A general semantics glossary.

validity and truth. Alfred Tarski (1902-1983) is "credited with advancing the semantic method, a procedure for examining the relationship between an expression and the object to which it refers"; what we might consider a subset of general-semantics related to the extensional orientation. (1) But Professor Tarski did much more than that, leading in the fields of mathematics (set theory, algebra), mathematical logic (symbolic logic, logistic, etc.), co-founder of metamathematics (David Hilbert is considered the other founder), formulator of the famous "Truth Tables," etc. Much of Tarski's formulating was done in collaboration with such luminaries as Jan Lukasiewicz, Stefan Banach, Andrzej Mostowski, and others whose work Korzybski knew and who, with Tarski, influenced Korzybski's work. (2) According to the Oxford Companion to Philosophy, though, "It is for his work in logic that he is best known to philosophers, for it established the foundations of modern logical theory." (3)

Nevertheless, despite his herculean efforts (straining at logic), Tarski's sharp complexity blurred the simple and most practical (promoting extensionality) distinction between statements that may be evaluated as valid (related to what he called "consequence" and others refer to as "tarskian biconditionals") (4) and those that may be evaluated as true (or false). Indeed, the term "valid" is not even indexed in his famous 'handbook' for the "educated layman" (him again!), Introduction to Logic and to the Methodology of Deductive Sciences. (5) (Nor, by the way, is valid indexed in Science and Sanity, although Korzybski does use the term in the sense I am emphasizing in these pages.) In much philosophical writing (most that I have read), authors shuttlecock between true and valid, suggesting that for them the terms are interchangeable.

Tarski himself has been credited with revitalizing the "correspondence theory of truth," (6) that statements are 'true' if they correspond to (match) 'facts'; what Korzybski might call a "structural fit," that is, the relations among the facts as known, eventually non-verbal, are well represented in some statement. Yet the bulk of Tarski's work is concerned with the "consistence theory of truth," with relations among statements such that statements are 'true' if they are well formed and deductively (concludingly) coherent. Tarski's internally consistent 'true' is what I prefer to call valid.

Over the years I have discussed the valid/true distinction in my Institute of General Semantics seminar lectures, usually with relation to presentations of Keyser's "Logical Destiny," or "Logical Fate." (I don't prefer that latter form because of its spooky sound. Yet I guess it's spooky enough. We'll (you and I) deal with "Logical Destiny" in the next installment of this glossary.) I have plainly said that I offer the valid/true distinction as a simple, homemade formulation that can help in alerting you to when you've come to the boundary between observation and speculation; a most parlous crossing point if we are not sufficiently conscious of abstracting.

In distinguishing merely valid from true statements, we need to first consider the difference between statements of 'fact' and statements of inference.

I put 'fact' in quotes because I recognize that determining what constitutes a 'fact' is no simple matter. As Mayper's Dictum has it, "No fact is simple." This must be the case when we recognize that we abstract, i.e., respond to some stimuli, 'ignore' others, and add our own experience-based 'content' to our on-going abstractings, project the results 'onto' the environment, etc.. So we don't want to be naive when we talk about 'facts.' I suggest a cautionary definition of a statement of fact, setting minimum requirements for accepting some statement as factual, while remaining formulationally dry under the Uncertainty Umbrella. (7)

I recommend, then, that before you accept a statement as a statement of fact, you require:

1. that it be about something observed, i.e., a report, a description

2. that it be public, i.e., more than one observer involved, and that the statement be the result of converging observations

I suggest that, if a statement does not meet those requirements, you should not accept it as a statement of fact, even if you may 'intuit' (quietly infer) that it may be true. I reiterate, a statement's having met these minimum requirements won't guarantee that it's 'true'; we know that people can hallucinate in private and together in public. Sometimes people's reports are lies. (Did you know that?) So I urge that, if a statement does not meet those minimum requirements, it's not even a candidate for secure evaluation as 'true.' And, let's remember, we require just as much data to determine that a statement is 'false.' That we can't at [time.sub.t] affirm that it's 'true' does not automatically make it 'false' (two-valued orientation). At best, we can say with Korzybski, "I don't know; let's see," i.e., let's try to get more data.

A statement of inference we can define simply as any statement that 'goes beyond' the data, often taking the implied logical form, "if so" (what has been observed, stated, recorded, etc.), "then so" (what the observer-formulator decides to conclude, what the implications of a proposition 'are,' etc.). Cognate with inference are interpretation, conclusion, deduction-induction, hunch, guess, speculation, etc. Inferences of different orders (inferences from inferences, inferences of higher order) may be made indefinitely. This is how science is built - but also fantasies, myths, etc., some of which may be deleterious to our health. Responsible abstracting requires eventual extensional checking of our inferences. (8)

Inferences may also be evaluated as uncertain in varying degrees. If, given more data, they mature to the (trans)form of factual statements, they may then be evaluated as probabilistically (in various degrees) true or false. But as long as statements retain the inferential character, they can most strongly only be evaluated as valid, i.e., verbally consistent with what has gone before.

Thus the three-valued (and more) logics of Lukasiewicz and Tarski: statements may be true, false, or indeterminate in varying degrees. (9)

We can distinguish Tarski's logical 'truth,' expressing verbal/verbal relations (what I prefer to limit to validity) from Tarski's "semantic truth," expressing symbol/referent relations, both verbal/verbal and verbal/non-verbal, the levels at which 'true' and 'false' may apply. For example, if John says "I am sick" and I, making what Tarski called a metastatement, say "John said 'I am sick'" (not "John is sick," which would be an inference on my part), John's statement serves as a referent for my statement, and my statement can be evaluated as true. If I report, "There's a rock on the road," the rock and the road, provided I'm not hallucinating, qualify as the referents for my statement. If I am hallucinating, then I as brain am the referent for my statement.

At seminars I often discuss "Four Ways to Examine Language," four modes of evaluation. There can be more, but I limit myself to four. They are:

1. grammar, wherein word-to-word relations are examined; basic unit: sentence

2. logic, wherein statement-to-statement relations are examined; basic unit: paragraph

3. semantics, wherein word-or-statement-to-referent relations are examined

4. general-semantics, wherein all of the above and non-verbal world (physics, neurobiology, etc.)-human-evaluations/behaviors relations are examined, evaluated, and, prophylactically and amelioratively taught about. (10)

Here's an example I have used at seminars. It's in the form of a classical aristotelian syllogism (major premise, minor premise, conclusion).

A gritch is a four-floogled hogwash. (Alternative form: All gritches are four-floogled hogwashes.) Alphonse is a gritch. [therefore] Alphonse is a ...

Note that you can reach the logical conclusion without having the foggiest notion of what constitutes a "gritch" (I invented 'it') or what qualifies as "four-floogled hogwashhood (or -ness)"; that is, you can reach a correct, formally logical conclusion about nonsense. Schizophrenics do it often. Lewis Carroll did it for fun. So the conclusion, "Alphonse is a four-floogled hogwash," is valid but very probably not true.

Note, too, that the statements are grammatically correct; only the vocabulary is somewhat suspect. So speaking or writing correctly from the grammatical-syntactical point of view, while necessary (if you want to do standard English), is not sufficient for making sense. I have read that, though he is not considered a great stylist in German writing, Adolf Hitler's Mein Kampf is expressed in standard German grammar. Thus, while there's no particular advantage to being ungrammatical or illogical outside of poetry or play writing (writing as play), correct grammar and impeccable logic are not enough.

At the level of semantic analysis, we first test for truth-value in Tarski's second sense. We first break out of the "neurolinguistic 'circle'" to check the relation between what we say and what what we say refers to; eventually, what we can observe. We become extensional.

Everything presented since 1991 in these glossary entries has hovered over the claim that general-semantics provides the broadest in-depth system for evaluating human-functioning-in-the-world in the world (in existence). Here we become concerned not just with correct expression, logical consistency, the structural connection between maps and territories (symbols and referents), but the self-reflexive effects of formulations on formulators - and the semantic reactions of other formulators they're in contact with.

Here's the diagram I have used at seminars to visualize these relationships:

Note that grammar and logic are fully encircled, i.e., they constitute strictly verbal methods for formulating and evaluating verbal methods. Here we are concerned with correctness and validity. At these levels it is quite possible (nay, common) to be correct and silly at the same time. Sometimes the 'silly' matures to pathology.

At the level of tarskian semantics, not unlike a chick breaking through its shell, we begin to partially 'break out' of the neurolinguistic 'circle'; we haltingly straddle the verbal-nonverbal nexus. Here we can check to see if our grammatically correct and logically valid formulating has resulted in 'true' statements.

The general-semantics level encircles the 'circle,' because here we can, through methods of silence, more nearly succeed in 'breaking out' of the too-often entrapping neurolinguistic 'circle.' (11)

Achieving and maintaining a sharp awareness of the difference between validity and truth, inference-type and fact-type (descriptive-reportive) statements, lower order and higher order inferences (first order inferences, higher order inferences generating generalizations, hypotheses, theories, theories about theories, etc.) - maintaining these awarenesses (consciousness of abstracting) can facilitate our most sublime formulating while keeping us anchored at the level where we may smell the coffee.

NOTES AND REFERENCES

1. Edward Vernhoff and Rima Shore, The International Dictionary of Twentieth Century Biography. New York and Scarborough, Ontario: New American Library, 1987, p.689.

2. Lukasiewicz and Tarski are particularly acknowledged in Science and Sanity. For a thorough examination of the Tarski-Korzybski axis, see Stuart A. Mayper, "Tarskian Metalanguages and Korzybskian Abstracting," General Semantics Bulletin, No. 46, 1979, pp.26-53. For a list of available sources for Tarski and his colleagues in Poland and the United States, see Note 2 to my essay-review of Karol Janicki's Toward Non-Essentialist Sociolinguistics in General Semantics Bulletin, No. 57, 1993, pp.89-100. See also Note 15 to my "Neuroscience [Update.sup.1995]," General Semantics Bulletin, No. 62, 1995, p.51. Pupils and pupils of pupils of these formulators are working in universities and 'think tanks' all over the world. For an authoritative brief account of Tarski's work, see Andrzej Mostowski, "Tarski, Alfred," in Paul Edwards, ed., The Encyclopedia of Philosophy, Vol. 8, New York: Collier Macmillan, 1962 (1972 reprint edition), pp.77-81. Irving J. Lee included a paper by Tarski, "The Semantic Conception of Truth," (pp.67-71) in his (as editor) The Language of Wisdom and Folly. New York: Harper and Row, 1949. Available in a reprint from the International Society for General Semantics. This is an excellent source for appreciating Korzybski's status as, allowing for his originality, a representative of a trend.

3. Ted Honderich, editor and writer of the Tarski article, "Tarski, Alfred," The Oxford Companion to Philosophy. Oxford/New York: Oxford University Press, 1995, pp.865-866.

4. John Corcoran, "Alfred Tarski," in Robert Audi, ed., The Cambridge Dictionary of Philosophy. Cambridge: Cambridge University Press, 1995, pp.781-788.

5. Alfred Tarski, Introduction to Logic and to the Deductive Sciences. Translated by Olaf Helmer. Third Revised Edition. New York: Oxford University Press, 1965, 1976 reprint. By "deductive sciences" Tarski does not intend the empirical sciences, i.e., science proper understood in a modern sense, but merely verbal constructs, such as those found even in such enterprises as 'theology,' once called "The Queen of the Sciences," when scientia was cognate with 'knowledge' in general. His book demonstrates that he would have better referred in his title to "formal deductive methods." Indeed, in the Preface to Introduction to Logic and to the Deductive Sciences, the original Polish title (1936) was translated by Tarski himself as On Mathematical Logic and Deductive Method. The first German translation (1937) ("an exact translation" says Tarski) bore the title Einfuring [Introduction] in die mathematische Logik und in die Methodologie der Mathematik. Interestingly, he strikes a Korzybskian posture, which he otherwise disdained, when he writes: "... it [his book] seeks to create a unified conceptual apparatus which would supply a common basis for the whole of human knowledge." (Preface, p.xi.)

6. "... Tarski's greatest achievement, and the real significance for the philosophy of the empirical sciences lies, I believe, in the fact that he reestablished a correspondence theory of absolute [!] or objective [!] truth which showed that we are free to use the intuitive idea of truth as correspondence with the facts." K.R. Popper, Conjectures and Refutations, p.223, quoted in Henryk Skolimowski, Polish Analytical Philosophy: A Survey and a Comparison with British Analytical Philosophy. New York: The Humanities Press (Routledge and Kegan Paul, Ltd.): 1967, p.46. (Skolimowski's excellent study is in the series, International Library of Philosophy and Scientific Method.) Yet Popper, that variable formulator, could write: "... although I accepted, as almost everybody does, the objective or absolute or correspondence theory of truth - truth as correspondence with the facts - I preferred to avoid the topic. For it appeared to me hopeless to try to understand dearly this strangely elusive idea of a correspondence between a statement and a fact." (Conjectures and Refutations in Skolimowski, loc cit.)

Skolimowski notes that other philosophers (Carnap, Ajdukiewicz, et al.) were similarly concerned. But then: "As Popper and others admitted, the correspondence theory of truth is rather vital for the development of the philosophy of science, which assumes that scientific theories deal with reality and are to be assessed in terms of truth and falsity. In this context Tarski's formulation is a prerequisite for inquiries in the philosophy of science." (ibid., loc cit.)

7. See Robert P. Pula, "A General Semantics Glossary (Part XIII): general uncertainty," ETC: A Review of General Semantics, Vol. 52, No. 4, Winter 1995-96, pp.476-481.

8. For excellent discussions of these issues, see Irving J. Lee, Chapter IX, "Descriptions and Inferences," Language Habits in Human Affairs. New York/London: Harper and Brothers, 1941, pp.177-208, currently available in a reprint from both the Institute of General Semantics and the International Society for General Semantics; and a videotape "Can You Make a Statement of Fact?", available from the Institute.

9. Korzybski refers often in Science and Sanity to the "logic of probability," "the many-valued logic," "the mathematical theory of probability," the "'intuitional' formalism" and "the restricted semantic school" of the Lwow-Warsaw school of mathematical logic and analytical philosophy which flourished during 1895-1939. In his autobiographical Keyes Document, as I call it, he says, "I had there [mathematical congress in Warsaw in 1929] some Polish mathematicians ... who were interested in mathematical logic and the application of mathematical philosophy and all that. Quite important men. Very. They are internationally known today. In many ways, I introduced them to America. You will find that, Lesniewski, Kotarbinski - Tarski at present is in America." (Keyes Document, p.274. I am editing this important autobiographical statement by Korzybski for eventual publication.) Tarski was professor of mathematics at the University of California at Berkeley from 1942 to 1968. The Lwow-Warsaw school, which has corollary centers in Krakow, Poznan and other places in Poland and abroad, continues to flourish, despite the depredations of World War II, when many of its leaders were shot or gassed. (See Jan Wolenski, Logic and Philosophy in the Lvov-Warsaw School. Dordrecht/Boston/London: Kluwer Academic Publishers, 1989. Volume 198 of the Synthese Library: Studies in Epistemology, Logic, Methodology and Philosophy of Science; and Kazimierz Kuratowski, A Half Century of Polish Mathematics. Translated by Andrzej Kirkor. Oxford/New York/Paris ...: Pergamon Press, and Warszawa: PWN - Polish Scientific Publishers, 1980.)

Here are a few pertinent quotes from Science and Sanity which show not only some underpinnings of general-semantics, but also of Lotfi Zadeh's fuzzy logic:

I accept the many-valued, more general, structurally more correct 'logic of probability' of Lukasiewicz and Tarski, which in my non-el system becomes infinite-valued ([infinity]-valued) semantics. [Korzybski's note: "I use the term infinite-, or [infinity]-valued in the sense of Cantor as a variable finite."] (p.93)

Boole's 'laws of thought,' and the many-valued 'logic' of Lukasiewicz and Tarski are also closely related to probability; and the new quantum mechanics uses it constantly,. [etc.] (p.210)

Lately, the theory of aggregates has led to a weighty question: Does one of the fundamental laws of the old 'logic'; namely, the two-valued law of the 'excluded third' (A is either B or not B), apply in all instances? Or is it valid in some instances and invalid in others?

The problem is the psycho-logical kernel of the new revision of the foundation of mathematics, which has lately been considerably advanced by Professor Lukasiewicz and Tarski with their many-valued 'logic,' which merges intimately with the mathematical theory of probability; and on different grounds has perhaps been solved in the present non-el, A-system. (p.281)

Finally, the difficulties of the law of excluded third have been solved by Lukasiewicz and Tarski in their 'many-valued logic,' which, when N increases indefinitely, merges with the mathematical theory of probability, a result reached independently by a different type of analysis in the present system [my italics: RPP]. (p.310)

Lately, Lukasiewicz has shown that a three-valued 'logic' can be so formulated as to include modality. Later, he and Tarski generalized it to an n-valued 'logic.' When n tends toward infinity, this 'logic' becomes the 'logic' of probability. If these disciplines are made non-el, we have what I call one-, two-, three-, and [n.b.] [infinity]-valued general semantics. Theoretically, and in practice, we are interested mostly in the one-, two-, three-, few-valued, and [infinity]valued general semantics. For my purpose, and for simplicity, I shall deal only with identification; that is, the primitive one-valued semantics, the influence of which is found in both the two- and three-valued semantics, and may only be completely criminated in an [infinity]-valued semantics [Korzybski's italics]. (pp.461-462)

And, finally, from "Supplement III" (Korzybski is listing the "more important schools" and approaches in mathematics):

4) The Polish school of: (a) 'intuitional' formalism with Lukasiewicz, Tarski, Legniewski as representatives, which may be called the non-aristotelian school. Lukasiewicz generalized the A 'logic' to three-valued 'logic' which covers modality. Lukasiewicz and Tarski finally produced a general many-valued 'logic' of which the two-valued represents only a limiting case. Lesniewski produced Protothetic, a still more general 'logical' system, by introducing variable 'funktors,'. [Korzybski's note: "At present Lukasiewicz and Tarski call their many-valued 'logic' non-chrysippian, but this name does not seem appropriate because these authors generalized both forms of the aristotelian 'logic' to a many-valued 'logic' of which the two-valued becomes only a limiting case. Thus it seems that their many-valued 'logic' is better described by the term non-aristotelian, yet still elementalistic 'logic'."] (b) The restricted semantic school represented by Chwistek and his pupils, which is characterized mostly by the semantic approach, and by paying special attention to the number of values, establishing the thesis that the older 'freedom from contradictions' depends on one-valued formulations, as discovered by Skarzefiski and quoted by Chwistek. This school has already produced new foundations (still elementalistic) for 'logic' and mathematics, and leads to generalized arithmetics and analysis. (p.748)

Modality in traditional formal logic refers to the character of propositions such that they are evaluated as being contingently true or false, possible or impossible, necessary, etc. Frederick Suppe defines modality generally as "the manner in which a proposition (or statement) describes or applies to its subject matter." Cambridge Dictionary of Philosophy, op. cit., p.499. See also, in the same source, "mode" (pp.502-503) and (if you can tolerate severe formalism) "modal logic," pp.499-502.

10. Many years ago, I was given a boost toward this formulation by Anatol Rapoport. See his "What is Semantics?" (sic.) in S.I. Hayakawa, ed., The Use and Misuse of Language. Greenwich CT: Fawcett Publications, 1962, pp.11-25.

11. For a related but different diagram, see J. Samuel Bois, Explorations in Awareness. New York: Harper and Brothers, 1957. Available in a reprint from Continuum Press, 1629 18th St., No. 7, Santa Monica, CA 90404.

ADDENDUM

My use of quotation marks in this glossary is in conformity with the conventions of the General Semantics Bulletin. To wit:

SINGLE QUOTES (Extensional device)

1. To mark off terms and phrases which seem to varying degrees questionable for neuro-linguistic, neuro-physiological, methodological or general epistemological reasons.

2. To mark off terms used metaphorically, playfully, etc. a. 'mind,"meaning,"space,' or 'time' used alone, etc. b. "...the semantic reaction formulation could serve as a 'bridge'... between Pavlovian classical conditioning and Skinnerian operant conditioning." (Silverman)

SINGLE QUOTES (Standard usage)

To indicate a quote within a quote.

DOUBLE QUOTES (Standard usage)

1. To indicate a term or phrase used by some referred-to person but not necessarily indicating a direct quote. Example: What Korzybski referred to as the "semantic reaction."

2. To indicate a direct quotation from a named source.

Robert Pula edited the General Semantics Bulletin from 1977-1985 and served as Director of the Institute of General Semantics from 1983-1986. He is Director Emeritus of the Institute.