Matt Faunce
7/7/2011 4:21:00 PM
On Tuesday, July 5, 2011 10:33:28 AM UTC-4, Matt Faunce wrote:
>
> This reminds me of C.S. Peirce's defense for inductive
I had this ready to go. So here it is.
C. S. Peirce's metaphor for science's corrective process:
To figure out the cube root of 2:
Start with any three numbers. (ex. 1, 0, 1)
Add the last two;
Triple the sum;
Add the product to the second from last number.
At any point divide a number by the next in the column;
Add 1 to get the answer. The farther down, the more accurate the answer.
1
0
1 + 0 = 1) (1 * 3 = 3) (3 + 1 =)
4 + 1 = 5) (5 * 3 = 15) (15 + 0 =)
15 + 4 = 19) (19 * 3 = 57) (57 + 1 =)
58 + 15 = 73) (73 * 3 = 219) (219 + 4 =)
223 + 58 = 281) (281 * 3 = 843) (843 + 15 =)
858 (etc)
3301
12700
3301/12700 + 1 = 1.2599213
More accurate answer = 1.25992104989
Error = +.0000002+
Same computation but with a mistake (!) in the fifth number:
1
0
1 + 0 = 1) (1 * 3 = 3) (3 + 1 =)
4 + 1 = 5) (5 * 3 = 15) (15 + 0 =)
16! + 4 = 20) (20 * 3 = 60) (60 + 1 =)
61 (etc.)
235
904
3478
13381
3478/13381 + 1 = 1.25992078
More accurate answer = 1.25992104989
Error = -.0000002+
This is Peirce's analogy for inductive reasoning in science. The first three numbers taken at random represent false premises. Examples, Earth must be the center of the solar system; orbits must be perfect circles, etc. This method of computation represents inductive reasoning in science. The error represents errors in measurement, computation or inference in science. The process of induction, over time, corrects the errors of premises and errors in the process.
C. S. Peirce, in The First Rule of Logic, from The Essential Peirce, vol. 2, pg. 43:
This calls to mind one of the most wonderful
features of reasoning, and one of the most important
philosophemes in the doctrine of science, ...
namely, that reasoning tends to correct itself, and
the more so the more wisely its plan is laid. Nay, it
not only corrects its conclusions, it even corrects
its premises. The theory of Aristotle is that a necessary
conclusion is just equally as certain as its premises,
while a probable conclusion somewhat less so. Hence,
he was driven to his strange distinction between what
is better known to Nature and what is better know to
us. But were every probable inference less certain than
its premises, science, which piles inference upon
inference, often quite deeply, would soon be in a bad way.
Every astronomer, however, is familiar with the fact that
the catalogue place of a fundamental star, which is the
result of elaborate reasoning, is far more accurate
than any of the observations from which it was deduced.
It's natural to induce conclusions. We do it all the time, because it works.. To think we're supposed to know better, i.e., to know that deductive reasoning is the only good reasoning, is indeed strange!
All this because you used the word rhetoric, which I think you got from Aristotle. Also, this is for all the so-called "critical rationalists" out there, and people who fancy themselves as logical but who really simply prefer one type of mistake over another.
I'd say in the evolution of psychology we're at about where 4/16 is in Peirce's analogy. Error of -.01 ain't bad.
Matt