In more general terms, Vlastos phrases the Socratic fallacy as the following: "If you do not know what the F is, you will not know if you are predicating "F" correctly about anything whatever-- you will not know if anything is F" (Vlastos 69). As an example, if you do not know what the beautiful is, then you cannot know whether someone is beautiful (Vlastos 69).
Vlastos provides an argument made by other analytic ancient philosophy scholars (such as Myles Burnyeat) which he refers to as STB. The TB part of the acronym stands for "true belief" and it hinges upon the idea that even if one does not know something, a true belief is sufficient for acting as though they know it. As such, Socrates can maneuver around such a fallacy by saying that even though he doe snot know what a friend is, he has a true belief about it which allows him to call a particular individual a friend (Vlastos 72-73). Arguing based on the work on the different types of knowledge from his previous essay, Vlastos explains that Socrates not only asserts that he has moral knowledge, but also that such moral knowledge is required for being noble and living any semblance of a good life and true beliefs cannot possbily suffice (Vlastos 73).
After a series of arguments, Vlastos proposes an alternative solution: the Socratic fallacy is not Socratic but mathematical. He contends that the influence of mathematics upon Plato's work (notably in the Meno) provides the first introduction of this fallacy and that the fallacy is a perfectly logical statement in geometry (Vlastos 85). He argues that those works which fall directly in the Socratic period, as he calls it, where he believes that Plato represents Socrates' thought, do not include this fallacy while those after the influence of mathematics do include such a fallacy .
- Vlastos discusses the example which appears during a discussion of τό φίλον which Vlastos renders "the dear" (Vlastos 68-69) The concept is a difficult one to translate into English, but it generally expresses love of the type that one would have for friends or family rather than a romantic partner.
- The fallacy is then accounted for by what Vlastos refers to as "the wildest flight on which Plato's metaphysical imagination ever took off" (Vlastos 79), or the theory of recollection in the Meno.
- I discuss dates extensively in "Dates in the Platonic Corpus," and more specifically in the first installment with an alternative scheme proposed in the third installment.
- My supposition is that the implicit notions about justice and understanding partially come from the community, which is why Socrates does not leave Athens except for military service (or at least part of the reason).