philosophy

16 June 2020

Stewart Notes, 01 of 02 c. 2020

Chapters 3 & 4 from Elements of Knowledge; Pragmatism, Logic, and Inquiry

Philosophy 1370: 01 & 02 - Online!

First Summer Session 2020

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Our’s is a course on “knowledge,” so, sooner or later, the subject of “reasoning” has to be taken

up. In these two chapters, we’ll do this from three standpoints: 01) form vs. content, 02) deductive

reasoning in its oldest and most venerable expression, namely categorical syllogisms, and 03) a group

of mistakes or “fallacies” associated with content problems with “relevance.”

Form vs. Content Remember Peirce’s “beans” illustrations of the three forms of reasoning? Here they

are, again. . .

Deduction

Rule: All the beans from this bag are white.

Case: These beans are from this bag.

Result: These beans are white.

Induction

Case: These beans are from this bag.

Result: These beans are white.

Rule: All the beans from this bag are white.

Hypothesis (aka Abduction or Discovery!)

Rule: All the beans from this bag are white.

Result: These beans are white.

Case: These beans are from this bag.

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Now, again, the contents of all three are exactly the same, right down to the punctuation. The

three very different results, namely, certainly with deduction, probability with induction, and new ideas

with abduction, come about because their formal designs, or, the order in which these statements are

exhibited, differ in each case. But now, focus on the first illustration:

Deduction

Rule: All the beans from this bag are white.

Case: These beans are from this bag.

Result: These beans are white.

Read it like this: All the beans in this bag are white. Now you ask me to scoop out a handful of beans.

And you know, with absolute certainty, even before my hand reaches the bag, that the beans I’ll remove

from the bag absolutely must be white. 100% certainty is, literally, at hand.

Now consider again (see “Notes” on chapters1 & 2) this example of deductive reasoning, found

at p. 83 in Elements of Knowledge:

All human beings as mammals (evidence, or “premiss”)

All mammals are warm blooded (evidence, or “premiss”)

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Thus, all human beings are warm blooded (conclusion)

We term this a “categorical syllogism” because 01) it deals with three groups, or “categories,” those

being human beings, mammals, and warm-blooded organisms, 02) “syllogism” is the term used by the

fellow who thought all this up, originally, namely, the ancient Greek philosopher Aristotle (384 - 322

B.C.) And, there’s an ominous importance to such syllogisms, especially in our day and age, still: such

syllogisms, when electrified in the 19th century by Peirce and Alan Marquand, literally produced the

modern computer. This is no exaggeration. If you’ll turn to pp. 96 and 98 in Elements of Knowledge, you’ll

see the wiring diagrams that they developed (ca. 1887), that, though at a very basic level, have defined

modern computing. So, Aristotle’s syllogisms lead, eventually, to the modern computer? Yes, and

without question. These wiring diagrams prove it. All computers are deductive machines. When I was,

by invitation, at the Russian Academy of Science (1997), attempts at building a computing device based

on inductive principles failed.

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Now, let’s delve a bit deeper into why this near-miraculous development was even possible. It

has to do with a special trait of properly organized syllogisms, namely validity. The old technical

definition of a valid deductive argument went like this: valid deductive arguments are formally arranged

such that it is impossible to construct one with exclusively true “premisses” that even once result in a

false conclusion. Makes sense, doesn’t it? If you have this processing procedure, deductive reasoning,

that can guarantee its conclusions as true, then you know that if this guarantee falters even once, the

argument cannot be valid. And here’s the magic combination: deductive arguments with valid formal

designs that are filled in with true premisses only, are termed “sound” deductive arguments. And these

are the ones whose conclusions bear the guarantee of truth.

validity of formal design + all true premisses = sound deductive argument

If there is even the smallest defect in formal design, and/or even the smallest fragment of falsehood (as

in, this isn’t true!!), then the guarantee of certain truth in conclusions, the guarantee that soundness

bestows, is lost. True conclusions may, by accident, emerge from defective, unsound arguments. Please

see the example of an unsound syllogism at p. 84 in Elements of Knowledge. It certainly contains a false

premiss: “All warm-blooded creatures are mammals.” Birds, for example.

But how to know that this example is also invalid? Structure not quite right. To our rescue

arrives a Swiss mathematician, Leonhard Euler (1707 - 1783). With an image, a picture, a diagram, that

makes it plain.

More on this, tomorrow.

-Dr. Stewart

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