Freethought & Rationalism Archive

John Page · 03-11-2003, 07:13 AM

I'm on a roll now, coherent or not! Here cometh the third law.

Quote:

The Law of the Included Paradox states "The process of comparing entities may produce a paradox when the implied or stated differences arising from an equality proposition (see Law of Contradiction) are ignored or misconstrued."

The implication of this law is that when one assumes that such and such is so and so a paradox (viz. a proposition in which one or more of its premises are inconsistent with its conclusion) will appear unless it is recognized that there is an implied or stated difference between "such and such" and "so and so".

The Law of the Included Paradox is so named because it implies that "such and such" give or take the differences with "so and so" is equal to "so and so". However, such a proposition falls foul of the Law of Contradiction. On the other hand, it can be concluded that The Law of the Included Paradox is internally consistent through its self contradiction.

All are invited to contradict me!!

Cheers, John

tk · 03-15-2003, 08:16 PM

jpbrooks:

Quote:

But how could "true" and "false" even be defined without assuming the LNC? For instance, how could the "definition" of "true" exclude what is not "true" without the LNC?

Interesting thought. While thinking about objective truth, axiomatic systems, and programming language wars, I sort of discovered why people agree on the "specialized LNC", that there's a distinction between "observed" and "not observed": because we actually define truth with this distinction!

Thus the following principle can be stated: A single observer cannot simultaneously observe a specific phenomenon and fail to observe the same phenomenon. (The "single observer" qualification is necessary to prevent a whole host of problems.)

I think the scientific method, the various formal systems, and other methodologies are in fact tools we construct and use to make sense of what we do and don't observe. In fact, as I mentioned some time ago, the above principle seems so basic that even religious fundamentalists make use of it (except they also add their own postulates to whatever's been observed).

It's also worth noting that when a crank K receives news N of some discovery D that contradicts his belief, the most K does is to discount N as a product of some conspiracy, rather than to deny the existence of N itself.

So where do we go from here?...

jpbrooks · 03-15-2003, 11:04 PM

Sorry for the delays in posting.

Quote:

Originally posted by tk
jpbrooks:

Interesting thought. While thinking about objective truth, axiomatic systems, and programming language wars, I sort of discovered why people agree on the "specialized LNC", that there's a distinction between "observed" and "not observed": because we actually define truth with this distinction!

Thus the following principle can be stated: A single observer cannot simultaneously observe a specific phenomenon and fail to observe the same phenomenon. (The "single observer" qualification is necessary to prevent a whole host of problems.)

If we substitute the word "test" for the word "define" in your comment above, then I would agree with it. The "specialized LNC" is just an instantiation of the "general" or "formal" LNC. (Though I suppose one might be able to get away with saying that the "specialized LNC" "defines" truth that is directly confirmable or verifiable by observation.) If we are using observation intentionally to determine truth, we are already making the assumption that truth may be verified/confirmed by observation, which is the denial of the claim or assumption that truth may not be so verified/confirmed. So, the "specialized LNC" actually relies (implicitly) on the assumption of the "general" LNC.

Quote:

I think the scientific method, the various formal systems, and other methodologies are in fact tools we construct and use to make sense of what we do and don't observe. In fact, as I mentioned some time ago, the above principle seems so basic that even religious fundamentalists make use of it (except they also add their own postulates to whatever's been observed).

Yes, observed phenomena may be "interpreted" differently by people who hold different views about what is, or is to be observed. And this, in turn, may affect the way the tools are used on the data of observation.

Quote:

It's also worth noting that when a crank K receives news N of some discovery D that contradicts his belief, the most K does is to discount N as a product of some conspiracy, rather than to deny the existence of N itself.

So where do we go from here?...

Right. But even in scientific inquiry, observational data that doesn't fit in with a particular theory isn't denied. It is just assumed to be an indication that more investigation and/or experimentation is required.

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