ForumsWEPRRadical Scepticism

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So I was going to make this the next topic in the Great Debates, but I figured it might be more fun in a more open format. Before getting to the discussion point, I should make a few things clear.

First, radical scepticism shouldn't be viewed as an actual position that philosophers hold. Instead, it is part of the dialectic that any theory of knowledge should be able to address. So if I develop some particular theory of knowledge, one of the desiderata it should meet it to provide an answer to the sceptical challenge.

Second, the sceptical challenge asks whether (and to what extent) we have knowledge. This is not to say that the sceptic is claiming that we don't know anything - that would be ridiculous! Very, very few philosophers would doubt that we know things such as "Triangles have 3 sides" or "Bachelors are unmarried". Instead, the sceptical challenge is focused on knowledge of the world around us - what we might call empirical knowledge.

So here's the sceptical argument:

1) If I know that I have hands, then I know that I'm not a handless brain-in-a-vat.
2) I don't know that I'm not a handless brain-in-a-vat.
3) Therefore, I don't know that I have hands.

This argument can be generalised to encompass pretty much any claim about the world around us (e.g. that I'm sitting here typing and not just a brain-in-a-vat). Here's what that would look like:

1) If I know very much at all, then I know I'm not a BIV.
2) I don't know I'm not a BIV.
3) Therefore I don't know very much at all.

There are a number of ways to attack the above argument(s), which I would like to be the focus of this thread. Rather than throwing a bunch of jargon in here, I'll just see where this thing goes (if anywhere!).

One helpful hint when looking to attack an argument. The two most important questions you have in your philosophy toolbelt are: 1) 'Is the argument valid?', and 2) 'Is the argument sound?'. (Feel free to take a look at my Introduction to Logic thread for definitions of validity and soundness.)

So the basic question: How can we avoid the above conclusion of radical scepticism?

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