Definition:Therefore

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Definition

If statement $p$ logically implies statement $q$, then we may say:

$p$, therefore $q$.


The symbology:

$p, q \vdash r$

means:

Given as premises $p$ and $q$, we may validly conclude $r$


So the symbol $\vdash$ is interpreted to mean therefore.

Thus, $p, q \vdash r$ reads as:

$p$ and $q$, therefore $r$.


A fallacy may be indicated by $p, q \not \vdash r$, which can be interpreted as:

Given as premises $p$ and $q$, we may not validly conclude $r$.


Also known as

The symbol $\vdash$ is sometimes called the turnstile symbol (or gate post), and is often (misleadingly) called the assertion sign.


Some older literature uses the symbol $\therefore$ but this is falling out of use.

In contrast to $\vdash$, which is a formal symbol used in proof writing, the $\therefore$ symbol is generally used as shorthand for "therefore," and as such is traditionally classified as a punctuation mark.


Also see


Sources