IGS Discussion Forums: Learning GS Topics: Truth
Author: Ralph E. Kenyon, Jr. (diogenes) Monday, December 5, 2005 - 12:37 am Link to this messageView profile or send e-mail


Earlier you said I thought that "truth" involved "all that I could say about anything". But since I didn't and couldn't know all about anything, truth did not exist.

In view of that, what can you mean by "the statement does not qualify as absolute truth ..."?

Your earlier statement can be interpreted that any statement about what is going on cannot be interpreted as "truth", consequently the statement that "change is constant" cannot be interpreted as "truth" in your view.

You also say, " since we have not visited or mapped all of Universe, strictly speaking, I see the statement as very highly probably true." This does not make sense to me. Having not visited nor mapped "all" the universe is evidence against the statement being "true", not evidence for it being true. Having mapped a lot of the universe and having found no contradicting evidence would constitute some corroboration for the statement.

The valid argument would take the form that, because I have not seen all the universe, there is a possibility that evidence to refute the statement is in the area of the universe that I have not yet seen. Consequently, the probability that that an "allness" statement about the universe such as "change is constant" being true would be reduced by the amount of the universe that has not been seen.

Your argument is invalid. You may see the statement as highly probably true, but that cannot be based on what you have not seen of the universe. It can only be based on what you HAVE seen so far.

Author: Ralph E. Kenyon, Jr. (diogenes) Tuesday, December 6, 2005 - 01:00 pm Link to this messageView profile or send e-mail

Milton said, "Re. "invalidity": Quite trueish...From your point of viewing, your standards, etc.," Milton, these are not "my" standards nor "my" point of view. I review the time-bound records prior to posting anything on the topic of validity or arguments. You speak of my citations of time-binding records in a way that does not acknowledge that my abstractions are citations of the history. I have not presented or constructed any "meanings" that differ in any unique way from time-bound records.

I find your statement, "My statement as I intended it ... includes both the part of Universe I have seen and the parts I have not seen. very interesting. I'm very happy that you can abstract from the part of the universe that you have not seen. The best I can do is extrapolate the map I have abstracted from only the part that I have seen.

Author: Ralph E. Kenyon, Jr. (diogenes) Tuesday, December 6, 2005 - 01:59 pm Link to this messageView profile or send e-mail

Bob wrote, "Ben says: "A map is 'true' insofar that it represents its territory well. A map is false where it does not match its territory." That is the Correspondence Theory of Truth, which Constructivism says is impossible to verify because of the territory's opacity to us. But we run experiments to "verify" models, and the empirical results add to our confidences in the models' form, fit, and function. I'm glad you put quotes around "verify". A more precises word would be 'corroborate'. "Verify" has too strong a connotation. We can verify an observation statement, but we can not verify a theory statement. When a theory predicts an event, and that event is observed, the statement of the event is "verified" by an independent observer. "Yes, I saw that happen." The theory that predicted the event gets "corroborated" when this happens. It gets "disconfirmed" if something contrary or conflicting happens in place of the predicted event. Constructivism, from mathematics, denies the method of reductio ad absurdum; it requires demonstration by construction. I'm not sure how this can be applied to theories of the physical world. Popper's method of falsification uses modus tolens to disconfirm a theory conditional statement. Can you comment on the constructivist approach using some specific example from physical theory?

By the way, http://en.wikipedia.org/wiki/Talk:Heresy refers to "the late Bob Eddy of the Institute of General Semantics". I trust you are here now.

Author: Ralph E. Kenyon, Jr. (diogenes) Tuesday, December 6, 2005 - 04:09 pm Link to this messageView profile or send e-mail

I use "verify" with respect to observation statements. Independent observers can verify that an observation statement reports events. Please verify that the apple is still on the table. Go look, see the apple, and report that the apple was on the table at time T. Someone else who observed the event at the same time can verify the first person's statement by repeating the observation statement (same statement by different observers) or by stating that the first observation statement by the first observer was "true" - that the first observation statement corresponded to the event observed by the second observer.

Your citation should have used double quotes, because you were quoting the term I used. I use single quotes when I am talking about the word itself: for example, 'Verify' consists of a concatenation of the letters 'V','e','r','i','f', and 'y'. This is not my invention. It is standard usage in mathematics, philosophy and linguistics. When a word is used in a strange way then double quotes or "scare" quotes should be used. This is also not my invention. It is standard usage. Only general semanticists, to my knowledge, insists on using single quotations for "scare" quotes to warn of unusual usage. A separate token is not needed because quotations are normally taken as either transparent or opaque, transparent when the words in the quotation can be changed with synonyms, opaque when they cannot. Putting double quotations around single words or phrases in a use context nigh always indicates opaque context, and that is equivalent to "scare" quotes. The use of single quotes in general semantics instead of double quotes adds to the "cult" perception of general semantics. My argument, in this regard, has fallen on deaf ears among the administrators, editors, and writers of general semantics.

I invite you to join my quest. http://www.xenodochy.org/gs/quotes.html

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, December 10, 2005 - 12:13 pm Link to this messageView profile or send e-mail

Hi Joe, Frank,
Your posts remind me of the ancient Greek questions about the nature of "being".

The question of "being" permeated the early pre-Socratic philosophy. The convoluted arguments centered around what appeared then to be worse than an oxymoron -- the apparently contradictory act of asserting the existence of something in order to deny it. The act of speaking or even thinking something was viewed at the time to have had existential import.
when the goddess points out to her listener that he could neither know nor point out what-is-not (2.7-8), she is precluding reference in thought or speech to the non-existent.(8)
This made talk of "nothing" or non-existence very problematic. It was the denial of this "void" that lead to monism. In the denial of nothing the early Ionians concluded that everything was one and that motion was impossible. Atomism has its roots in this concept of "the one" or unity -- which later became associated with the idea of indivisibility. (Click on "Being" or Existence)
The perspective of "motionless" was part of the discussion at the time.

Joe said, "Note that all equations by the simple process of division reduce to the same thing, the dimensionless One (1). This is true! As a side note, I can also show that in addition to it being dimensionless, it is also motionless and therefore timeless."

IF you divide both sides of an equation by one side, the one side cancels out symbolically and reduces to one, but the other side remains a complex of symbols with the numerator remaining what that side was and the denominator becoming what the other side.

Suppose I say y = f(x). If I divide both sides, I get y/f(x) = f(x)/f(x) = 1. I think this is what you are saying.

When I was in high school algebra we did this little exercise.

1. Let A=B. (by definition)
2. A2=AB (multiplying equals by the same quantity "A" gives equals.)
3. A2-B2=AB-B2 (Subtracting the same quantity, B2, from equals gives equals.)
4. (A-B)(A+B)=B(A-B) (factoring both sides) Notice that there is a common factor "A-B"
5. (A+B)=B (dividing equals by the same quantity gives equals - divide by "A-B".)
6. (B+B)=B (Substituting equals, B for A, does not change the value.) See 1.
7. 2B=B (combining like terms.)
8. 2-1 (dividing equals by the same quantity, B, gives equals)?

Whoa, Dude, Far out!

We arrived at something we "know" is false when we divided symbolically without paying attention to the value of "A-B". Because of 1, A=B, so A-B is zero, and division by zero is undefined.

We must include the restriction provided f(x) is not numerically zero). If f(x) is numerically zero, the expression is undefined, and therefore, so is y/f(x). If we take the limit as f(x) approaches zero, then z/f(x) gets bigger and bigger, provided z itself is not 0, for the cases where z is not initially numerically equal to 0. Darn - another exception. If y is defined to be f(x) for all values x of X, then y/f(x) equals 1 everywhere except where x = 0. It's like a line at the height of 1 unit of Y above the X axis with a single hole above where X is zero.

________ ______________

So, the reduction is not always to "one". It can be undefined. Other than that "little exception", what you say is tautological "truth".

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, December 10, 2005 - 03:59 pm Link to this messageView profile or send e-mail

Bob wrote, "Bob says the step 5 error of division by zero was preceded by the step 2 error of arbitrarily assigning "2" and "B" as equals, and by the non sequitur step 4.

And I presume the "2-1" in step 8 should be "2=1."

Yes the "2-1" in step 8 should have been "2=1".

As for the other, the fact that what I see in your posting does not match what I see in my posting suggests to me that the formatting may not have looked "the same" to you.

I wrote the symbol A raised to the power of 2, which is the same as the symbol A times the symbol A, is equal to the symbol B times the symbol A.

If the exponent 2 does not show up correctly in your viewer, I could write it as AA=AB, as A*A = A*B, where '*' means multiply, or even as A^2 = A*B, using the carrot as the conventional symbol for exponent.

As for the "non sequitur" step 4, perhaps I just left out too many subordinate steps.

I'll do this without using exponents.
(A+B)*(A-B) by the distributive law becomes
(A+B)*A - (A+B)*B

By applying the distributive law again, this becomes
(A*A + B*A) - (A*B + B*B)
which further becomes
A*A + B*A - A*B - B*B
By the communitive law this becomes
A*A +A*B - A*B - B*B
and the +A*B - A*B becomes 0, so the expression simplifies to
A*A - B*B, which is A squared minus B squared.

This step had to be gone over a number of times in our beginning Algebra class, because the beginning students did not see the cancelation process. They "expected" the product of two binomials to have at least three terms, for example (X+2)*(X-1)=X*X +X -2, a trinomial.

The right side of the equation involves one application of the distributive law.

So I'll go from step 3 to step 4, which I'll restate without using exponents, by a process of smaller steps. It looks like:
3.0 A*A-B*B = A*B-B*B [Subtracting the same quantity 'B*B' from equals gives equals.]
3.1 A*A-B*B = (A-B)*B [Applying the distributive law in reverse to the right side of the equation]
3.2 A*A+0-B*B = (A-B)*B [adding zero does not change the value.]
3.3 A*A+(A*B-A*B)-B*B = (A-B)*B [Zero in a different form.]
3.4 (A*A+A*B)+(-A*B-B*B) = (A-B)*B [regroupting]
3.5 A*(A+B)+ -B(A+B) = (A-B)*B [applying the distributive law "in reverse" twice by factoring out an A from the first two terms and factoring out a minus B from from the third and fourth term.]
3.6 A*(A+B)-B*(A+B) = (A-B)*B [simplify the expression]
3.7 (A-B)*(A+B)*(A-B) = (A-B)*B [applying the distributive law in reverse.] But this is just step 4 without the exponential notation.]
4.0 (A-B)*(A+B) = B*(A-B) [factoring both sides] Notice that there is a common factor "A-B"

And I did like pun. If you like math related puns, try this one: http://www.xenodochy.org/ex/quotes/double.html

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, December 10, 2005 - 11:08 pm Link to this messageView profile or send e-mail


My original post included We arrived at something we "know" is false when we divided symbolically without paying attention to the value of "A-B". Because of 1, A=B, so A-B is zero, and division by zero is undefined.

Bob didn't "bring up" the division by zero error, he referred back the step my text above was referring to.

Dividing by A-B symbolically is permitted, but the caveat "provided A-B is not equal to zero" must be added at that step, and then carried through to any further steps in any subsequent chain of reasoning. Whenever it is know that A-B is zero, then the process must be stopped at the symbolic division step.

Thanks for the Wikipedia reference. It was a delight to trip down memory lane, recalling my long love of pure math. It was like visiting a lot of old friends.

This little digression was originally meant to show that Joe's original idea "In the manipulation of equations, when you divide one side of the equation by the other, you always get the same result, the dimensionless number, 1." was flawed, because it does not work for A-B=0. If we divide by A-B and get (A-B)/(A-B)=0/(A-B) the result is not 1. The operation is forbidden. There are a few mathematical objects, such as some communitive rings and wheels, where the operation can be defined, but what "0" is in those cases is the identity element for the first operation, which is usually denoted by the addition sign.

If there is an element "0" in a set on which an operation "+" is defined such that a + "0" = "0" + a = a, for all elements a, "0" is called the "identity element" in the set over which the operation "+" is defined.

These specialized objects aren't exactly the numerical zero that we are accustomed to dealing with.

Joe wanted, I think, to somehow "identify" that special dimensionless unity with "truth" of the permanent and immutable kind, because, if I understood correctly, he thought that this division procedure was 100% dependable to produce 1.

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, December 10, 2005 - 11:20 pm Link to this messageView profile or send e-mail

In reviewing my last post, I noted something that I should add, "look at (A-B)/(A-B)=0/(A-B)".
If A is not equal to B, the result is 1=0, so the expression is inconsistent, it entails the opposite of "Truth".

Author: Ralph E. Kenyon, Jr. (diogenes) Monday, December 12, 2005 - 12:31 am Link to this messageView profile or send e-mail

Milton mentioned general semantics as a context for understanding "truth". With that reminder in mind, recall that Korzybski referred to Tarski's strict mathematical work and the works of other mathematicians who were developing logics using multiple "truth values". Korzybski was also enamored of probability, which he characterized as having infinite truth values.

Tarski's work provided a formal model for the correspondence theory of truth, and the map-territory analogy that pervades general semantics goes right along with this approach when it talks about the similarity of structure between the map and the territory.


Here are the names of various theories from our time-binding record at http://plato.stanford.edu/contents.html#t
axiomatic theories of (Volker Halbach)
coherence theory of (James O. Young)
correspondence theory of (Marian David)
deflationary theory of (Daniel Stoljar)
identity theory of (Stewart Candlish)
pragmatic theory of (Christopher Hookway)
revision theory of (Eric Hammer)
Tarski's theory of truth -- see Tarski, Alfred: truth definitions


Time-binders throughout history have passed on many formulations for us to peruse.

Me, I'm inclined to look at "truth" as a multi-level concept with different formulations at different levels.
For logic levels, "truth" is one of two arbitrary values (T|F) assigned to proposition.
For formal languages and model theory, it is the name of the condition where objects in the model under the map between the objects and the language satisfy a statement in the language.
For semantics, it expresses a relation between language and referents (Correspondence theory), but the question of whether truth can be known is another story.
In a legal context, it is not misrepresenting oneself in conjunction with applying due diligence to insure the representation is "accurate".
Everything else is a matter of conditional belief or theory.

Often the "search for truth" means the search for knowledge, or the search for a model to account for one's experiences.

I tend to hold the notion that if a statement is "true", then it cannot be proved false, so no empirically based theory statements can achieve this level of certainty; they can only be corroborated.

After all the variations I've read, I lean towards the correspondence theory as part and parcel of the general semantics perspective, but I'm open to other possibilities.

I think of probability values as ranging from 1=T and 0=F with all the values between 0 and 1 representing "degrees of truth". I also think of computers as using a three-valued logic system consisting of true, false, and disconnected at their base physical level.

In computer science, a "finite state automaton" can be thought of as a multi-valued logic system with one "truth value" for each of the many states the automaton can achieve. (For an extremely simple analogy, consider rolling a die. It has six faces, so it can end up in six different states.)

So, as Milton reminds us, from a general semantics point of view, we can consider "truth" as having many different semantic reactions including two-valued, three-valued, multiply valued, and infinity valued, all based on the correspondence theory, each appropriate to a different context and or level of abstraction.

Author: Ralph E. Kenyon, Jr. (diogenes) Friday, December 16, 2005 - 02:40 pm Link to this messageView profile or send e-mail

In terms of time-binding, and meaning in people, do you think "an agreed on definition" (for "truth") a "realistic" possibility?

Author: Ralph E. Kenyon, Jr. (diogenes) Saturday, December 17, 2005 - 12:02 pm Link to this messageView profile or send e-mail

Are you saying some people give more importance to their maps than to the territory?

Do you think we can we ever get "past our maps" somehow directly to the "territory" itself?

Personally, I give highest priority to continually updating my maps.