which the symbols admit “of the values 0 and 1, and of these values alone”. The SEP describes his “Rule of 0 and 1” as a truth-table-like method for checking arguments, more than sixty years before the truth table’s usual 1921 debut.

Boolean logic reached the computer through Claude Shannon. His MIT master’s thesis, A Symbolic Analysis of Relay and Switching Circuits, signed in August 1937 (degree awarded 1940), showed that the algebra of switching circuits is “exactly analogous” to the calculus of propositions used in symbolic logic. Open or closed maps onto false or true, and Boole’s name now sits on a data type in many programming languages.

Frege, Russell and the Letter That Broke a Book

Gottlob Frege’s Begriffsschrift (1879) gave logic the quantifier “for all” (with “there is” defined from it plus negation), and with it what the SEP calls, in effect, the first predicate calculus.

Frege’s larger aim, according to the SEP entry on Frege, was to derive arithmetic from logic alone, a project called logicism. On 16 June 1902, as Frege was preparing the proofs of the second volume of his Grundgesetze der Arithmetik, a letter arrived from Bertrand Russell showing that Frege’s system allowed a contradiction. The culprit was the set of all sets that are not members of themselves, which belongs to itself exactly when it does not. Frege answered in an appendix, but the SEP judges that he never fully recovered from the flaw.

Russell and Alfred North Whitehead tried to rebuild the foundations in Principia Mathematica, three volumes published from 1910 to 1913, using a theory of types to block the paradox. It takes its time: in volume I, in the section on “Cardinal Couples”, proposition 54.43 carries the authors’ note that 1 + 1 = 2 will follow from it once arithmetical addition has been defined, and the formal result only arrives in volume II. Kurt Gödel’s incompleteness paper of 1931 named Principia Mathematica* in its title, because it was the system his proof used as its example.

That pace inspired a second logic meme. A pink blob in a box says “I think I like philosophy” and “I want to learn more”, takes a fist to the face labelled “800 pages full of logical operators”, proving that a = a is always true, and hides back in its box: “I like literature”. The slow proof that made Principia notorious is 1 + 1 = 2, whose final steps sit on page 86 of volume II, where the authors remark that the result is “occasionally useful”, as photos from Dartmouth’s Rauner Special Collections Library show. Nobody has to start there, and our guide to philosophy for beginners suggests gentler first books.

Who Drew the First Truth Table? Wittgenstein, Post and Peirce

A truth table lists every combination of true and false for a statement’s parts and shows the truth value of the whole in each row; in its familiar form it entered print in 1921, with Wittgenstein and Emil Post, though historians have found earlier drafts.

The Tractatus first appeared in German in 1921, according to the SEP entry on Wittgenstein, which says it presents logic in what became known as truth tables. In proposition 4.31 Wittgenstein writes that “the truth-possibilities can be presented by schemata” of this kind (Ogden translation), in 4.442 he writes out a full table for “if p then q”, and in 4.46 he names the two extremes: a proposition true in every row is a tautology, one false in every row a contradiction. By those definitions, the last column on the meme’s scroll is neither, with four T and four F.

Post’s “Introduction to a General Theory of Elementary Propositions”, his 1920 Columbia doctoral thesis published in 1921, systematically applied the truth-table method (Dictionary of Scientific Biography), and the same source credits Peirce and Ernst Schröder with introducing the method. Priority is still argued over: John Shosky argued in 1997 for a 1912 sheet in the hands of Russell and Wittgenstein, while Irving Anellis, in a paper on Peirce’s truth-functional analysis, points to a truth-table matrix in a Peirce manuscript dated to 1893. What Wittgenstein did next is in our post on Wittgenstein and linguistic confusion.

Fuzzy Logic: When Something Is Only Sort of True

Fuzzy logic, launched by Lotfi Zadeh’s paper “Fuzzy Sets” in 1965, lets statements be true to a degree between 0 and 1, which makes it a well-known challenge to strictly two-valued logic.

The SEP entry on fuzzy logic describes it as a family of many-valued logics whose truth values are degrees of truth, from 0 (totally false) to 1 (totally true); the idea is older than Zadeh’s paper in Information and Control: Jan Łukasiewicz worked on many-valued logic in the 1920s, Post’s 1921 paper already set up many-valued truth tables, and the SEP dates the logic of Łukasiewicz and Alfred Tarski to 1930. Vagueness is the obvious use: is a man with 40,000 hairs bald? With 39,999? The SEP notes that fuzzy logic can treat a sorites premise such as “one hair less makes no difference” as almost, but not completely, true, which blocks the slide to “everyone is bald”. With the common reading of “or” as the higher of two values, “p or not p” comes out only half true when p is half true, so the law of excluded middle loses its guarantee; the SEP notes it is “not a tautology under any t-norm based interpretation”.

Fuzzy logic extends Aristotle’s toolkit, and the SEP treats mathematical fuzzy logic as a branch of mathematical logic, and classical two-valued logic is still what the meme’s truth table, and standard introductory logic courses, run on. See also our post on where Aristotle contradicted Plato.

If the scroll left you wanting the opposite of valid reasoning, read Five Frustrating Fallacies We Probably All Use.