(This is something I’ve been interested in for a long time and so am sharing in lieu of an actual post. Feel free to elaborate, offer an expansion, or your two cents on this, as I plan to do so in future posts. ~ Henry James Anderson)

** **0.** Introduction**

The following three propositions form an inconsistent triad:

P) I do not know that I’m not in the matrix*

Q) I know that X

R) If I know that X, then I know that I am not in the matrix

(X is to be thought of as a proposition with content about the external world, such as ‘it is 3PM’ or ‘I am wearing trousers’, etc, rather than ‘I believe it is 3PM’ or ‘I am receiving sense-data about wearing trousers’, whose content is *internal* to the subject.)

We can represent the logical form of the propositions as follows, where p = ‘I know I am not in the matrix’, and q = ‘I know that X’:

P) ~p

Q) q

R) q → p

There are three ways that we can formulate an argument using these propositions which generate three positions…

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