Tautology

Tautology is any circular proposition. The circularity is concealed in different but synonymous terms. Thus, tautology is not identity, in which terms are repeated. The principal epistemic characteristic of tautology is that it does not say anything about any specific term that is not already implicit in the term. However, this definition is deficient because it does not allow for what is actually known rather than for what is known by individuals. Consequently, a tautology does not say anything about any specific term that is not common knowledge. This still is a rather vague because there is really no way to define accurately what common knowledge is, i.e., it would be oxymoronic. The only reasonable way out would be to define tautology within a context of enquiry, which presupposes a shared specific fund of knowledge. And in this sense it can be argued that tautology is any proposition that does not advance knowledge. For the rest tautology is any observable circularity of thought or expression.

The following is a tautology (from Flew):

(p  v  q)  v
T  T  T   T
T  T  F   T
F  T  T   T
F   F  F   T.

Flew describes this tautology as a truth-functional compound. Truth-functional is any operation or formula that yields or possesses truth-values. He concludes: "For this reason one can say that a tautology is an empty, or vacuous, proposition, that says nothing about how things are in the world, since its truth-value is independent of the way things are. It is a logical and not a factual truth..."

Wittgenstein extends the vacuity trait to all formal-logic operations, e.g., the syllogism, i.e., a = b, b = c, ergo a = c. And in effect without the cognitive operations of variable-substitution and truth-functional qualification of the substitutions, this formula is meaningless and empty. However, the same thing cannot be said of intuitive logic, which does indeed follow the vacuous formulas of formal-logic, derived from intuitive logic, but is itself never empty of contents. Intuitive logic is always interactively operative with other basic-cog's or with the inputs of experience.

Theology

The question about theology is whether it is merely private philosophy. Belief in God is not a purely private-philosophy attitude, but what you elaborate from this premise might just be. If you hew to logic on non-personal issues, you could escape the private-philosophy trap, i.e., the belief that purely personal beliefs are philosophical, but if you believe, e.g., that God is with you, then you are totally out of the philosophical field. It may be good for the ego and for well-being, but it doesn't lead to any valid inferences about reality.

Theory of types

According to Quine, self-reference is the source of paradoxes. This is true to a certain extent. Consciousness is quintessentially self-referential and it is the source of paradox. However, in my view it is the mistaken application of the identity relation that engenders paradoxes. The Quine explanation of Russell's paradox is that class of classes is self-referential. My own explanation is that class of classes posits a self-contradictory identity relation. A class of classes does and does not include itself.

One solution to Russell's paradox is to ban talk of classes of classes. But this is like denying that there are classes of stars or that there is no concept of concept. In point of fact, stars can be studied as a group or set and there are also different classes of stars which can also be studied in themselves. Concept is the mental representation and equivalence of the verbal expression "x is or exists". Is there a concept of concept? The concept of concept is the mental representation or equivalence of the expression "concept is or exists": the "expression `concept exists' exists".

Russell's theory of types is a solution to the paradox that bears his name whether it is self-reference or identity that produces the paradox. The theory of types consists in the exclusion from set theory, or from talk of classes, of any proposition involving classes of classes. Classes of classes, e.g., classes of classes of stars, become types in the theory, and in the case of types of types, they become type A, B, etc. But what this amounts to is simply accepting that stars can be studied in themselves and not necessarily only as specific classes and that there is the concept of concept however circular the expression may seem. In sum, Russell tried to muddy the waters and they of themselves cleared themselves up. It was, to put it another way, a storm in a puddle. I cannot speak for set theory, but it seems his paradox had no consequences to speak of, just as Gödel's "proof" is but a curiosity in the history of mathematics.

Theseus' ship

This is a metaphor implying ad lib. It is also used in connection to the relation of identity. It also implies flexibility.

Thought

See   Representationalism

Thought and meaning

Dummett, The Origins of Analytical Philosophy (1993)

p. 134
"It is because concepts...cannot be spoken of as coming into the mind as ideas can that they cannot be described as contents of consciousness; and it is precisely this that gives the strongest grounds for believing the fundamental axiom of analytical philosophy, that is, that the analysis of thought both can and must go via the analysis of the linguistic expression."

I hear and repeat the sound of the word "paparazzi". I know what the word means. Something has come to my mind: not an image, nor other words. Suppose we do not call it concept: but whatever it is it comes to my mind and with it meaning can be expressed in sentences, such as "celebrities resent paparazzi". It all occurs inside my mind. Dummett does not know any more than I do what exactly went on, but something did and the expression "to come to mind as awareness" is as good as any other. Supposedly my ability to apply the concept constitutes my having the concept. But in fact I can say and know "pararazzi" without ever using it and therefore my ability to apply the concept must be independent of language: it has to be a mind thing. The meaning was brought forth from the subconscious by the appearance of the word.

Supposedly only from a theory of meaning for a language can we account for thought. But a theory of meaning for a language understood as being the expression of thought is a singularly circular proposition. What is thought? Thought is language! And what is language? Language is meaning. Logically, thought is meaning. But what is meaning? Meaning is language and, logically, meaning is thought. You never get away here from the use of three terms!

Alternatively, how do we know thought? From the meaning of language. The use of language is equivalent to the meaning of language. Logically, the use of language is the way to thought. But how do we distinguish between the use of language and thought since thought is the meaning of language? And since the meaning of language resides in its use, thought is equivalent to the use of language, and so on. But language is not foundational/basic enough for this sort of circular reasoning. Even if there were some kind of relation between the ability to think and the structure of language, you would still have to go to thought directly with language rather than to language in order to comprehend thought, for it is perfectly possible to have thought without language syntax/sentence structure, as in "ride bicycle man", and in countless examples.

What can propositionality do? It must accommodate the basics of physicalism into its account. It must include the recognition that thought is material and takes place in a nervous system. This brings in the theory of squiggles. We can describe cognition in propositions including wffs but we cannot not even contemplate the possibility that we think in a public communicative language. We think therefore in something that Fodor has unoriginally dubbed "mentalese". The questions is: what is the nature of mentalese? It is a form of representation that we could interpret if we had it in written form. But it is not a verbal language. It is a system of "grammatical" symbols which produce the symbols which express all our cognitive processes from images to symbolic logic. There is a visible "analog" for this mental system and it is the squiggles that appear on operational computer files. But this merely gives us the possibility of a name. We shall call mentalese squiggles. The more important point lies elsewhere.

Time

 Time is one of the necessary conditions of existence. Time envelops all existents. Without time there would be no existents. In sum, existence is inconceivable without time. But the concept of time comes into existence from life as awareness. The source of the concept of time is awareness: awareness of the past, of the present moment of awareness (which is shattered by continuity), and of possibility in the future. In fact, time and awareness could be said to be "consubstantial". Time is the essence of awareness. Awareness is the basis of time, since time cannot but come to be through awareness.

We know two versions of time: measured time and lived time. Measured time is its division into seconds, minutes, hours, days, years, eras, etc. It has a history going back to the birth of civilizations. Lived time is the memory of the past and the thought of the future. It cannot however be divided into equal, measurable lapses the way measured time is.

Lived time is usually categorized into past, present, and future, but in fact there is no present at all: it is the future going into the past. The most that can be said of the present is that it is the instant of recognition which has been measured as 1/24th of a second (42 msecs). Beyond this, the present does not last and it seems to exist only from the sustainment that memory gives to cognition and to awareness. In sum, we think we are aware of a present because we remember clearly the passing instants of recognition, but as time continues these become less and less precise leading to the unavoidable conclusion about the relativity and fugacity of any possible present.

From the perspective of lived time, the past can be divided into more or less discrete periods of measurable time depending on the criteria use. This applies equally to the lives of individuals and to history, thus leading to the issue of the relation between time and history. History is, to put it briefly, the public and collective version of time. Our lives are historical to us in the sense that we can divide them into periods in the way that history is divided. When they have a public and collective significance or impact, they are historical in the strict sense. In other words, time is always potentially historical but it is not the same as history. If, e.g., we argued, as we will, that it is history that validates interpretations and that this is the becoming of being, we can indeed claim that history, but not time, is the basis for the refutation of the being/knowing dualism, which is the origin of all forms of dualism.

We can say that history is public and collective time. But we cannot say that time is strictly individual, because paradoxically time, much of which is excluded from history, envelops history entirely the way it envelops everything else.

From "The Enigma of Time", in NGM, v.177, no.3, March 1990
The statement that "Early people presumably first realized time passed when they saw that they lived in a world of constant change" is at best dubious, and very likely false. "The long struggle to affix numbers to the passage of time parallels our organizing ourselves in a complex, modern world" is also a suspect statement. There is no practical and/or meaningful distinction between "organizing ourselves" and measuring time, because organization presupposes time, it happens in time, it assumes time, hence the need to measure time is necessary to the task of "organizing ourselves". Another incoherent statement: "Without an event, there is no time. This means, [John] Wheeler [Princeton physicist] believes, that time may be a secondary feature of nature, not a basic one."

More absurdities: "In contrast, [Edward T.] Hall [New Mexico anthropologist] says, many peoples of Asia, the Middle East, Africa, and South America live in `polychronic' time. Everything goes on at once--talking. eating, reading, praying...Similarly, almost everybody may have lived this way once, since time was usually viewed as a circle, turning back or in on itself, all things possible at all times. This view of time remains central to Buddhist and Taoist belief, in which linear history is a fiction, since all things return to a former state" [but the cycle exists, so time too exists]."

 Chronological time is clock time or objective time. We "endure" in clock time. Duration is subjective time. Duration necessarily involves affects.

Our thoughts in the present connect to both clock time and duration and they involve the categories of present and past. Both from experience and logic we know the present is the instant. What defines the instant is recognition which is discrete. The restriction of present to the instant means that the past is all of reality excluding the instant-present. The past contains the manifold of experience. Hence, it is the source and the repository of the categories of time. The categories of the past are both conventional and relatively discrete. i.e., they have boundaries which are not iron-cast. Since the instant is part of a continuity with the past, the present too is a discrete category of past. We can define the present in different ways. The present as instant is evanescent and cannot really be categorized. In this sense it is non-existent.

Are the categories of the past arbitrary? Cognition is the source of the categories of pastness. Since the foundation of cognition is logic, then the categories of time in the past cannot be arbitrary. However, since cognition produces interpretative as well as apodictic and necessary inferences, and the inferences about time, except that it is and other such fundamentals, are neither necessary nor apodictic, then the categories of time must be interpretative. My present is not your present and to each his future. Historiography is controversial. Yet reality moves to the rhythm of clock times so that the subjectivity of time is predicated on the objectivity of time. It is time itself as history that can validate interpretations.

Contrafactual reasoning is useless for the understanding of the past, the "present", or the future. The past can only be (a) recalled as accurately as possible, and (b) analyzed from facts as impartially as subjectivity will allow. The "present" is self-evidently the future going into the past or becoming past, but it is possible to perceive and conceive the present as "situation" in very restricted or very precarious temporal and spatial terms. For instance: the "present" of Sikkim is hardly the "present" of Germany, and the "present" of Germany, which is very different from the recent past of Germany, is quite likely a very impermanent situation, so that even its future could, from a certain perspective, seem more "solid" than its "present".

The future can be conceived as either clock-time or duration. It is the instant "projecting" the past. Since the instant is evanescent, the future must also be nearly non-existent. But the future can also be seen as threatening and this is the contrary of evanescence or non-existence.

El futuro parecería ser indefinible, pero sólo en apariencia: aunque no sepamos nada de lo que va a pasar, el porvenir admite categorías, y sólo las cosas que existen pueden ser categorizados. El pasado ciertamente existe y sus categorías son palpables: ayer, antier, las cosas más importantes la semana pasada o el último mes, el año pasado, y así regresivamente. Las categorías del futuro se basan en el concepto de infinito, en los proyectos a corto y a mediano plazos, y en la inevitabilidad de las actividades cuotidianas. El infinito es la renuncia, la muerte, la indiferencia. El mediano plazo implica que la vida tiene que tener algún sentido. El corto plazo es la inevitabilidad del tiempo. La verdad es una función del futuro. Las actividades del ser humano surgen con relación al futuro. Los hombres y las colectividades se relacionan entre sí con relación al futuro. Es difícil generalizar, pero como norma a mayor desarrollo intelectual, científico, social, etc., mayor proyección hacia el futuro.

Time and knowledge are reciprocally implicative. Before we applied cognition to time. But time has its effects on cognition. The totality of knowledge is as temporal as it is psychological. In a sense, temporal and psychological are equivalences. Such being the case, we can only have "descriptions" of reality. We do not have reality beyond its temporal knowledge, which is pure transience. Time permits knowledge to arise. But since time and change are bound by adamantine chains, knowledge changes, and the change of knowledge inspires the distrust of knowledge. History, which is also time, must re-establish our confidence in knowledge.

Objective time plays havoc with knowledge. History is time restoring knowledge. But if history must be categorized and the categories of time are interpretative, then history is interpretative also. The dilemma of history and knowledge is that of interpretation validating interpretation. But have we alternatives?

The most extreme reification of time, as well as its highest exaltation, appears in the late Zoroastrian text known as the Persian Rivayat (Whitrow): "Except time all things are created. Time is the creator; and Time has no limit, neither top nor bottom. It has always been and shall be for evermore. No sensible person will say whence time has come. In spite of all the grandeur that surrounded it, there was no one to call it creator; for it had not brought forth creation. Then it created fire and water; and when it had brought them together, Ohrmazd came into existence, and simultaneously Time became Creator and Lord with regard to the creation it had brought forth."

The present is also reified in pain. The following quote is from the late 70's:
"Sólo existe el momento doloroso del presente. El pasado existe pero es un vacío de realizaciones. El futuro es más que todo incertidumbre aunque la conciencia se proponga los proyectos más grandiosos. Los negocios fallidos se mantienen en la memoria como acechanzas. Se trabaja y no se ven beneficios. La vida es siempre la misma lenta brega. Y encima de todo, los negocios, que no producen nada pero siguen haciendo sus reclamaciones impostergables, le roban tiempo al trabajo intelectual. El sexo es un dilema particular. El amor es un mito, una conveniencia y nada más. El libertinaje es un fuego fatuo en el que más se pierde que se gana. El saldo final es la traición de lado y lado, la desconfianza y el resentimiento. Lo que queda es una soledad abrumadora. La paradoja más grande es que cada pensamiento tétrico es como un mordisco a un queso distinto: suizo, camembert, reblochon, pimiento. Es una tragedia comoda, hasta grotesca. Casi se diría que la conciencia herida no merece ser tomada en cuenta: es la nada de la nada." Pain, or pleasure, would seem to affirm the present. Yet the text contains the refutation of the premises.

J.R. Lucas, in The Future: An essay on God, temporality and truth (1990), has another concept of present: "Time is the passage from possibility through actuality to unalterable necessity...Whereas the present and past are real, the future, as long as it is still future, is not; only by becoming present is it actualized into reality: hence the passage and the direction of time."

Time and space

If we apply the idea of precedence, it might perhaps seem that time must exist before space, for how can anything come to occupy space unless there is duration? Suppose something just suddenly came to be, or that everything came to be in an instant. This is conceivable, in which case both space and time would be simultaneous. Yet without time the instantaneity of space would imply its instantaneous extinction. But does this imply the precedence of time? The more rational proposition would be that one cannot be without the other and that there are no precedences here. We cannot have space without time, nor time without space.

We can more easily conceive of time without space, e.g., a thinking entity that just thought about itself without any connection to things outside of itself. There are many analogs of time, e.g., a clepsydra. Can we say the same thing of space? Space arises from physicality, hence any physical object can be a representation of space. But using the instantaneity argument, the physical necessitates time to survive. We go back to thought aware of itself, but strictly speaking there is no awareness of awareness as such. To go beyond this would mean positing some transcendental reality for which we have no evidence from our experience. We cannot have knowledge without something to know and that something is reality. But it does not make one whit of difference to knowledge whether time is more fundamental than space or vice versa! This codependence between self and reality entail the denial both of pure idealism and pure realism.

Even though time and space constitute an indissoluble continuum, language at least makes a clear distinction between them so that we cannot say an hour of space or a mile of time.

TNT (Typographical numerical theory)

See Artificial intelligence (AI) and TNT

Token

see   Type and token

Totalities

(A) Richard Bellamy on Giovanni Gentile, Opere filosofiche (Edited by Eugenio Garin; Milan: Garzanti), in the TLS, November 8 1992, p. 6

"In his search for a philosophy without presuppositions of any kind--either empirical or a priori--Gentile was driven to make our present activity of reflective consciousness the absolute foundation on which all else depended. The act of thinking became in this way the `pure act' which provided the source of all human experience. Through thought we literally created ourselves and the world around us...Thus, each individual act of thought constituted an element within the development of human consciousness as a whole." This statement defines the imaginary concept of the totality of awareness.

(B) Gregory Currie on Gordon Baker, Wittgenstein, Frege and the Vienna Circle (Blackwell) in TLS, February 17-23 1989, p.163

"The world is fully described by the totality of true propositions. As a consequence, the limits of language are the limits of the world."

Comment
(1) The "world" here implies a controversial "realist" version.
(2) Otherwise, "true propositions" means all thought, because our fantasies are "true".

(C) "Reality is the totality of all possible conscious experience." (Peter A. Angeles, Dictionary of Philosophy (1981)

Transactionality

I can qualify propositions as knowledge by myself. But I am also aware that I am error-prone. Therefore, when I undertake to qualify propositions epistemically, I take into consideration the propositions of others on the same subjects or themes. This does not mean that I am going to accept what others say instead of what I believe. It means that I am going to be engaged in transactions between my beliefs and those of others. The eventual qualification of propositions will be a transaction and my knowledge will be transactional.

Even factual propositions, arise from the interaction between the propositions which constitute the contents of mind. In this sense of an ideal totality of propositions which are knowledge, knowledge in general, as opposed to my knowledge, is also transactional. There is knowledge that is not transactional, but without transactionality we could not have an accurate understanding of knowledge.

Reality can be said to define knowledge. But reality that is not my reality does not exist, and to define reality as knowledge does not clear up matters. I have to work with reality, as I grasp it, and to extract knowledge from reality there must be a propositional transaction between myself and the world.

Since knowledge is a transaction between the self and the world, then obviously knowledge must emerge from the interaction between my self/world transactions and the self/world transactions of others. The sum of these transactions is reified or manifest in artifacts, e.g., books, gatherings, etc.

Who possesses the sum of these transactions? Who decides between all these transactions? No one, and the only possible answer is that the bounds of knowledge are impossible to fix, i.e., if I am right, someone else may be wrong, and vice versa, and these relative positions can change over time. The bounds of knowledge are never fixed and they can never embrace their imagined totalities, although the historic tendency is towards their continuous expansion.

Transactionality is merely the "external" process of comparing our beliefs, with the beliefs of others. It does not involve any special basic cognitive propositions. Transactionality is a rational process, but it is not reason itself and as such it does not merit a category different from reason/perception/etc.

Transactionality per se is ancillary to cognition, i.e., it can, e.g., reinforce a probability judgement, and therefore it can take us no closer to the understanding of cognition than the analysis of probability judgements themselves.

Nevertheless, transactionality is the essential "element" in the external perspective on knowledge, the perspective that allows us to discover the possibility of error, the perspective that requires additional justification in search of validation, and the perspective from which we are less liable to error than from the internalist justification of propositions.

Evidently, the external perspective on knowledge is only possible from individual awareness, for which all is belief in or indifference to propositions. Even without the external perspective I can on reflection modify or abandon a belief, but the possibility of error is diminished with the addition of inter-subjectivity and transactionality. Even with intersubjectivity and transactionality, I could still be entertaining false belief, so the increase in the possibility of knowledge is all that, for individual awareness, emerges from the externalist perspective on knowledge. Another believer could have valid belief in some area where I, even from an externalist perspective, entertain a false belief. This believer in turn could have false beliefs, which, from his externalist perspective, could be subject to correction or modification or renunciation of belief. However, in the case of certain propositions, e.g., perception, justification is tantamount to validation, i.e., transactionality would be superfetatory.

Transcendental idealism

The Kantian doctrine that there is a noumenal world outside of its phenomenal representation but that it is a world that cannot be grasped by mind. Even though we can only have our thoughts we can make some necessary inferences about the external world, one being the law of cause and effect.

Trivially true

Basically this phrase embodies a maneuver against any access to mind involving awareness. Wittgenstein's argument against introspection was that if its yields were so self-evident, then there was nothing interesting in them.

Truth

Circularity and circularity

"Our account of the truth of `snow is white' in terms of facts has come down to this: `snow is white' iff snow is white. "Here, as Tarski has urged, is the significant residue of the correspondence theory of truth. To attribute truth to the sentence is to attribute whiteness to the snow. Attribution of truth to `snow is white' just cancels the quotation marks and says that snow is white. Truth is disquotation. An ignominious end, one may feel, to the correspondence theory of truth."

Flew: "Any interpretation affords a way of describing the set of true sentences of a language. But if it is to count as a truth definition, an interpretation has to satisfy the constraint that it assigns the value `true' to all those sentences which are already, intuitively, regarded as true, and to no others. Tarski expressed this constraint by saying that we want to assign `true' to the sentence `snow is white' iff snow is white. In general, `p' is true iff p. This last formula expresses the condition that any adequate truth definition must satisfy, and is called by Tarski, `the material adequacy condition' .(It is also known as `convention T')."

"The disquotational account may be said still, in a sense, to define truth. It intelligibly demarcates all our intelligible truths, by rendering the truth of each sentence as intelligible as the sentence itself...But in a stricter sense it does not define truth. It does not tell us how to eliminate the adjective `true', by paraphrase, from every context in which it can grammatically occur. It only tells us how to eliminate it when it is attached to a quotation."

"There is no independent inquiry into the nature of truth other than one into what it is to say that something is true". Deflation means that it suffices to say "S knows p" rather than "S knows that p is true".

But all this is saying is that if we can attach the word true to a statement it is because the statement is true and therefore this account of truth presupposes that truth is known and it applies only to propositions that we know already, or can know as self-evident. It does not contain a criterion for qualifying propositions as true. It is therefore perfectly circular, and the problem is that truth is not tautological: it does not contain its own definition.

According to Putnam, there is a is a distinction to be made between "truth conditional semantics" and "assertibility conditional semantics"

"But the notions on which causal theories of knowledge and reference depend--the difference between a cause and a mere background condition, the legitimacy of counterfactuals--are precisely what is called into question by the `inference-licence' interpretation of causal statements and counterfactuals"

Correspondence

Thomas Baldwin on Gerald Vision, Modern Anti-Realism and Manufactured Truth in TLS, March 3-9 1989, p.227

"The traditional objection to the correspondence theory--that, in order to accomodate non-physical truths it requires non-physical states of affairs (mathematical, modal, ethical, etc.) of a kind that we find it intrinsically difficult to countenance and to fit into a theory of reference"

"We say of some utterances that they are true, of others that they are false...The realist holds that something about the state of the world, independently of our view of it or the concept with which we grasp it, accounts for the difference."

"In fact, a minimal description of Correspondence says very little more, if anything at all, than does global realism. I shall use these terms interchangeably throughout this work; for Correspondence--the view that truth-bearers are true by virtue of their relation to a situation in a mind-independent world, save for truths about minds, their states and properties--is virtually the only option for fleshing out the global realist doctrine...Correspondence..is a theory of truth. And it contrasts primarily with other traditional theories of truth, such as Coherence and Pragmatism, and with various deflationary theories about truth, such as Redundancy. Global realism contrasts not with other theories of truth--at least, not directly--but with various views that impose adequacy conditions on truth for any theory of it to satisfy, and which rule out Correspondence by virtue of the conditions imposed."

We do not in fact doubt that we see what we see, but since it is not a question of whether this is true or not, but of how we define truth from this fact, we need to set up a model for truth as correspondence from this fact of perceiving something. In this model, we must have, from the meaning of correspondence, three elements if we wish to sidestep the sceptical, internalist perspective: a perceptor, the thing perceived, and a verifier that the perceptor and the perceived are the same. The question of absolute identity could come up, which would from the start invalidate the model. Let us simply suppose that correspondence does not imply identity but an indubitable facsimilar relation. But once we set up this model, we right away encounter two difficulties. One difficulty is that there is no way for the model itself to work, for we cannot look into any mind at all to determine correspondence. And the other difficulty is that, even if we could have someone look into another mind, some else would have to look into his mind to verify the correspondence, and so on, again and again.

Truth as correspondence is not a relation of identity (x = x), but of near similarity or close resemblance (x = x'). As such it cannot be apprehended or verified. We can have an apparently true representation in our mind. But in order to perceive or verify correspondence on its own terms, we would have to verify our own perception or representation. But we cannot verify correspondence even if we stand as an external observer to another's claim. Some believe that it will be possible in the future to express the physical condition that denotes a specific perception, but even if this were to be so, it will not be an image that we as an external observer perceive but most likely a computerized encoding of the physical condition, and therefore, not even a relation of similarity.

But even if we accept that x = x', the verification of correspondence requires not only the observer that relates the image or its code to the tree, but a third observer that actually relates correspondence to the evidence for it, and so on ad infinitum. In brief, the truth of sensory data cannot strictly speaking be defined as correspondence. Correspondence simply does not work as a definition of truth, and it doesn't work because of the difficulty in verifying the veracity of perception itself. It is, in sum, a circular proposition. We could arguably make it a foundational statement, but this would be stretching the application of foundationalism since we do have alternatives to the concept of truth.

Correspondence, in the final analysis, is nothing but a metaphorical definition of truth. A metaphor in the epistemic sense tries to cover the hiatus between a concept and the justification of a concept. In this case, we posit truth as perception. But the contents of mind are different from the things outside of mind. Therefore, we appeal to the concept of correspondence.

What do we mean when we think "correspondence exists" or "there are correspondences in the world or in mind"? Do we mean that an image always "corresponds" to some external reality? But this is not the usual meaning of correspondence. We mean that, e.g., Bloom's movements in Dublin "correspond" to Ulysses' travels (Webster), and this is a rather loose relation. We also mean that this washer "corresponds" to this screw. Correspondence implies similarity, agreement, and analogy (Webster again). But is this the relation that the correspondence theory of truth pretends to establish between mind and reality? Truth is then similarity, agreement, or analogy? My perception is similar to the things I perceive. Hardly! My perception agrees with the things I perceive. Again hardly!! My perception is an analogy to the things I perceive. Hardly and hardly and hardly!!! We are back to the metaphorical sense of correspondence.

Predictability is also a fundamental reason why science cannot give substance to the theory of correspondence, for truth cannot be said to consist in what has yet to be verified, which could very well be true, unless it is assumed that science is infallible and that like effects will always submit to the same explanation.

As in other areas of knowledge, truth in science is not absolute and unchanging. A set of propositions that fulfill the criterion of predictability, e.g. Ptolemaic astronomy or the Julian calendar, can lose explanatory or predictive efficacy as evidence accumulates, all of which suggests a possible relation between the "density" of knowledge and the production of truth, somewhat in line with the belief that technological progress has to do with cultural or social "density" or economic development with population density. In the knowledge of the universe, truth has moved from creationism to Newton's laws to relativity and quanta to the search for a unified field; and the center of the cosmos has shifted from the Earth to the Sun to the original Big Bang of a virtually inconceivable fist-sized ball of matter (in fact, expressible only in mathematical terms, although that does not make mathematics the necessary source of the concept). On the changing vistas of truth, today it could be argued that, since we do not know for certain where the center of the cosmos lies, the Earth has rationally as much right to that position as any other astronomical reference. We have been assuming that predictability is the only criterion for truth, but science can also be descriptive, in which case the applicable criteria are closer to those of formal truth than to those of physics, and natural history involves probability and yields quasi-truths, which can never be more than partially verifiable.

A thought experiment about correspondence that affects the concept of a realist definition of truth starts with the proposition that the year 2030 will arrive. Suppose the Earth disappears on the year 2029. Will the year 2030 arrive? If the year 2030 means a certain imagined disposition of matter, then it will not arrive. Yet we know that the year 2030 as a moment in the future will arrive. If we suppose a Twin Earth which will not be destroyed on the year 2029, all the arguments against identity and identicals apply: it is another Earth, another disposition of matter. If time is a perfect universal clock somewhere, then 2030 will indeed arrive, but it will not be the year 2030. Finally, therefore, we can only say something as simple as that there is something that can be called "future time", but we cannot specify it any convincing way. And if no future, what? A truth as simple as that is not a truth at all.

The ultimate and non-reducible, basis of knowledge is perception. But this claim invalidates itself for it has no basis in perception. The inherent un-demonstrability of perception and apperception is proof that truth is not demonstrable.

In the sense that a metaphor intervenes at a hiatus between a concept and rational talk about that concept, correspondence as a physical relation is a valid metaphor for truth. We cannot verify any proposed mind/world correspondence and there certainly cannot be correspondence in any practical or realistic sense between ideas about ideas, but the idea of correspondence conveys the "texture" of one fundamental area where truth is applicable, and it could even be appealed to (in some instances) as a paradigm of what truth must be about in general.

If we define correspondence in terms of sense-data, i.e., without bothering to demonstrate it by its own standard, we will be assuming a solipsistic stance. However, I am not alone in believing that there is a tree in my backyard--although admittedly all those that have never been in my backyard could have a logical basis for not believing that there is a tree in my backyard--and it is not unreasonable to say that my statement is true and that truth can indeed be defined as the correspondence between a mental state and some external reality. But this argument configures a definition of truth as consensus in that it claims that correspondence is ultimately a matter of agreement, i.e. it is accepted that I have the image of a specific tree and that others besides myself have, or can have, an image of the same tree. Truth then can involve correspondence, but correspondence per se is a metaphor, and the truth of sensory-data requires the consensus of language. We cannot say that correspondence is a foundational claim, but we can claim for it that it reduces complexity and that it is rational enough to serve as a metaphorical expression of the character of truth as sensory data. However, its rationality stops at its being non-reducible, which means that the epistemic uses of this or any metaphor are limited.

I believe that the world is independent of perception, but also that truth is a concept of awareness. Truth about reality is "S knows R". S has truth through the knowledge of R. But, as we saw, we cannot know that S knows R. How about "I know R"? True, but then truth is un-demonstrable, hence solipsistic. Solipsism in this sense is equivalent to a proposition about the world that we cannot justify, e.g., I firmly believe that there is a pot of gold at the end of the rainbow. And ultimately what is R? It is an instant ago of perception: it is never fixed. It cannot be known. There is R but it never stands still in time for us to establish a definition of truth. R is R only from memory and other cognitive processes. And cognitive processes justify and validate propositions.

Coherence

Barry Stroud on Ralph S.Walker, The Coherence Theory of Truth: Realism, Anti-Realism, Idealism (Routledge), in TLS, July 7-13 1989, p.741

"For those beliefs which cohere with enough other beliefs in the right way, there can be no logical gap between their being accepted and their being true...The question then is how to identify that special class or system of beliefs with which a given belief must cohere in order to be true and which its being true requires that it cohere with." Walker refutes coherence theory from the fact that belief founded on belief is tautological.

Math

Certainly, there is no way or form or manner that we can apply perception or correspondence as paradigms of truth to logic and mathematics
Mathematics is applicable to all of the physical world, yet it can never pass itself off as any part of it. If it is true that mathematics are needed to construct ziggurats, it is no less so that a mud hovel can be built without any sort of calculations, and mud hovels and ziggurats have more in common with each other than they have individually with numbers.

Unless we simply define truth as proof-theory, i.e., truth is what we can prove with the rules of logic and math, there is no reason why we should not say of logical inferences and of mathematical derivations that they are valid, and in fact this is perhaps the most common usage of the qualifier.

Mathematics is a formal system whose rules have nothing to do with mental events and only instrumentally with the natural world. In contrast with language, where definitions are frequently moot, mathematics is the perfect embodiment of consensus.

However, mathematics is in general reliable for its uses, and if it does not provide a good basis for an absolutist definition of truth, it is because numbers exist principally (though not exclusively) as means. But even as an epistemic system--rather than as an end in itself--mathematics cannot help us in defining or grasping scientific truth, because it is not adequate in dealing with the crucial historical question of the "degradation of truth".

Truth

There is the concept of truth, i.e., truth exists. Truth must be defined as the totality of true propositions. The definition of truth is not the concept of truth, but the propositions "Factual propositions are true", "logical and mathematical derivations are true", and so on. None of these individual propositions by itself is truth. If truth is the totality of true propositions, the concept of truth cannot be identical to truth. Truth itself is not true.

Alternatively, truth is the same as the totality of true propositions. True propositions are of different types. Of necessity, then, the definition of truth is the totality of truth-types. Since the concept of truth is identical to the definition of truth as the totality of truth-types, but the totality of truth-types is not identical to the totality of true propositions, then truth is not the totality of truth-types and the concept of truth does not include the concept of truth.

Truth is the totality of true propositions. The totality of true propositions must include the definition of truth. But the definition of truth is not identical with the totality of true propositions, and truth cannot be the totality of true propositions. Therefore, the concept of truth is contradictory. Truth is not true! However, "truth" does exist and necessarily then it is true that truth is not true.

To define truth we can say that truth comprises factuality, logical and mathematical inferences, and self-validating propositions. These are types. If the types cover all instances of truth, then we can indeed say that such is a definition of truth. However, all we have done here is to appeal to the typology of propositions. Underlying this typology are basic-cog's and the use of basic-cog's. Basic-cog's are processes and processes involve a constant intermingling of basic-cog's.

To define truth we would have to involve all the processes of cognition. if this criterion were met, then we would have a definition of truth. But this criterion cannot be met. No definition of truth covers all instances of truth. And all the instances of truth do not justify a univocal definition of truth. Our definition of truth is never the same as truth.

Truth is correspondence which cannot be proven. There are shades between truth and falsehood. If a proposition is not true, it doesn't follow that it is necessarily false. A proposition need not be true to be valid.

There is a "natural" relation between cognition and truth. It is natural to assume that knowledge is truth. Since knowledge is what cognition is all about, it is generally supposed that the products of cognition are truth. However, cognition also yields propositions which cannot be said to be true yet cannot be said not to be knowledge. We can know for sure that some of our beliefs are true because they are reliable, and from this, e.g., that we see that wall, we can deduce the concept of truth. But since we rely on propositions which are not false but less-than-true as if they were true, i.e., probabilities, we are faced with the ambiguity of truth. If knowledge can be less than truth, how do we find a definition of truth that covers both categories, i.e., factual and probabilistic propositions? Nevertheless, from this we cannot at first deny that truth exists.

[We are here doing a clarification of language to arrive at truth. There is of course language-usage which assumes "truth", as in the expression "tell me the truth". This can be translated as "tell me what you believe to be true" and this could elicit a true or a false proposition: it does not involve the actual knowledge of what "true" is. In other words, it does not justify the proposition that "truth can be defined univocally". It can be described as "elliptical truth", or mere "usage" of the term "truth".]

Our awareness of the propositionality of knowledge means that we know propositions to be true or false, but not that truth does not exist. But our awareness of the existence of truth and that some propositions cannot be qualified as either true or false, means that propositions can be true and less-than-true, and again we are faced with the problem of the univocality of truth. But the denial of the univocality of truth does not imply the denial of true propositions, true beliefs, and so on.

Less than true propositions can be termed probable or likely, and we can restrict truth to strictly or rigorously true propositions. How true are strictly true propositions? The example we gave of a true proposition, e.g., there is wall there, is based on perception, i.e., a proposition based on perception, perception itself in fact, which is propositional.  Is our claim that perception is true indefeasible? What is the basis of our claim? For perception to constitute a definition of truth, it would have to involve perception alone and not any other cognitive process, but as we saw perception involves memory and logic and other criteria. Therefore, we cannot say that perception as such can be the paradigm for defining truth.

Validation

Given the difficulties in defining truth itself--without, however, having solved the problem of true propositions--and given the category of propositions which are not false but are less than true--which are useless for a definition of truth--we have to find some alternative to the concept of truth, or an equivalence without the conceptual problems of truth, and this is the use we have been making of the concept of validation. Instead of "true statements", we can speak of "valid statements", and instead of "false statements", we can say "invalid statements". In this way, we cover true and less-than-true propositions and we need not bother trying to find a valid, undefeasible definition of truth. Additionally, we lose nothing for we can claim that the function of truthful propositions is totally covered by that of valid propositions, i.e., valid for deriving other valid propositions, valid as in reliable, etc.

Finally, are justified propositions valid? We know that some justified propositions are not knowledge but we also know that all valid propositions are justified. It is merely a question of adjusting our "estimate" of propositions, i.e., ours and others as justified or valid, to their degree of reliability, or conversely, to their degree of controversiality, from an external perspective.

What, in the final analysis, we are claiming is that we have no indefeasible truth criterion, we have only the processes of the propositionalty of mind, but these are adequate for justification and for the qualification of propositions as valid or invalid, with the necessary proviso that, whereas justification is universally applicable to knowledge from an internalist perspective, validation cannot be applied to all propositions from an internalist perspective, and, though not necessarily in all cases, it generally involves the transactional aspect of cognitive processes, hence the externalist perspective on knowledge.

To speak of knowledge implies truth. When we say that cognition yields knowledge, do we mean truth? The critique of the concept of truth leads to the concept of validity. What is validity? Validity involves reliable propositions. Valid propositions are such that we can use them to obtain other valid propositions.

Nevertheless, reliability is a vague notion. Perception is reliable. Interpretation can also be reliable and there are significant differences between perception and interpretation. Validity implies universal consensus. This means that cognition in toto is reliable. This needs to be argued. For the moment we shall proceed on the assumption that validity does imply reliability.

The concept of validity admits the possibility of partial validation. This derivation is useful when we come to the question of interpretations. Truth does not admit the concept of "partial truth", i.e., propositions, for the concept of truth and its derivations, e.g., truth-value et al, are either true or false. But it is possible to have propositions which are neither demonstrably true nor demonstrably false. Such propositions can be said to be partially valid. And such being the case, where knowledge can be defined in an abstract, imaginary sense as the totality of valid propositions, it cannot be defined solely as the totality of true propositions. The latter definition would, e.g., disqualify much of historiography as knowledge.

Knowledge must be understood in terms of valid propositions rather than in terms of the concept of truth. All truthful statements are valid, but there are also statements which are neither true nor false but which can be valid. Valid and validity cover a greater number of propositions than truthful and true.

There is no univocal definition of truth. Is there an univocal definition of validity? Validity covers what people consider true on a basic level. But since truth is equivocal, then so must validity be. Therefore, we need to have a definition of validity equivalent to truth which eschews the problems involved in the concept of truth. A simple approach would be to say that valid is what is true without the need to specify truth. In other words, something to this effect: whereas truth requires specification, validity is truth without the requisite of specification. Does this imply some sort of intuitive knowledge? If truth is an absolute, validity is a relative concept. True propositions are valid without qualifications whereas valid propositions can be absolutely and relatively true. If absolute truth is self-evident to mind, e.g., perception and logic, then relative truth is not self-evident to mind and involves the idea of consensus. Validity then is the concept that applies to propositions that run the gamut from absolute truth to the consensual, which is certainly not known intuitively. Valid and validity can always substitute for true and truth, although it is not necessary to suppose that they displace entirely the concept of self-evident, absolute truth.

Now let's take another tack. If something is true it cannot be false. Truth is the opposite of falsehood. But something can be not necessarily true yet not be false. In such cases, validity is the appropriate designation. In sum, validity is a linguistic usage which allows us to overcome certain semantic difficulties which arise when we restrict the qualification of propositions to either true or false. How large is this area cannot be said with accuracy. Probably we deal mostly with truths in our everyday lives, but we are also frequently dealing with propositions that are are neither true nor false, and it is in this vast grey zone that validity is justified and needed, i.e., where validity is valid, i.e., correct usage. This suggests that validity is contextual as well as consensual and this may very well be so. Since what we are having to do with are matters of usage and valid can do the role of the self-evident true without inaccuracy and without misleading, then valid and validly can substitute for true in all possible cases. Despite all our strictures concerning truth and knowledge as truth, what the distinction between truth and validity in the end represent is the purely verbal claim that "validity" is a more flexible and more comprehensive term in the sense that it can be used more often and more accurately in connection to propositions that "truth".

Knowledge

Justification is the elaboration of propositions. It is possible to establish a distinction between justification and validation. Validation can only be defined in the circular sense of the processes that validate propositions. To explain this circularity it is necessary to reach the universal consensus argument about knowledge, i.e., knowledge is knowing how to use basic-cog's. Validation is not infallible. The definition of knowledge as the totality of valid propositions is abstract and bloodless and does not do away with the difficulty of the validation of propositions.

We have just seen that any that the historicity of propositions means that all propositions are knowledge. Similarly, it can be argued that all awareness is knowledge, even if this knowledge is interspersed with erroneous propositions, e.g., I know this belief and I know that I have this belief whether it is valid or invalid. Language in itself is knowledge, or at least, the basis on which to build propositions, both valid and invalid. There is an evident inconsistency in these definitions of knowledge that include the possibility of error and the definition of knowledge as only valid propositions, i.e., the specification of knowledge either takes or does not take into account what is not knowledge. Strictly speaking, knowledge is knowledge and the knowledge of what is not knowledge is a paradox.

Awareness does not tolerate false belief, i.e., it cannot knowingly have false belief, yet it can have a false belief. Since awareness cannot knowingly have false belief, how can false belief arise in awareness? Evidently, through faults in cognition, assuming that interpretations can be validated, i.e., that all justification is validating. This is an "internalist" perspective on knowledge. From this perspective we can only say: I believe or I do not believe that p. However, we can also say: I believe that p although it is possible that p may not be a valid proposition. The proviso implies that I am not the only believer, and this proposition points to an external perspective on knowledge. The external perspective on knowledge necessarily involves intersubjectivity, which means that just as I am a believer, so it is reasonable to presume that others too are believers, and it may be that the beliefs of others are perhaps valid and mine are not. It is at this juncture that transactionality--another feature of the external perspective--kicks in: my belief either yields to or is modified by the beliefs of others, or simply ceases to be my belief, and of course the opposite results are also possible.

From the externalist perspective, I can know that some beliefs are not valid. In other words, then, if knowledge is the totality of valid propositions, we can only define it from an externalist perspective, i.e., from the operation of basic-cog's in conjunction with inter-subjectivity and transactionality. Since valid belief requires transactionality, knowledge must be transactional, and without transactionality there can be no knowledge. Nevertheless, since our awareness of propositions includes many valid propositions, the internal perspective of knowledge cannot be entirely disqualified. And if we cannot disqualify the internalist perspective, we cannot disqualify that my knowing my belief, whether my belief is true or false, is knowledge. But since my belief may be false, then we cannot define knowledge as the totality of valid propositions. This paradox can only be solved through the full development of the propositional theory of knowledge. The solution involves the tricky and subtle distinction between propositional bases and propositions content. This corresponds, approximately, to the distinction between cognition and reality excluding cognition.

The best approach to knowledge is through the concept of process rather than through the results of process. The process itself is knowledge. Process implies that knowledge tends to expand, but we cannot discount that it could diminish if only on the margins or in certain specific areas, e.g., politics. If it is indeterminate and variable but expansive, then it is like any historical process, the course of which cannot be predicted or defined with precision and which often takes wrong turns but appears to be "progressive", e.g., there is no immediate perspective of a political dark age,

The wrong turns both of society and science become part of knowledge, so that in a sense science is also the knowledge of what is not science and social progress includes periods of political obscurantism, e.g., fascism. What this means is that all propositions, whether valid or invalid, become knowledge in becoming part of history. History at each moment in time--assuming, of course, a distinction here between history and time--embraces an imagined territory of knowledge which includes propositions which are not knowledge. If such is the case, then knowledge is what history at any one point "categorizes" as knowledge. In this appeal to history, all that we are doing is substituting the definition of knowledge as the totality of valid propositions with the proposition that history is knowledge, i.e., that each moment of history contains the totality of knowledge, assuming that we have already specified how history does this. But isn't this as bloodless and abstract as the other definition? No, because when we say history we are referring not to an imaginary concept, but to the real world and to real propositions, to those in reified forms of knowledge, i.e., books, articles, etc., to actual producers of knowledge whether individuals or centers of learning, to congresses and gatherings and all forms of communication and inter-communication, in brief, to the historical concreteness of knowledge. It is the substitution of a robust, concrete, world-oriented concept of knowledge for the imaginary and inaccessible concept of the totality of valid propositions.

Now, supposing that the invocation of history does get us somewhat closer to the understanding of knowledge, that still does not provide us with some really copper-bottomed means to avoid justified but erroneous propositions. What we need to explore is if this appeal to history, which does seem to have some strength in relation to the concept of knowledge itself, can be transposed or applied to the wider question of the validation of propositions. And what this means in essence is applying the proposition that history validates to the propositional theory of knowledge. Can history, in sum, strengthen our theory of knowledge? Some of the propositions that we have considered so far--logico-mathematical, factual, probable, etc.--can be validated without recourse to history. Therefore, what we must start by doing is to specify the sorts of propositions that would require such an appeal. In other words, where does this appeal to history become inevitable? Additionally, can we find some "intimacy" between knowledge and history? One basic argument is that we cannot go very far in the exploration of cognition if we do not start by considering the temporality of knowledge. Time is also the essence of history. Therefore, we can already perceive that there is an intimate connection between history and knowledge across the bridge of the concept of time.

Once we have solved the paradox of awareness as knowledge--which consists in explaining how false belief can be knowledge--can we claim that knowledge is indeed the totality of valid propositions? By then such a definition will not be needed, for we will have in place the propositional theory of cognition and the universal-consensus argument. However, the definition of knowledge as the totality of valid propositions is the clew that leads to the arguments about the historicity of knowledge. And historicity is, with propositionality and universal consensus, one of the foundations of our theory of knowledge.

Truth gates

Truth gates are operations that the mind does naturally when confronted with certain variables. These variables can be symbollically expressed as 1/not-1 or as 1/0, where 1 is perceived as valid. These operations are called "and", "or", "equivalence", and "negation". Assuming 1/not-1 where 1 is valid, then the operation "and" invalidates 1/not-1 and not-1/not-1 and will only allow 1/1. The same applies to 1/0 assumning 0 to be not-1. The operation "or" will allow all combinations of 1/not-1, but not not-1/not-1. The operation "equivalence" allows the combination 1/1 and not-1/not-1. The operation negation transforms the validity assumption invalidating 1 and validating not-1. In the operation flip-flop, if a proposition assumed to be valid is validly denied, then its valid derivations are also invalidated.

These operations are such that the validity of a proposition derives from another proposition. Hence, if 1, then 1 but not if 1, then -1. However if -1, then 1 or -1. If the sun is out, then it is day. True. If the sun is out, then it is night. False. If the sun is not out, then it is night. True. If the sun is not out, then it is not day. True.

In a concrete example using variables T and ST, if "T and ST", then not "T and not ST", not "T and not T", and not "ST and not ST". If "T or ST", then not "not T or not ST". If "T is equivalent to ST", then "T is not equivalent to not ST". We can go further. If "T and ST", then necessarily "at least T v T1" and "S>ST". Now, if "T and ST" and "T and T1", then "T1 and ST1". This can also be derived from: if T, and "T and ST", then ST, and if "T and T1" and "T and ST", then "T1 and ST1." It would be possible to deduce til the "end of time" but this is pure logical or mathematical thought, which must light a fuse in the mind and go on of itself.

The foundation of these processes is the recognition of "1/0" or "1/not-1" which is the principle of identity also known by the name of the indiscernibility of identicals, and this principle is made possible from the existence of things and time, or, more accurately, the inseparability of space and sequences of events. Its operation is present in the existence of things and in the origins of life.

Logic originated with life. The impersonal and abstract "application" of the principle of identity transmuted experience into logical forms. Logical forms are innate and apply to experience without the need for their previous deduction or for instructions on their use, as can be shown by how R recognizes A: R --> A v B; in R, that (A --> R) entails A and that [(B --> R) -/-> A]; if (A v B) v (A =/= B), then R --> A. Strictly speaking, A and B in this equation are sensations. Since it can be shown that sensation is logical, does this mean that logic antecedes even the experiences on which logic is based? The material conditions for logic existed before motion, but logic did not. The antecedent for logic was motion, which entails T and S.

Truth-table

Truth-tables are matrixes with either (1) variables and symbols for connectives or (2) T/F notation. The idea of truth-tables is to determine truth-values mechanically. Truth-values of propositions or expressions refer to their truth-functionality, i.e., their epistemic qualification as either valid, invalid, or probable. Truth-functional propositions either have or produce truth-values. However, for truth tables to be anywhere near useful it is necessary, in the case of a matrix with variables and connectives, (1) to substitute propositions for variables, (2) to determine cognitively the truth-value of the propositions, and (3) to apply intuitive logic to determine the validity or non-validity of the result. In the case of T/F notation, there are no variables to substitute for. Propositions are judged according to their-truth value and a determination by logic is made concerning the truth-value of the connective, which is supposed or given to start with but is not made explicit in the matrix.

The truth-table with variables and connectives runs as follows:

(1) p & q   statements
(2) p v q   and (conjunction)
(3) p ^ q   p or q (incompatibility)
(4) p  <--> q  p iff q (biconditionality)
(5) p > q   if p then q (conditionality)
(6) ~(p v q)   not both p and q (alternative denial)
(7) ~p v ~lq    neither p nor q (joint denial)
(9) ~p    denial of statement

Basically what this truth-table contains is a catalogue of posssible logical relations, i.e., in the sense that such relations license truth-value inferences But in itself the list says nothing. How then do we derive it? This is a classic example of intuitive logic deriving the rules of formal logic from itself.

In the case of the truth-table with truth-value notations, assuming the or alternative connective, it is possible to determine the truth-value of the connective for each possible combination of T or F propositions. Truth-tables are inert and useless without basic-cog's and cog-processes. They tell us nothing if we do not first determine the truth-value of propositions and then determine the truth-value of conjoint propositions or of the connectives that join them. In fact, truth tables tend to confirm Wittgenstein's thesis that all logical propositions are tautological and empty and senseless. There is one apparent use for truth-tables and that is to give a formal-logic expression of tautology. In a tautology no matter what the truth-value of connected propositions the truth-value of a further connective to other either true and false propositions is always necessarily true.

Truth-value and truth-functional

Truth-value is the property of propositions of being true or false. Propositions without truth-value cannot be shown to be either. Truth-functional refers to means for having truth-value.

Turing

Turing's legacy of a thinking-machine that can replicate human thought is contradicted by the lamentable circumstances of his death. Would a machine have "killed" itself because it thought that it had been caught out in something shameful? We cannot suppose that the affects that lead to Turing's death can be discounted from any attempt to replicate mind.

Type and token

A token is an specific event, such as love for three oranges. Type is love itself. Hence, mental tokens are specific mental happenings, also known as dated particulars and in other ways. Between type and token there is a reciprocal relation. It is the relation that subsists between the general and the specific. Mind recognizes the specific under cover of the general just as conversely types necessarily derive from tokens of experience. If a token theory about anything at all is a specific theory, type theory would be the ideal theory, the valid theory, etc. This, however, is special usage.

A token is a dependent variable of a type. This is so in thought, but these concepts also represent how things are in reality. We can interchange talk of thought and talk of what thought refers to, but sometimes this is not possible and our cognitive processes tell us so. The dependence of token on type consists in that all tokens share essential properties with type and with each other. The basic concepts in theory of knowledge are valid for all the concepts in token theories of knowledge. Knowledge involves the interaction of cognitive processes. But since all theories of knowledge are tokens, even the claim that knowledge involves interactive cognitive processes is specific and open to controversy.

A theory of knowledge--although for that matter any theory on any subject--must assume a type-theory. We assume that all token-theories are attempts to embody the presumed type-theory. If we state that the expression of a type-theory of knowledge are objective cognitive processes, then token theories are attempts to specify objective cognitive processes. A type-theory implies an "object-self". But since all cognitive theories are elaborations by specific selves, then it is not possible that any token theory should manage to discover the type theory. Yet a token theory of cognition must apply to all human tokens. Theoretically, any attempt at a theory of knowledge is bound to fail. We can only try to break the seemingly hopeless circularity at the heart of a theory of cognition by addressing the specificity of self, which is as much of an assumption in theory of knowledge as is the object-self.

What is proposed here is that token theory A permits the derivation of token theory B. Despite being a derivation, token theory B is a theory in its own right. Token theory A entails object-self. It is token theory B, the autonomous derivation from token theory A, that can explain human tokens as defined by their specificity. More concretely, cognitive theory is about the object-self whereas its derivation is about specific selves. However, as we are talking of a token derivation from a token theory, we seem to be trapped in the same circularity. To address this problem, another maneuver is necessary. In cognitive theory it is possible to argue for an  "universal-consensus theory of knowledge". Knowledge consists in the use of basic cognitive propositions. This ability is innate. It permits us to distinguish between valid propositions and propositions which can be validated but are not necessarily valid. However, this knowledge does not mean that we can validate interpretation from specific cognition. The specificity of self and its cognitive consequences manifest themselves through history. The flaws of token theories derive from the historicity of cognition. But it is also its historicity which gives some scope for the possibility of the validation of token theories or interpretations, if only through the argument that error is unavoidably part of the historical process of knowledge.

Typology of propositions

From the use of logic we can derive a typology of inferences. And from the typology of inferences we can derive a typology of propositions. It is the typology of propositions that gives us access to basic-cog's.