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Friday, March 09, 2007

You Don’t Even Know if You Know

Definition: Let SK stand for the skeptical hypothesis that (i) there is nothing more to you than your brain, since your brain was removed from your body some years ago by a team of evil scientists, (ii) you are being kept alive in a vat of nutrients in a laboratory at MIT, (iii) you are connected to an extremely powerful computer that monitors all of your thoughts, (iv) the sense experiences that you have had in the past were all due to electric pulses inside this computer, and (v) the pattern described in (iv) continues to obtain in the present.

When we reflect on SK, we see that for any time T, the perceptual experiences that SK claims that you have at T are exactly the same as the ones that you actually do have at T. In other words, SK predicts all of your perceptual experiences. Moreover, SK explains all of your experiences, in the sense that it proposes a causal account of why they are occurring. There are many other hypotheses that resemble SK in that they have the same predictive and explanatory power, with respect to human perceptual experiences, as our common sense beliefs. An example is Descartes’s hypothesis that each of us is a mere disembodied mind who is being caused to have perceptual experiences by an evil demon. Let us say that all such alternatives to our common sense beliefs are skeptical hypotheses. Descartes pointed out that our intuitive sense that our common sense beliefs count as knowledge is called into question by the existence of these skeptical. There are several ways of interpreting the argument that he used to make a case for this observation. Here’s one:

Premise 1: Your perceptual experiences are the only evidence you have concerning the truth or falsity of propositions about the external world.

Premise 2: For any time T, the perceptual experiences that SK claims that you have at T are exactly the same as the ones that you actually do have at T. In other words, SK predicts all of your perceptual experiences. 2

Premise 3: If a proposition predicts certain events, then those events have no tendency to show that the proposition is false. They are evidence that the proposition is true, not evidence that it is false.

Lemma 1: By Premises 1, 2, and 3, you have no evidence that SK is false.

Premise 4: If you have no evidence that a proposition is false, then you do not know that the proposition is false.

Lemma 2: By Lemma 1 and Premise 4, you do not know that SK is false.

Premise 5: Your common sense beliefs imply that SK is false. Moreover, since it is obvious that this is so, you know that it is so.

Premise 6: If you know a proposition, and you know that the proposition implies a second proposition, then you know the second proposition.

Conclusion: By Lemma 2 and Premises 5 and 6, you do not know that your common sense beliefs are true. Premise 4 is a special case of the more general claim that to know that a proposition about the external world is true or false, one must have evidence that counts for or against the proposition.

Comments

Sparkie,

Not to intrude on your private little perceptual matrix here, but we’ve all seen this movie.  Trinity brings Neo back to life with a kiss, and they get to keep all that cool leather clothing and the 10th degree Black Belt program.

Seriously, when you get some time this weekend, go find a copy of Douglas Hofstader’s book, “Goedel, Escher, and Bach, An Eternal Golden Braid.” It’s long, and not exactly easy to read.  But you should have no problem with it at all.


“Poverty of goods is easily cured; poverty of the mind is irreparable.”

Bat One on March 9, 2007 at 03:12 pm

“Goedel, Escher, and Bach, An Eternal Golden Braid.”

I own it already.


rasberry

Sparkie Arbuckle on March 9, 2007 at 03:22 pm

Its “Gödel” BTW. I read the first 300 pages like 2 years ago. I don’t know nearly enough about math or music to appreciate it fully.


rasberry

Sparkie Arbuckle on March 9, 2007 at 03:26 pm

I own it already.

Sparkie,

Curious.  I should be surprised… but I’m not.

As for the music and math, don’t think of them as “music and math.” That’s not what’s important.  They are merely illustrative areas of interest because both Bach and Goedel (lazy) operated within and beyond the framework of the self-referential.

Escher’s work is easier because of its visual nature, but the basic principle is the same regardless.  I grew up with Bach (my father was a world-class organist with a photographic memory and a penchant for Bach.)

If you’ve read the first 300 pages or so, then the whole concept of self-referential perceptions and expressions is certainly familiar to you.  Interesting.

I’m looking forward to that paper of yours.


“Poverty of goods is easily cured; poverty of the mind is irreparable.”

Bat One on March 9, 2007 at 03:49 pm

Bat
I like the atonal classical composers. Berg.

I like narrative studies, broadly. Memory, narrative, self-reference, spatial processing/neuroscience and consciousness (in consort) is a broad swath I obsessively think about. There’s just alot there you know?? Its mystery. Its good.


rasberry

Sparkie Arbuckle on March 9, 2007 at 04:47 pm

Sparkie,

For the moment, I won’t quibble with you over whether “classical” and “tonal” belong in the same sentence describing the works of the same composer.  We can leave musicological semantics for some other rainy day.

In the meantime, I’m taking my family out to dinner.  I won’t attempt a serious critique of your work without reading it carefully several times.  Later.


“Poverty of goods is easily cured; poverty of the mind is irreparable.”

Bat One on March 9, 2007 at 05:35 pm
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