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So this essay covers the idea of "antisets," which are such as A, B such that AB = 0 (without A and B being themselves 0). This concept is extended in another essay to talk of antigraphs, which when merged with their antitheses result in a null graph.

How would this play into the theory of epistemic graphs? For it would seem like carrying over the theme into the epistemic domain would mean talking about "antiknowledge." Arguably, it would be like saying that one method of positively knowing something X means negating a state of antiknowledge inside one's judgment/mind: there is, or can be, an epistemic force that actively tries to block our acquisition of some X-samples, and it is necessary to overcome(?) this mental(?) force to know/understand those samples.

On the other hand, that kind of sounds absurd. I appreciate that we might go to an epistemic game theory, or game-theoretic semantics for a logic, or what-have-you, and so we might imagine the antiknowledge factor in terms of a competing agent in an epistemic game, so maybe interpreted in that manner, talk of antiknowledge seems less fantastical.

Is antigraph theory relevant to graph-theoretic epistemology, or is this a case where graphs/related concepts are not relevant to epistemology?

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    One interpretation could be that anti-knowledge is something considered known but false, so it is "annihilated" by the falsifying knowledge, and as a result, we end up knowing nothing other than what we thought we knew we didn't.
    – Conifold
    Mar 6, 2023 at 1:26
  • I've never heard of antiknowledge, but I have some idea of what it could be. Wait, it's quite simple, but then why all this Sturm und Drang? Mar 6, 2023 at 13:31

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Building on the idea of the role of doubt, put forward by Thinkingman, I wonder if there is a meaningful parallel with certain methods in formal options analysis. When deciding between a number of options which have multiple ramifications, one technique is to quantify and weight the anticipated positive and negative impacts of each option, netting off the cons from the pros, with the option having the highest overall score being judged the winner. Another related method might be judging the evidence relating to a hypothesis by quantifying the evidence for the hypothesis as a positive number, and the evidence against as negative, and netting one from the other. In both of the cases I have mentioned, it is possible for the overall result of netting cons off from pros to be zero, signifying the conclusion that your analysis has confirmed that there seems to be no rational way to choose between two or more positions.

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This is arguably a scientific and not a philosophical question. The correct answer would be to say that we simply don’t know since we don’t know how we gain knowledge and assess the truth of it from a neurological perspective and this can probably differ from person to person.

Interestingly, on this topic, perhaps doubt could function as a sort of epistemic force that may block you from knowing the truth. After all, you can doubt anything. Individuals who have a higher propensity to doubt may need to overcome doubt in a “stronger” way to get access to the same true information compared to others. At the same time, doubt can be useful for catching false beliefs. It’s a catch 22.

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  • I am upvoting this answer, although I want to object that any abstract analysis of the concept of knowledge can count as philosophical. Anyway, your considerations about the concept of doubt seem extremely pertinent. There is in paraconsistent negation theory an emphasis on lack-of-agreement as distinct from active disagreement, and so perhaps this distinction can be read off the graph-antigraph distinction, and doubt assimilated to a specific kind of antigraphical function (maybe doubt turns a backflowing edge into a looping edge, "caught on the hook" of the dubious node). Mar 6, 2023 at 1:53

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