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In logical argument and mathematical proof, the therefore sign, ∴, is generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is read therefore. While it is not generally used in formal writing, it is used in mathematics and shorthand.
The second is a link to the article that details that symbol, using its Unicode standard name or common alias. (Holding the mouse pointer on the hyperlink will pop up a summary of the symbol's function.); The third gives symbols listed elsewhere in the table that are similar to it in meaning or appearance, or that may be confused with it;
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
The form of a modus ponens argument is a mixed hypothetical syllogism, with two premises and a conclusion: . If P, then Q.; P.; Therefore, Q. The first premise is a conditional ("if–then") claim, namely that P implies Q.
A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises ...
In the AMS Theorem Environment for LaTeX, the hollow square is the default end-of-proof symbol. Unicode explicitly provides the "end of proof" character, U+220E (∎). Some authors use other Unicode symbols to note the end of a proof, including, (U+25AE, a black vertical rectangle), and ‣ (U+2023, a triangular bullet).
The symbol is definitely not my invention — it appeared in popular magazines (not mathematical ones) before I adopted it, but, once again, I seem to have introduced it into mathematics. It is the symbol that sometimes looks like , and is used to indicate an end, usually the end of a proof.
So in AAI-3, the premise "All squares are rectangles" becomes "MaP"; the symbols mean that the first term ("square") is the middle term, the second term ("rectangle") is the predicate of the conclusion, and the relationship between the two terms is labeled "a" (All M are P). The following table shows all syllogisms that are essentially different.