Tuesday, April 26, 2011
The Bayesian Grinder
The core problem that the non-empiricist has to explain is how (s)he goes about deciding what to believe. As a Bayesian empiricist, the question is unpleasantly simple. Prior Probability * Evidence = Posterior Probability. As anything but, we're stuck with a problem of how to assign weights to propositions in a non-insane fashion. Any data (sense data, other people's information, books you read) should be taken as data, and fed to the Bayesian grinder. If not, you've either given up on rationality, or you don't get Bayes yet.
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Could you illustrate with an example how would one go about assign weights?
Based on a non-random sample of historical occurrences, I judge my probability of finding that my visual evidence correlates with my tactile evidence to be ~99.9% (+/- 0.099%). Of the cases where I have found that my visual evidence does not correspond to my tactile evidence, about 99% (+/- 0.99%) of those were due to an item being behind water (or another refractive surface like glass), and about 1% were due to deliberate hacking of the senses by people intentionally trying to trick me (for fun or profit). As a base proposition, therefore, I assign a prior probability of 99.99% that if I see an object that I could touch outside of water, that if tried to touch it, something will be available to touch in the position that I see it in. If I do 1-digit Arithmetic problems, I make substantially fewer than 1 mistake in 100, but since I remember making mistakes sometimes, my incidence is clearly above 1 in 10,000. My estimate of my accuracy on my own first response to 6*7 is about 99.97% So...I expect that errors in simple logic occur more often than errors in simple perception. If logic thus disagrees with perception, I should expect on the order of a 3x ratio in favor of perception being right on 1-step simple disagreements. On more complex problems, the preference for perception over logic quickly becomes overwhelming.
All that is given that I was a math prodigy with 20/10 vision. Most folks probably don't do simple math/logic as reliably as I do.
But if one deliberates, then 6*7=42 100% of time, no?
Does empiricism goes together with the Blank Slate?.
Gyan,
1. Fortunately, I have historical math tests. On tests that I had insane amounts of time for (PSAT, long time ago), I finished all the problems, on the math section. Then...I covered my answers, and redid all the problems on the math section. Then...I checked my work a 2nd time. On the 4th run through the test, time was called. None of the math, at that point, was new to me in the past 5 years...it was all old, stable, and easy. And...I missed one. The question:
What is greater? 8*8*8 or 64*4?
On 4 separate tries, over the course of half an hour I got it wrong. And this is human standard.
2. Steven Pinker argues pro-blank slate. He is an empiricist. I am inclined to believe presently that the present scientific evidence weighs against innate ideas, and is therefore at least moderately pro- blank slate. It is NOT a core position, but rather a conclusion.
What does "innate" mean precisely?
I believe that man can grasp truths by his intellect (such as 1+1=2) and reason his way to other truths by constructing chains of ground/consequent relations.
Is it innate position or blank slate position?.
What does a blank slater has to say about 1+1=2?
I'm primarily an educator, and only secondarily an epistemologist.
That's simply not how people-brains work.
I've watched children learn that 1+1=2. I've watched kids NOT learn that 3+3=6 by 7 years old.
Kids learn 1+1=2 by experience, and ONLY by experience. Furthermore, it is ONLY after 20+ years of experience with 1+1=2 that you can forget that it was observed first, confusing for a while, and then sufficiently regular that you concluded that it was true. This notion of grasped truths...either I misunderstand it...or it's nonsense on stilts.
I continue to recommend to you Montessori's work on learning math.
Blank Slaters are a specific subgroup of experimental psychologists who argue that our mind contains no innate ideas. It may contain structures (a language center)...but it is natural world input that feeds the brain.
Fundamentally...the radical empiricist (like me) tends to think that the structure of the human mind makes A LOT of sense when understood as something bootstrapped entirely from sensory input and evolved brain structure.
May I ask where the blank-slate questions are coming from? That's a part of a position inside the empiricist space.
Kids learn 1+1=2 by experience, and ONLY by experience.
Do you believe 1+1 could conceivably be something else ?
Gyan,
I believe your question hides the biggest mistake ever made in philosophy...the notion that imagination is a relevant guide to reality.
No...I don't understand how 1+1=2 could be different. Nor do I understand how gravity could be different (g~=G*M1*M2/d^2).
"Were we to fully understand the world, then the law of gravity would be as necessary as 1+1=2"
This is, I think, position of the physicists that seek Theory of Everything.
Detractions of this view exist. And given that TOE does not exist, we conclude that law of gravity is contingent.
There's multiple lines of argument here...
1. Could gravity be different? I don't know. Do you? On what grounds do you assume it could be different since you don't know? Imagination? I'm not impressed.
2. Why does what we imagine to be possible have anything to do with anything?
1+1=2 is, to me, among the most certain claims I know how to make...99.9999+%. Up there with reality exists.
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