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Conventional wisdom on the progress of knowledge: Aristotelian discourse-universes

December 2005

© Henry A. Flynt, Jr.

Conventionally, the enterprise of knowing is correlative to speculation and unknowable knowledge. As for me, I am averse to speculation and unknowable knowledge. I am averse to the assumption that: there are a vast number of assertions which must be true or false but which have not been judged with confidence. (And which may never be judged with confidence for reasons of principle.)

My conception of personal authenticity or dignity is directly affected by these aversions. I conceive the fault named credulity far more broadly than conventional wisdom does. (That means that my view of personal authenticity—or dignity—is especially narrow.)

It seems that I need to spell out my stance as a formal stance regarding the logic of assertions—a stance which may be unheard-of, and by no means straightforward.

Before I can spell out my stance, I will have to codify the conventional wisdom where conventional thinkers have failed to codify it. That is to say, I have to address the vernacular conception of acquisition of knowledge in force for thousands of years. In that conception, a sentence is not the world—symbolization is at a remove from reality. (Although magical thinking has always wished to identify symbolization and reality.) The gaining of a given fact is a local and somewhat independent step. We acquire, and need to acquire, facts in advance of generalizing.

As a first approximation, I am concerned with the total of natural-language assertions which are in play cognitively. Vernacular thought is Platonist. It assumes that assertions which are in play cognitively are true or false: even if we have not judged them yet, and even if we can never judge them. The problem is to focus that total. I will not be concerned with “how we know,” the methodology of an inquiry which aims at a judgment. It is the Platonist bias: the assertion already has a truth value, and it is secondary what we have to go through to judge the assertion.

As for the process of symbolization, the introduction of vocabularies and so forth, language does not conveniently cleave to reality. Language has a distinct fate. I will be forced to consider it here.

Recent fashion in science has given the vernacular conception one ironic twist in particular. The recent results purport to show that there are blocs of knowledge, set in stone, which we cannot access. (Gregory Chaitin, Lawrence Krauss.) As I said, I am not hospitible to unknowable knowledge. Among scientists, the total of that knowledge is growing to mountainous proportions. For one who sees science at the high end, science has become an ignorance machine. It is poetic justice indeed; it shows how contemptible the scientific project was. But this development notifies us of the need of a caution. Chaitin, for example, presents a computational notion of knowledge which is far removed from the vernacular notion that has been in force for thousands of years. It is not that Chaitin does not invoke piecemeal and experimental acquisition of knowledge. It is that he excludes such acquisition from his picture of knowledge (which is essentially systemic). In other words, Chaitin is a classic hypocrite. I will not mention these recent specialists again unless I want to make them the topic of an appendix.

Again: I have to explicate the vernacular notion of acquisition of knowledge, something which has never been done in an apposite way. I must explicate or reconstruct the conventional wisdom because the conventional wisdom has never codified itself. The role of instructing the Establishment regarding their own doctrine is, in fact, a role I detest. I reconstruct what I do not advocate because the people who do advocate it have never codified it.

The test of any explication is whether the reader experiences the shock of recognition upon seeing it. But it will not be so easy now, because academic thought has become more and more divorced from vernacular logic and epistemology. In fact, that divergence will be a difficulty throughout this inquiry. People live and die every day by what academic thought dismisses with contempt. The professors dismiss with contempt the medium of thought by which they live their everyday lives. [They sneer at “religion” but secretly or not-secretly give their ultimate allegiance to their childhood religion.] If they are from the science pole of the science-humanities polarization, they are usually Platonists, which means that they dismiss the vernacular medium of thought in favor of an icon of pristine truth (which may, however, be inaccessible). To the extent that these attitudes directly affect what we are trying to do, we will encounter them below.

•

Our target topic is: “open questions which are subject to becoming settled questions as knowledge progresses.” A statement is presented which must be true or false, but we don’t know which it is. Later, because we “delve more deeply” in some way, the statement is confidently judged true or false. The existence of resolvable open questions is the basis of the notion of growth of knowledge, or scientific progress. It is also the basis for regarding speculation as legitimate; somebody could have believed that Sol had more than seven planets prior to the discovery of Neptune, and conventionally, they would have been right.

As we have already said, there is another possibility: statements which must be true or false even though we can never know which. However, we focus here on open questions which have a chance of being resolved.

If one wants conventional examples of assertions which must be true or false but which have not been judged with confidence, various assertions about the total of Sol’s planets would have served: in one or another past century.

Sol has exactly 7 planets.

Sol has exactly 8 planets.

Sol has exactly 9 planets.

Between the years 1610 and 2003, assertions about the total of Jupiter’s moons would have served.

Jupiter has exactly 4 moons.

Jupiter has at least 4 moons.

Jupiter has exactly 39 moons.

Jupiter has at least 39 moons.

Jupiter has exactly 47 moons.

Jupiter has at least 47 moons.

The very fact that we give years during which the propositions about Jupiter’s moons were to be in play signifies that we are essentially talking about statements subject to belief or disbelief as “knowledge progresses.”

Incidentally, the example illustrates another feature of the increase in, or metamorphosis of, knowledge: the last-discovered moons are so small that they devalue the vernacular word ‘moon’. New experience shows a previously sharp category to have a vague boundary. As we said, knowing harbors symbolization as a distinct phase, and symbolization does not cleave to reality identically. But we do not focus on that phase.

While the examples just given are natural-language assertions, they are “already” quantitative. The generalization that all ravens are black says something quantitative. In knowledge, the quantitative is not partitioned from the qualitative.

A more urgent example of an unjudged assertion is

There is life on Mars.

The scientific community could announce at any time that this proposition has been judged confidently. It had not done so as of April 2005.

We should mention that mathematics has open questions which are decided not by “observing the world” but by bringing to bear a heavier machinery of proof. The Four-Color Problem, the Poincaré Hypothesis, Fermat’s Last Theorem. (Something else that is never talked about is that errors are discovered in proofs of theorems the profession wants to believe, and a whole series of proofs is published and discredited before the profession becomes confident that the theorem is provable. The Jordan curve lemma.)

Our perspective of knowledge is a wide one here. If I take examples from science, it is because the more definite and less arguable assertions illustrate my points more readily. I do not meant to make positivist exclusions. All academically accredited discourses are included in the total.

In other words, we do not restrict “knowledge” to the physico-mathematical sciences. The original unity of science is found in the cognitive core of a natural language. The cognitive core embraces certain aspects of natural science (adjoined to technical extensions). It also embraces all facts concerning dated occurrences. (History, chronicle, determinations of fact in legal cases.) It embraces speculative propositions about history, so-called social theory. As a matter of fact, I want to include any speculative proposition which a large public regards as binary-decidable, such as propositions about clairvoyance or even propositions of astrology.

On the one hand, natural language’s capacity to embrace quantitative facts and relations has to be viewed optimistically. On the other hand, we have to allow for assertions in disciplines outside hard science.

All males are subject to the Oedipus complex.

Shakespeare is a Renaissance playwright.

When such assertions as the latter are taken into account, it opens up a further epistemological dimension, because scientific fact and theory, on the one hand, and accredited opinion in general, on the other, get treated differently. Relative to accredited opinion, “true” may mean “professional dogma.” We refuse to worry about that, lumping such “truths” with the others.

•

The common medium of academic discourse is natural language and its technical extensions. We arrive at the notion of

the assertoric cognitive core of natural language

the cognitive core of binary-decidable declarative sentences

What I find to my embarrassment is that logicians have not addressed this medium. Logicians since Aristotle have discussed definitions and inferences in this or that case, but have never viewed the cognitive core as a category to be delimited and idealized so as to make formalization etc. possible.

Where the cognitive core of natural language is concerned, savants have addressed the trees, never the forest.

My Philosophy Proper (1961, published 1975) has a chapter on how the individual sentence asserts. However, I did not address the topic of a total of assertions, from one natural language, subject to truth-judgment, such that new judgments come in all the time. For the purposes of Philosophy Proper, that topic was extraneous. But now I need the notion of this total.

The point, of course, is that one has to perform a clean-up on natural language, to idealize it, in order to arrive at a total of servicable assertions.

The initial notion is that of the cognitive core of a natural language, which is a collection of sentences, of assertions. Some of those assertions are confidenty judged true. The collection of truths changes over time as new truths are added and formerly accepted assertions are discarded. ‘Sol has exactly 7 planets.’

The collection of assertions confidently judged true is called “our knowledge.”

Once we conceive the collection of truths, we can idealize or model “the progress of knowledge”—“our advance toward final truth.”

It is not that logic textbooks, from the time of Aristotle, do not offer natural-language assertions as examples, and discuss the logic of those examples. But again, they do not address the assertoric forest, only the trees. They know that there has to be a clean-up to extract a serviceable cognitive core, but they only hint at such a thing.

Up until the moment when the Fregean vision overran logic, the logicians were simply negligent. Then Frege convinced philosophers that logic should be nothing more nor less than a hostage to mathematical apologism. Our right to do elementary arithmetic as we do was to be proved by making hundreds of pages of arcane calculations. Every feature of “reality” which did not square with Platonism was to be eliminated from logic, e.g. time, e.g. non-actualized possibility. (Even if there are academic sideshows which purport to address these topics, they are understood to be mere reconfigurations of the formalism of eternally present actuality.) In Mathematical Logic, Quine says if it’s not mathematical, it doesn’t belong in logic. In Tarski’s most famous paper, he says, logic is a branch of number theory.

Rosser’s and Turquette’s Many-valued Logics was written to expound a notion which then seemed revolutionary and audacious but is now viewed as an insignificant algebraic formalism (except in fuzzy logic?). All the same, this monograph is useful in registering some conventional wisdom, especially in the staged debate which opens the book. Here are some remarks in play in this staged debate. “Every statement is either true or false” (page 3). They go on to note, quite properly, that most conversational sentences are statement-matrices and not statements at all (see below). Then one of the interlocutors says, “Ordinary discourse is just so much nonsense to me” (page 5). That tells you who academic logicians really are. The book which follows this announcement is another contribution to algebraic formalism, one whose hints of revolutionary audacity are now known to have been utterly unwarranted. It is written in English (with technical extensions)—of course. The authors present all of their statements (except for the staged debate) as true—of course.

Even though ordinary discourse is secretly or openly believed to be nonsense, there are lowbrow logic textbooks written by eminent contemporary logicians which purport to sort out some of ordinary discourse.

After 1970, something else happened. If you can believe it, once the Fregeans had carefully reconfigured logic so as to shoulder out natural language, it became fashionable to apply Fregeanism to the study of natural language. Books poured out on natural-language semantics.

Let me list some specimens, all at once, of what the profession does with natural language.

Hans Reichenbach, Elements of Symbolic Logic (1947), Chapter VII, Analysis of Conversational Language

W. Quine, Elementary Logic (1941)

W. Quine, Methods of Logic (1950)

Patrick Suppes, Introduction to Logic

Semantics of Natural Language, ed. D. Davidson and G. Harman

Approaches to Natural Language, ed. Hintikka (1973)

Formal Semantics of Natural Language

Anna Wierzbicka, Lingua Mentalis (1980)

Let us return to Rosser and Turquette; they are at least capable of registering the state of play. Again, they acknowledge that most conversational sentences are statement-matrices; they translate

It is raining.

as

It is raining in Ithaca, New York, at 2 P.M., July 14, 1950.

Having become a bona fide statement, it is binary-decidable. (The authors’ affectation of revolutionary audacity is no challenge to that, as we already began to note.)

With this clarification, a dismaying observation can be made about all the books listed above. The few natural-language sentences they present are underspecified, of the type

Jack got lost.

So most of the natural-language sentences they treat are not in the cognitive core. It is not a small oversight.

They also offer sentences such as

Turkey is in Asia.

This sentence is a problem because it can be taken in two ways. “The Alps are in Europe.” Very well, a fact of physical geography, if you will. But “Turkey is in Asia” can be a report of an agreement about a classification—which is approximately what a defintion is. A doctrine of definition-sentences is hardly a contribution to the modelling of the cognitive core.

Where is the treatment of assertions which are candidates for facts? Skimming all of these books, the examples the authors give us are precious few and even silly, peculiarly so.

Norwegians are tall.

Sugar causes tooth decay.

Lincoln was born in Illinois.

Every pacifist is crazy.

The authors show no interest in the cognitive core, yet they purport to produce specimens of it: they write textbooks, scholarly papers, monographs, and treatises.

When I have raised the topic of formalizing the cognitive core of natural language, academics have affected to find it foolish, saying that we are so advanced now that there is no question of:

—knowledge articulated in declarative sentences

—requiring a sentence to be true or false uniquely

—making a list of sentences which must be true or false but which we are unable to judge with confidence

(Well, is it that they say we are advanced now—or is it that they say that the binary-decidable declarative sentence was never in play, not even during the Aristotelian and Scholastic centuries?) This “sophistication,” evidently an unsavory hybrid of quantitative fetishism and deconstruction, is so insincere as to be rude. It is stupid.

If there are no binary-decidable declarative sentences, then language properly speaking never existed. Language cannot then do what philosophy has always required it to do primarily: to articulate the self-revelation of entities. (“To portray reality.”)

Granted that sentences in scientific works may be loaded with jargon, all of them are offered as truths. (It is unimportant to review the exceptions, such as the staged debate mentioned earlier.)

Unless and until I supply some highly unconventional repositioning, all the commentary in this manuscript is offered as true.

For the scientific sophisticate who is not philosophically sophisticated, let me remark that the language for knowledge includes all the grammatical assertions—the falsehoods and the truths. If it is required to judge astrology false, then it definitely has to be included in the language. (If astrology does not utter declarative sentences, it cannot be false.)

Judgments of fact in the course of trials at law technically have the character of historical fact. All the while, it is common to find that an allegation cannot be proved to the required standard. The court does not deny that the allegation has a truth-value. At times forensic advances can settle a question which a trial failed to settle. It is an excellent example of an assertion which was true or false when it was first uttered but which can only be judged confidently at a later time. If scientists never have any contact with the courts and with the effects of a court’s judgments, then they are extraordinarily sheltered. Well obviously one or the other of Rosser and Turquette are extraordinarily sheltered, or would like to be, since he does not condescend to recognize natural language. We wonder why he has been afforded so much social privilege.

Without the conveying of information via declarative sentences, there would be no “human life” as we know it. To mock somebody who wants to take cognitive discourse as a topic for the anthropology of vernacular logic is just rude. If the topic has never before been addressed, that shows that institutional expertise is extremely alienated.

We are shocked at the amount of effort we have to spend belaboring the obvious to mediocre academics who think it is clever or sophisticated to deny the obvious. If you say to them, ‘Snow is white’, they say, ‘Oh?—where did you get that ridiculous idea?’ Why are they paid to be so rude?

In dealing with a bank or with the police, you cannot afford to pull a Rosser-Turquette. You cannot afford to pretend that you find natural-language sentences too flawed to deserve your priceless attention. If you interact with a bank or the police the way academics interact with me, the bank will not give you the money. The police will … but academics would not try with the police what they try with me. The academics (sitting as they do in offices and performing administrative duties for an institutional authority) do not live as their posturing would imply. It is a cocktail-party ploy to cut inquiries short.

•

I said at the beginning that I will not treat how we know. Let me remind the reader that this study is a formalization of conventional wisdom. I say nothing about what I support (until the end). I am willing to take the methods of judging assertions as stipulated; to delve into epistemology or method would be a vast detour for my purposes.

Only some framing observations are necessary. Truth is partly a social category here: which is as it should be. “The store of knowledge” is partly a social category. Every scientist relies on “secured knowledge.” In fact, there is even a label for that: the correspondence principle.

If the topic is the advance of knowledge, then social belief must be at issue. Truth is consensus belief—presumably the consensus is warranted. If that were not how it was, then there would be no textbooks. As to how an assertion is warranted, judged, that belongs in an exposition of method, which is not the concern here.

Up to a certain year, the consensus was that there were seven planets. It was based not only on observation, but on the tenet that God preferred the number seven.

Today we are sure that the people in the past were wrong because we have overwhelming observational evidence of two more planets. We have more resources—and we are freer from certain articles of faith. We find all this carefully chronicled in

James Burke, The Day the Universe Changed

(But I don’t want to rely too heavily on Burke’s interpretation of the chronicle he provides.)

It is no disgrace that the consensus changed when more sophisticated methods of detection were introduced and scientists became less deferential to articles of faith. That is the “advance of knowledge” with which we are concerned. It is no disgrace that mathematical propositions which used to be undecided are now regarded as proved. Again, that is the “advance of knowledge.”

Since Galileo discovered 4 moons of Jupiter in 1610, more moons have been discovered, and the count is at 47 at the time of writing. Anybody who can sneer at the notion that there are binary-decidable propositions about the number of Jupiter’s moons—and can sneer at the replacement of one consensus by another on account of increasing observational sophistication—is not a scientist (no matter what job they may have in a university department).

We assume for the purposes of this exposition that there is a human collective which has some consensus knowledge and knows how to get more of it. (It is exceptionally unlikely that we will change our minds about the number of ribs a human has.) Our assumption is not very daring. All we are assuming is, for example, that textbooks exist. The academic scientists who mock the assumption when I put it in play are just being unbelievably dishonest about their own lives and work. They are being unbelievably rude.

•

We proceed to a first look at the cognitive core—preparatory to modelling or formalizing it. I make no pretense to absolute philosophy here. Again, the exercise is armchair anthropology—a contribution to the natural history of vernacular thought. (As we have just seen, it is not-so-vernacular, since all scientists employ it all the time, even Rosser and Turquette, even as they announce that ordinary discourse is nonsense.)

It is late in cultural history to want to formalize the notion of the discursive cognitive core of language. It would have gone down better before Frege succeeded in capturing logic for mathematical apologism. That was followed, as we said, by a fashion of jamming natural language into the Fregean template.

All the while, the paradigm of physics (a term from Aristotle) changes. With Galileo, science became quantitative, and scientific knowledge came to be embodied in the equation—not the declarative sentence. Perhaps scientists imagined that they should communicate solely in equations—although that is out of the question. More recently, scientific knowledge has come to be thought of as algorithmic, as a family of computer programs. “Analysis by synthesis” is wanted by Stephen Wolfram to replace the inherited paradigm.

Given an assertoric cognitive core, the sentences confidently judged true are “pieces of knowledge.” We do not care here whether knowledge is important or unimportant; what we care about is whether the assertion is sufficiently specific to be subject to judgment “without context.” Let us collect some more examples of binary-decidable assertions, including a few that have not been confidently judged.

Snow is white.

Grass is green.

Crows are black.

The sun rises in the east.

All humans are mortal.

Socrates is human.

The Empire State Building is in New York.

The earth is flat.

The earth is round.

The earth is a planet.

The planets revolve around the sun.

Whales are fish.

All humans have the same number of ribs.

All humans have 24 ribs.

The Theory of Evolution is true.

There is life on Mars.

There is intelligent life elsewhere than earth.

The foregoing statements have the character of encyclopedia discourse, or of newspaper discourse (give or take reliability issues). They are sufficiently specific to be subject to judgment “without context.” They are, we say, candidate facts. Or factual generalizations.

The sentence about Socrates needs to be time-corrected to block the implication ‘Socrates lives today’. In Elementary Logic, Quine notes (in effect) that mathematics eschews temporality. He wants sentences with tense to be rewritten in the eternal present. To adapt his example,

The Seven Sisters cartel is formed in 1928.

The Seven Sisters cartel is formed after 1921.

The Seven Sisters cartel is formed before 1950.

Tense is replaced by reference to a universal calendar for all temporal occurrences. The latter two examples allow for statements which are essentially made on a different date from the event itself, i.e. predictions and retrodictions. The date is the date on which the statement is made. (Note that the Seven Sisters cartel did not become public knowledge until 1952. To assert its existence after it was formed but before it was publicly disclosed would indeed be a non-trivial retrodiction.)

The statement about the number of ribs has the character of encyclopedia discourse. It requires a convention to the effect that we ignore mutants with an abnormal number of ribs (if any) and those who live after losing ribs (if any).

As to the Theory of Evolution, we appeal to natural language’s suitability for painting with a broad brush. Evolutionists may or may not have quarreled about details of their doctrine. (That itself is a matter of fashion.) For all that, to the extent that biology has a part in public affairs, the savants broadly affirm Darwinism as the explanation of speciation, and that is what is being said here.

•

We come to a complication which we cannot avoid: the vicissitudes of symbolization. The meanings of words are in play for several reasons. The meaning of the biologist’s term ‘life’ is put in play by the “advance of knowledge” itself. As I noted, something has already happened to the word ‘moon’ as more moons are ascribed to Jupiter.

In the case of ‘Whales are not fish’, the closer study of whales leads to the word ‘fish’ being redefined in a preferred way. The same happened with the word ‘planet’ when earth was reclassified as a planet by the work of Copernicus and Galileo.

Incidentally, the latter is an example of how abrasive an advance in knowledge can be. There were all sorts of common-sense proofs that the earth was not a celestial body like Venus or Mars. One by one, reasons had to be given for not crediting those proofs. Ancient cosmologists made two mistakes in particular.

i. They believed things for “aesthetic” reasons, without observation. Males and females have different numbers of ribs.

ii. They assumed that they could infer what was from what seemed. They did not expect reality to be wildly counter-intuitive.

To continue reviewing our facts, when an inaccuracy embodies a customary simplification, as in calling the earth “round,” it is a matter of convention whether the inaccuracy will be forgiven.

‘The sun rises in the east’ has remarkable difficulties. After Copernicus, it was permissible only as the report of an objective illusion. After General Relativity, it again became a possible truth, but now only an arbitrary one. Beyond all that, ‘east’ may be defined as the direction in which the sun is seen at first light. Unless we have a reference-point for direction other than the sun’s transit, the assertion is a tautology. (When was the magnetic compass invented?) To sort that out is quite beyond the scope here.

Issues of definition go out of control with respect to the assertion ‘God exists’. People quarrel over the existence claim without making any explicit commitment as to what ‘God’ means.

It seems hopelessly unrealistic to select a vocabulary at some point in time and assume it never changes. Common words, such as ‘life’, get redefined in expert discourse because of the “progress of knowledge.” Words drop out of the language. It is hard to say ‘Phlogiston does not exist’ because nobody will remember what phlogiston was. ‘energy’ and ‘inflation’ are relatively recent words which are now taken for granted in physics and economics (and physics).

It can be more extreme than a mere revision of the vocabulary. There can be a paradigm shift, a Copernican revolution, as we mentioned above. We won’t try to address that frontally. One should imagine it to be included vaguely.

On the one hand, judgments about what we know and don’t know are always made relative to a language fixed at the present moment. Savants did not speculate what they would believe about “energy” before the term was introduced. On the other hand, our very goal here is to model “the progress of knowledge,” the “advance toward the entirety of truth.”

So much knowledge is quantitative nowadays. Where indeed do equations, such as ‘1 + 1 = 2’, fit on this map? You may believe that they do not have the same epistemology as statements of fact. On the other hand, there are propositions such as Boyle’s Law which make quantified generalizations and do count as factual. Provisionally, we include all propositions called true on this map, even if they are expressed in symbols.

One reason for including propositions of pure mathematics in the collection of assertions is that mathematics has famous unsolved problems. With the passage of time, they are solved, usually by methods of proof which involve extremely heavy machinery. It is clear-cut and amazing: that our knowledge gets increased in this sense. And before the propositions are proved, they have entire careers as speculations or hypotheses. Philosophers are not as astonished at this phenomenon as they should be. Let me mention

George Owen, The Universe of the Mind

which is helpful in registering “the differences in the progress of physics and mathematics.”

And natural-language tautologies? Do we count them among the truths? ‘Water is wet.’ ‘Every bachelor is unmarried.’ There is a convention of applying the same word ‘true’ to ‘Every bachelor is unmarried’ and to ‘Grass is green’. It has always been a sore point. I don’t like seeing such sentences in the cognitive core. If there are facts in play, the facts concern the language in which the statements are made as a social convention.

It is more difficult if it is believed that pure mathematics consists of tautologies, of truths of convention. But the “truths” of pure mathematics do not behave like definitions. That is what George Owen was telling us about. They are not true by inspection. “They are true if provable.” That they are provable means that there is a game and that one “position on the board” can be derived from another, possibly as the result of a long number of obscure “moves.” One of them may have been posited as a speculation for centuries before it is proved.

Should the model of the cognitive core cover definition-sentences? I don’t like that solution. Just as we find it far more fruitful to separate statement-matrices from statements, I prefer a separation of definition-sentences from facts. But how tricky will it be to pare off natural-language tautologies or definitions? Vernacular English grammar does not pare them off.

Tautologies bring us to that other nuisance, declarative sentences of the sort ‘I always lie’ or ‘I am not here’.

If you assign T to ‘I always lie’, then it is F. Part of what allows that is that the assertion characterizes itself as one of a collection of utterances. Part of what allows it is that the characterization is an assignment of truth-value.

To free the cognitive core of these nuisances may be the most difficult, technically. But in practice this and other of the paradoxes which engross philosophical logic are not impressive problems. The occurrence of such an utterance requires the speaker to have an intent which is never observed in practice. We choose not to treat them here.

I do not want to embark here on the contemplation of sentences such as ‘This sentence is in French’ or ‘Language does not exist’. They are so “bad” that they shatter the discourse-universe. Analytic philosophy has no inkling of any of this. If these sentences had been taken seriously by previous thinkers, I wouldn’t have to write this.

•

Natural language is oceanic and multipurpose. Figures of speech can be in play at any time, a feature which is inseparable from ambiguity or polysemy. “Home is where the heart is.” “A blue mood.”

The problem which surfaces here is not easy. Statements meant to do the work of facts do employ figures of speech, including regularized metaphors—and to expect a literal translation in every case is quite confining. (I employ figures of speech in this manuscript and the tone would suffer if I tried to literalize them.) On the other hand, there is a case for neutralizing figures of speech and so forth as far as possible. One may not be pleased to lose “a blue mood” from the universe of discourse, but at some point the combinatorial generation of the cognitive core will be proposed, and we don’t want to end up with sentences such as

Chartreuse thoughts cause cancer.

So far we have focused on declarative utterances. Presumably the cognitive core would be drawn so as to exclude the apparatus of non-declarative utterances. All the same, that apparatus is important instrumentally to the cognitive core, and is closely related to it grammatically. The question-form. Directives and permissions: laboratory science must have them.

Assertions have to be taken at face value; they cannot be offered as shamming, as sarcasm, etc. Strictly speaking, Rosser’s and Turquette’s staged debate is not part of their book. It could be rejoined to the book as a collection of specimens of professional views, mainstream and marginal.

•

The destination of this explication is not just the core of binary-decidable “factual statements” (as opposed to e.g. statement-matrices) in a natural language. Nor even the collection of all statements confidently judged true on some date.

The destination is the claim that knowledge advances, that science progresses, which presupposes the cognitive core as its material. The claim of the advance of knowledge, as we intimated, appears stereotypically in the propaganda for science. It is also a key tenet for any number of out-of-fashion middlebrow philosophers (including Adorno, who is not so out-of-fashion).

I reach arbitrarily for authors who pontificate on the advance of knowledge. Namely, the aforementioned Owen and Burke. Owen’s history presupposes that “remarkable progress has occurred.” On his page 9, he draws our attention to a point which will matter to us: “the differences in the progress of physics and mathematics.”

Burke’s book would be a perfect model except that it seems to have been written at a moment (1985) when an idiotic cultural relativism was fashionable. The substance of Burke’s book is an unremarkable chronicle of scientific progress. But he also puts the notion in play that the earth was flat when, and because, people believed it was. Given an author who cannot contribute any substantial dissent from the conventional wisdom (say an incontestable proof that 0 = 1), his faddish teases amount to insincerities and errors which I will leave it to the reader to identify.

Nothing sells better than fake radicalism and nothing sells worse than geniune radicalism.

•

We assume that for each year, for example, we have the combinatorially generated declarative sentences suitable to the cognitive core as spelled out above. As customarily understood, they are binary-decidable.

For each year, we have the vocabulary; it assuredly changes from one year to another. If we want to, we can imagine a core which employs a common vocabulary which is stable over the long term. That would allow us to tell ancient people that the earth is round. It would allow us to tell ancient people that the earth is a planet.

[As we saw, it would not be as straightforward as telling them what they do not want to believe. If you use a word in a sentence offered as true, and that sentence clashes massively with accepted fact, there is a problem with whether the speaker respects the word’s meaning.

Angels live in burrows like moles.

It is conceivable that there could be an empirical observation to that effect. Nevertheless, people who believe in angels would have to give up so many of their assumptions that a strain would be imposed on the word ‘angel’. People who don’t believe in angels would have to give up even more assumptions.

In fact, consider a known falsehood.

The Empire State Building is is Albania.

This sentence does not challenge us because: nobody advances this proposition as a truth and suggests that we should discard the beliefs that make it improbable. The sentence is in play only to make knowledge grammatically symmetrical. If somebody began booking tours to Albania to see the Empire State Building, that would put a different complexion on the matter. We would ask, has something happened to the meaning of ‘Empire State Building’? Stability of meaning of an entity-term depends on stability of the fabric of facts bearing on the entity.]

This project in modelling is made more difficult because the vocabulary changes. And because a reconstruction of notions, meanings, may be initiated by the introduction of a new word. If all of this is an unwelcome complication, that again tells us something about the tools which contemporary logicians have given us. Again, contemporary logic is subservient to mathematics—and not to mathematics as it develops historically. Quine and his peers proceed from a Platonic fantasy of eternal truth.

Evidently we must acknowledge time-dependent considerations in the language and in the world which it may be imagined the language is supposed to depict. Each new day brings facts, about the weather, about geologic occurrences, about people’s doings, which simply add information. Even if we believed we had a universal deterministic law, so that every later occurrence was rigidly predicted by the law we already had (as we do with planetary motions), we would want to continue to collect data independently to confirm our law. We have no safeguard against a generalization which works every time except the last time.

Time-dependent considerations give us our very topic. Namely, that sentences are meaningful but cannot be judged, or judged with confidence—then subsequently are judged with confidence.

Riding roughshod over all difficulties, we imagine the set of sufficiently specified assertions made in a vocabulary which is stable over the long term—so we can correct a previous generation in words already known to them. Now we can begin to speak of “the progress of knowledge,” and “speculation” as one of its adjuncts.

A sentence is binary-decidable. If we judge it confidently, if our judgment is that it is true, then it becomes a piece of knowledge. For symmetry, the known falsehoods are just as important as the truths. It is false that the earth is flat—and it is false that the whale is a fish (although as noted, that may involve redrawing the scope of a word).

In this context, an increase in knowledge means an increase in sentences which we judge confidently.

As knowledge progresses, is it that more sentences are judged, or that there are more sentences judged true? There are two reasons why our stock of true sentences might grow. One is the sheer passage of time. Then the stock of facts allocated to chronicles will grow steadily. As there are more days, there will be absolutely more sentences announcing whether it rained on a given day, for example. We already noted that.

The other occasion of an absolute increase in the number of truths has to do with the growing vocabulary which has been found difficult to incorporate in the model. There are entire new collections of truths keyed to the introduction of new words.

•

We finally come to “the progress of science.” “We already have some knowledge and we know how to get more of it.” “We trek endlessly toward the totality of truth without ever reaching it.”

We make inroads on the collection of sentences which we were unable to judge. We acquire the means to judge sentences confidenty whereas we did not have these means earlier. The number of planets. Jupiter’s number of moons. The composition of water from two gases. As with the proposition ‘The earth is flat’, it may involve revising what was previously accepted, on the basis of what is considered overwhelmingly greater confirmation. It is not just that we change our minds, but that we have far greater warrant for our judgment.

Now we understand why speculation conventionally has a place and is conventionally respectable. Speculation is directed at the subset of well-formed assertions which we presently cannot judge with confidence.

There is life on Mars.

In the absence of disproof, one elects to believe an undecided sentence. In fact we see certain scientists committing in advance to life on Mars, literally because to find life there would excite the public more, and would add to the prestige of space exploration.

The person who speculates may go further, and imagine that there will be a paradigm-shift which will vindicate a proposition that seems most improbable. (The earth is a planet, asserted before Copernicus—?)

•

So far, cultural anthropologists that we are, we have assumed that a vast discourse is in play. The problem is to pare it down, and to brush up sentences which are mere proxies for important truths, or at least for truths.

Socrates is human.

The earth is round.

The sun rises in the east.

So-and-so’s mood is blue on such-and-such a day.

We can turn all this around. We can imagine a vocabulary and syntax to be specified, along with special restrictions on word-order, scope of qualifiers, etc. Then we can speak of all declarative sentences which can be formed combinatorially. Then we would have all the well-formed propositions, which would be binary decidable.

That closure of the formation-algorithm (?) would be the universe of discourse. It would be standard practice to order the sentences by word-length, and suborder them alphabetically. Knowledge consists of assertions which are confidently judged true. (The earth is round.) Anti-knowledge (if you will), which symmetry requires, consists of assertions which are confidently judged false. (The earth is flat.)

> ‘There are seven planets’ is false and ‘There are nine planets’ is true. (Given that these assertions are well-understood shorthand, as natural-language sentences usually are.)

There remain a vast number of assertions which are undecided. Over time, “knowledge” will more or less expand into this latter collection; undecided assertions will be decided. Meanwhile, the undecided collection holds great opportunities for legitimate speculation.

There is life on Mars.

There is intelligent life elsewhere than earth.

•

I want to proceed now to more revealing implications of the conventional wisdom. (Conventional wisdom for James Burke or whomever you like.)

Thought, the universe of discourse, is made up of assertions such that undecided assertions “have a half-chance” of being right. More precisely. Each unsettled assertion is binary decidable. If one tosses a coin, letting “heads” be “true,” there is a half-chance that the coin will give the right verdict on the assertion.

There is an equivalent observation for already-judged assertions. With respect to the Theory of Evolution (it appeared in one of our examples), if you toss a coin, there is a half-chance that the toss will yield the authoritative verdict, i.e. will yield “heads.”

It is the undecided assertions which are showcased here: because relative to them, the coin-toss gives you a half-chance of obtaining a right verdict and so of adding to your knowledge.

That is in interesting comment on questions which have solid answers we can never find, a popular topic in today’s hard science. You can toss a coin, obtain an answer and espouse it, and you may be right. The answer is not necessarily inaccessible. It is a matter of being content with a gambler’s chance.

“Our knowledge is an accumulation of truths.” (Together with a certain amount of discarding what were previously accepted as truths.) “But while more and more assertions are settled, we never settle all of them.” That is the basis for the standard attitude toward (scientifically permissible?) speculation.

[We abstract from the case where there are reasons of plausibility to reject something even in the absence of an exhaustive empirical investigation. We set aside issues which would be detours, as all inquiries do.]

So we have a culture of “treking endlessly toward the truth” and of legitimate speculation.

“It is reasonable to infer cosmic consciousness from quantum nonlocality because tomorrow the majority of physicists might agree with the inference.” “It is somewhat reasonable to believe in visiting aliens because the belief is binary decidable and might be ‘socially confirmed’ tomorrow.”

An officer of the NYU Atheists Club told the student newspaper c. 1999 that the existence of alien visitors is better than the existence of God because it is subject to empirical proof. If I may put words in his mouth: the literal existence of alien visitors is a legitimate speculation.

A scientist’s attitude toward an as-yet unjudged assertion must be: we haven’t accepted that … yet.

• • •

Because the conventional wisdom allows a half-chance of being right to so many assertions, it gives a broad legitimacy to speculation. (Remember that all academically accredited discourses are included.) It also accords legitimacy to unknowable knowledge.

This state of affairs does not convict itself of being a fault. (Except that it starts to be suspicious when we realize that science is an ignorance machine.) It is customary to be hospitable to speculation, in the sense spelled out above at such length.

Here is where I shall take my leave of the conventional wisdom. My perspective proceeds from insights which I hinted at when I spoke about sentences which are so “bad” that they shatter the discourse-universe. I have told that story in various of my publications; I assume it here. I am a cognitive nihilist, outside “human thought.”

To resort to metaphor, I am an anthropologist from another planet. Anybody who engages with humankind is confronted with a ready-made mass of fantasy, an inherited mass of fantasy, for want of a better word. (Forget about constructing it combinatorially out of clean elements.) When I want to interact with the civilization, I glean devices from cognitive nihilism to metamorphose the determination of reality. It is hypocritical of me, as I explained elsewhere. The social constituency which is the target of my intervention does not see my hypocrisy.

My intervention is implanted in the “fantasy” they espouse, and builds on it. I engage selectively with assertions as an interloper, targeting the assertions which are socially compelling.

Taking astrology as an easy example, I don’t deem it to be socially compelling, so I wouldn’t intervene in it.

My iconoclasm allows an “epistemology” which would be illicit, conventionally. I do not posit a universe of binary decidable assertions: such that you may espouse an (undecided) assertion and have a half-chance of being right. What I do not choose to engage with I regard as a blank so far as its “role in knowledge” is concerned. The culture of “treking endlessly toward the truth,” and of “legitimate speculation,” is intolerable cognitive clutter.

Again, the areas in the universe of discourse which I don’t engage with are blank for me as far as judgment or espousal is concerned. Assertions which I don’t find formidible, socially compelling, are not on standby waiting to have their truth-values discovered. They are clutter.

I do not endorse the perspective in which: “the literal existence of alien visitors” is an acorn waiting to be added to the storehouse of knowledge.

It is worse than this. I may change my mind about whether a doctrine is worth fencing with. Later in life I began to write about the Diagonalization Lemma, the Completeness Theorem, literary grammar, theoretical linguistics (if that is the right term), world history, history of religion, and even clairvoyance. I wrote notes on the social history of the occult and on the political history of flying saucer reports. Just to protect my own credibility, let me underline that the latter topics are no different in principle from any topic in the field of public affairs. [Flying saucers have a political history which has nothing to do with belief in flying saucers. The problem is that it may involve a lot of unrecoverable government secrets. We need what the courts need: better forensics.]

I don’t know whether I branched out into these areas because I have too much time on my hands, or because I wanted to take a chance on changing minds which otherwise would not be in my prospective audience.

It may seem particularly illicit to deem discourses in the established fantasy a waste of time—and then, later, worth bothering with. But that is indeed how a visiting anthropologist treats native belief. No logical permission is needed when I decide to heed a discourse I previously ignored—because the notion that discourses connect up rigorously in a system is another fantasy.

The culture of “treking endlessly toward the truth,” and of “legitimate speculation,” is superstition. So it is that I conceive the fault named credulity far more broadly than conventional wisdom does. In consequence, I conceive dignity far more narrowly than conventional wisdom does.