In De Trinitate (On the Trinity) Augustine tries to refute to position held by some of his contemporaries, that the mind is just another physical body, like air or fire or some other physical thing (Book X, ch 10, paragraph 15-16). That the mind is material is an argument that had been held previously by the Greek atomists Democritus, Epicurus & presumably Leucippus. The popularity of Epicureanism in Rome makes it unsurprising that there would be contemporaries of Augustine that would avow such beliefs. But for Augustine, who wanted to argue for a non-material part of the self, in particular to justify a soul that is imperishable and can ascend into heaven after death, this was unacceptable.
In Augustine's argument, he first asserts 1) the mind is known to itself. But then he notes 2) to truly know a thing is to know the substance of a thing. 3) Thus, we can say that the mind knows the substance of itself. In addition, 4) to know about a thing is to be certain about it. 5) Thus, the mind knows its substance with certainty. We notice, 6) that the mind is not certain that it is a body like air or fire or any other body or even a property of a body. Thus, 7) since the mind knows its substance with certainty and is not certain that it is a body or a property of a body, then it can't be a body or a property of a body.
The big problem with this argument is the premise that the mind knows itself. In the vague sense of know that we usually use, this seems uncontroversial. The mind is that by which we know other things, thus it would seem that the thing which knows would automatically knows itself. But Augustine very precisely defines knowledge as to know the substance and to know with certainty. Thus, if we plug in this definition, when he is making his initial premise that the mind knows itself he is actually saying, "the mind knows its substance with certainty." Step 5, as I labeled it, is not a conclusion from premises, it's merely a restatement of the initial assumption using the given definitions. To say that the mind knows its own substance with certainty is a dubious claim, which I think most people would want to deny.
"Know" in the opening premise is used as a weasel word, used to present what seems like an uncontroversial premise. But then "know" is redefined to present a more radical premise, which Augustine needs in order to prove his final point.
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