** **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 about knowledge, which I am calling ‘skepticism’, ‘falliblism’ and ‘anti-skepticism’. Each argument is derived by having two of the propositions as premises with the negation of the remaining one as the conclusion.

**Skepticism**

The skeptic formulates her argument as follows:

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

P) I do not know that I am not in the matrix

~Q) Therefore, I do not know that X

This argument has the form of modus tollens:

q → p

~p

Therefore ~q

2. **Fallibilism**

In contrast, the fallibilist argues from the truth of P and Q to the falsity of R, i.e.:

P) I do not know that I am not in the matrix

Q) I do know X

~R) Not-(if I know that X, then I know that I am not in the matrix)

This has the form:

~p

q

Therefore, ~(q → p)

What does this rearrangement say? It says that because we do know something, yet we do not know whether we are in the matrix, it follows that knowing that we are not in the matrix it is not a necessary condition for knowledge. Thus one can have knowledge without being able to rule out the skeptical hypothesis.

3. **Anti-Skepticism**

The final combination, the anti-fallibilist (which perhaps represents G.E. Moore?), runs as follows:R) If I know that X, then I know that I am not in the matrix

Q) I know that X

~P) I know that I’m not in the matrix

The form of this argument is modus ponens:

q → p

q

Therefore, p

On this argument, the requirement of ruling out the matrix as a necessary condition for knowledge is accepted, and the fact of knowledge of X is affirmed, with the consequence that one knows they are not in the matrix. A refutation of the skeptical hypothesis has been achieved (hence the name ‘anti-skepticism’).

4. **How to choose? **

So now we have three rival arguments, each of which picks two of the members of the triad and rejects the third. The question of which argument to pick turns then, not on logic as such, but on the question of which proposition to jettison. Which one seems the least plausible? The problem is that they all seem eminently plausible.

P says that you cannot rule out the matrix, or evil daemon hypothesis. It seems very plausible, at least to anyone who has read Descartes or watched the Matrix. Denying this premise seems to require a refutation of skepticism.

Q says that you know that X. This is obviously going to depend on your choice of X, but why not make X as plausible as you like? Let X be ‘it is now 3PM’ (if it is 3PM), or that you are wearing trousers (if you are wearing trousers), etc. It can be the most run of the mill, ordinary knowledge claim you can think of. By definition, Q should be very plausible, if any knowledge claim at all can be. And P, Q and R are all knowledge claims.

R says that if you know that you are walking down the street, or that it is 3PM, or that you are wearing trousers, or whatever, then you know you are not in the matrix. This is also very difficult to deny. If I know that I am walking down the street, then it is true that I am walking down the street. If it is true that I am walking down the street, then I am not in the matrix. Thus, if I know I am walking down the street then I am not in the matrix. Therefore, it seems that if I know that X, then I know I am not in the matrix.

Where is the weak link here?

*for ‘in the matrix’, feel free to substitute in ‘am a brain in a vat’, ‘am being deceived by a Cartesian daemon’, etc.

The problem appears to me that there isn’t a strong coupling between knowing X and knowing that you are not in the he matrix. But then again I’m no logician.

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I would say that R is weak because it doesn’t argue why knowledge about the matrix would differ from knowledge about reality, or even why the matrix doesn’t qualify as reality.

Model dependent realism is the accepted form of materialism in science at least, since the acceptance of quantum physics and it’s concept of sum over histories etc. you can no longer distinguish reality from a model of sufficiently predictive power. Or rather a model independent reality would be every possible state and history and therefore hostile to the concept of knowing things like whether you are wearing trousers, the only way to pin down a reality where it is possible to know something is to create a good model of how the sum over histories and possible states converge statistically to match our macro level observations reliably, and “the matrix” could be that model so it’s not necessarily hostile to the concept of knowledge.

A perfect model of reality would be reality, since our concept of reality is model dependent in the first place.

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I would say that R is weak because it doesn’t argue why knowledge about the matrix would differ from knowledge about reality, or even why the matrix doesn’t qualify as reality.

Model dependent realism is the accepted form of materialism in science at least, since the acceptance of quantum physics and it’s concept of sum over histories etc. you can no longer distinguish reality from a model of sufficiently predictive power. Or rather a model independent reality in the face of these discoveries would simply be every possible state and history and therefore hostile to the concept of knowing everyday things like whether you are wearing trousers, the only way to pin down a reality where it is possible to know something is to create a good model of it in which knowing things makes sense, and “the matrix” could be that model.

In other words a perfect model of reality is reality, since the concept of reality and knowledge are model dependent to begin with you can’t make the claim that knowledge and models are contradictory, it’s rather the case that knowledge outside of a model is a nonsensical concept.

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I would think that the solution to R in moderate fallibilism is simple: reject the notion that “knowledge” requires certainty and instead have it be probabilistic, requiring a certain approximate cutoff point.

Example: Let’s say that it’s 95% and I’m 94% sure of negation of skeptical hypothesis, and it would under that be 50-50 for everyday proposition X.

Then I can be ~97% sure of X. So I don’t know negation of skeptical hypothesis but I do know X.

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