Calculus

"Calculus. Essentially a system of rule-governed symbols (which may be marks on paper but which might equally well be beads on an abacus) designed to facilitate reasoning of various kinds...To reduce reasoning to a calculus is not just to make reasoning like arithmetical computation or the solving of algebraic equations, but to make it mechanical in the strong sense of being something that a machine (computer) could do...The rules must be such that they could be programmed into a computer. This requires that it be possible to treat all proof as a matter of symbol manipulation, each proof being only of finite length. The rules for its construction are rules for processing symbols. These rules must be such that there are effective (mechanical) procedures for checking whether any given sequence of symbols is, or is not, a proof.

"The two logical calculuses most commonly encountered are (classical) propositional calculus and (classical) first order predicate calculus. Any formal system of logic can be called a (system of) propositional calculus if it consists of" a formal language with variables and connectives and of "a set of axioms and/or rules of inference governing the connectives of the language...However, the phrase `propositional calculus' is usually used to refer to any system in which the formally valid arguments are exactly those that can be shown to be valid by application of the standard two-valued truth-table definitions of the logical connectives...When used without qualifications, the phrase `predicate calculus' usually means `classical first order predicate calculus'. This is the system obtained by extending the axioms and/or rules of propositional calculus by adding axioms and/or rules for the quatifiers which are designed to treat universally quantified sentences as infinite conjunctions and existentially quantified sentences as infinite disjunctions" (Flew, "Calculus")

Causality

Causality is the relation whereby an event is antecedently and necessarily related to a previous event and not its continuation. In more concrete terms, a cause is an event which makes another event come to be. Between events, a cause is an event which is a necessary and sufficient explanation for the existence of another event. Causes are therefore explanations, but explanations do not necessarily involve causes.

According to Kant, causality is a formal knowing that is lodged in us. P.F.Strawson, who shares this conviction, says that causality is "a presupposition of a world of objects". However, I can have the representation of things as such in my mind and if causality were a necessary part of things we could never have things as such. A chair, e.g., could not come to mind without the representation of a carpenter or a set of tools and so on. I knoy myriad things of which I ignore the cause. Since basic-cog's are the innate means of cognition, e.g., logic, memory, etc., and they are present in all cognitive process, whereas we have no arguments for the innateness of causality or its indispensability to some cognitive processes, causality cannot be thought of either as innate or as a basic-cog.

Cause

There is a difference between a cause and a background or antecedent condition, which see above. Cause is usually defined as a sufficient and necessary antecedent condition. But is it possible to say that a cause is a sufficient antecedent condition? It would be if sufficient entailed necessary. There could be two sufficient causes for the same event. Nothing in either logic or nature excludes it. Of course, it would be quite astonishing if this happened in nature, but then we do not know all of nature. Does necessary then do the trick of specifying one and only one sufficient cause? It could under a certain conventional definition, which is that sufficient cause entail an event to the exclusion of all other possible sufficient causes. Under this definition a cause is a sufficient and only a sufficient cause. However, if events required something more than sufficient the usual definition would be necessary.

Take a case from Dennett's The Intentional stance. He says that for purposes of predicting knowing motivations is just as accurate as having a Laplacean explanation of conduct. Therefore, the knowledge of behaviour can be explained either from the knowledge of motivations or the knowledge of all possible laws of the universe. There would then appear to be two sufficient causes. As it turns out, though, knowledge of motivations does not necessarily yield accurate predictions. There being one and only one sufficient cause in this case, if we generalized fro it, we could say that a cause is a sufficient background or antecedent condition.

Cause and effect

According to Kant, cause and effect is a transcendental category of thought. In other words, he believed cause and effect to be innate, like time and space and probably logic too. However, there is really no conclusive proof of the innateness of cause and effect, which is more likely an inference based on the experience of successiveness. Central state materialism.

Chisholm

DUMMETT ON RODERICK CHISHOLM

p137

"Such cases of barely verbalised or even quite unverbalised thinking, increase the attraction of what is in any case more natural, namely a reversed strategy which explains language in terms of thoughts, conceived as grasped independently of language, rather than conversely: for if possession of the relevant concepts is sufficient as a background for having a given thought, and if it is possible to manifest possesion of those concepts in non-linguistic behaviour, then, after all, it will be possible to explain what it is to have that thought without appeal to its linguistic expression. Such a strategy of philosophical explanation, long advocated by Roderick Chisholm, will, of course, need to avoid falling back into the illegitimate code conception of language, illustrated by the quotation from Saussure."

Chomsky

(A) Chomsky claims that there are innate rules for language learning. These would be different from the other abilities or faculties of the propositionality of mind. But even assuming such rules, we would not be positing anything different from the abilities and the means of the abilities of the propositionality of mind. We would simply be adding abilities to the abilities, i.e., logic, reason, perception, et al, that we have already posited.

(B) If we read "man mountain up" or "hurricane shambles house", we immediately understand that the jumbled sentence must mean something much like "a man went up the mountain". From this simple exercise we can make various deductions. Since we can understand jumbled sentences without difficulty, we could infer that meaning does not necessarily depend on syntax: it must be in the words themselves. But words have an inherent value and a relational value. The inherent value is in any of the specific meanings of words, including their figurative senses. The relational value is either semantical or syntactical: words have verbal equivalences and words have specific grammatical functions. Most significantly, though, it is reason that tells us how to interpret a jumbled sentence. We do not reorder the words of the sentence and we do not add words to the sentence: we understand its meaning directly without much effort. Meaning and reason, then, go together: meaning involves reason and reason operates on meanings, and neither meaning nor reason in themselves necessarily involve syntax or grammar. We can have meaning without syntax or grammar. However, syntax and grammar are also meaningful and therefore they too obey reason. So what then is the upshot? It would seem, then, as if syntax and grammar were products of reason to make public language more rational. A caveman could speak in words devoid of syntax and grammar, and his words were intelligible from reason alone. Syntax and grammar came later, also from reason.

Were grammar and syntax inherent to words? Reason as a combination of logic and experience also had to do with words and their meanings. What were "inherent" to words were not grammar and syntax but reason. And this holds even if we took a step backwards and searched for words in the squiggles, for the squiggles were also affected by reason. The squiggles, as means for reason and logic, were there, so to speak, but they "developed" through the complex interactions between logic and experience that is reason. The propositional contents of mind certainly do not involve syntax. And since words are the basis for syntax, the implication here is that there is no such thing as the meaning of words, at least in the mental system. Meaning is always propositional. It also means that it is not necessary for the squiggles to have a grammar parallel to the grammar of the verbal, communicative language. The squiggles of reason suffice to interpret jumbled sentences. And since this is the case, reason and grammar must be two different orders of mental events. We know how to speak grammatically, and this is not necessarily and strictly a rational activity. And we can apply reason to the public language without necessarily requiring the use of grammar.

An implication of concept in the mental system is that, since the active squiggles operate on the inert squiggles, there are no specialized squiggles. The squiggles that "represent" propositions are not different from the squiggles that "carry" basic-cog's. Does this mean that grammatical rules are not any part of mental language? They have to be squiggles, and if they are squiggles, they must be rational. Therefore, reason "is present" in the squiggles and grammar must be rational. This can be argued in another way. Logical principles are innate and a priori. Reason implies the interaction of logic and experience. From the above argument about jumbled sentences, we know that we can determine the meaning of combinations of words from rational principles. Since rational principles are empirical, we can gather that the grammatical ordering of words is dependent at least partially on experience. Grammar is a rational, empirical phenomenon. Chomsky's thesis that language-learning is innate cannot be right.

The Chomsky perspective on events is global and deliberately and emphatically anti-exploitative, anti-nationalist, and anti-racist. If you start by denying race and nation, nothing prevents you from measuring all events with the same scale and from judging means in relative rather than absolute terms. If life and freedom are absolute values, terrorism in their defense is justified, but not terrorism in defense of race, the state, or an ism. Means are justified by their ends. But ends are justified in absolute, universalist terms. One standard for all the peoples. The Chomsky attitude is ideological because of its absolutism. It embodies a gran rifiuto. And absolutes--like truth, being, or deism--are meaningless, inconclusive, unrealistic. In the end, the Chomsky attitude is wasted.

Church-Turing thesis, Tarski, and logical rules (from Hofstadter)

Hofstadter (Ch.XVII)

"Church-Turing thesis, standard version: Suppose there is a method which a sentient being follows in order to sort numbers into two classes. Suppose further that this method always yields an answer within a finite amount of time, and that it always gives the same answer for a given number. Then: some terminating FlooP program (i.e., some general recursive function) exists which gives exactly the same answers as the sentient being's method does."

"Church-Turing thesis, artificial intelligence version: Mental processes of any sort can be simulated by a computer program whose underlying language is of power equal to that of FlooP--that is, in which all partial recursive functions can be programmed."

"The proposition that it is impossible to have a decision procedure for theoremhood in any formal system with the power of TNT is known as Church's theorem. The proposition that it is impossible to have a decision procedure for number-theoretical truth--if such truth exists...follows quickly from Tarski's theorem (published in 1933...)...If there were a uniform way by which people could decide which of the classes `theorem' and `nontheorem' any given formula X fell into, then, by the Church-Turing thesis (standard version), there would exist a terminating FlooP program (a general recursive function) which could make the same decision, when given as input the Gödel number of formula X. The crucial step is to recall that any property that can be tested for by a terminating FlooP program is represented in TNT. This means that the property of TNT-theoremhood would be represented (as distinguished from merely expressed) inside TNT...But...if theoremhood is a representable attribute, then Gödel's formula G becomes vicious...It all hinges on what G says: `G is not a theorem of TNT'. Assume that G were a theorem. Then, since theoremhood is supposedly represented, the TNT formula which asserts `G is a theorem' would be a theorem of TNT. But this formula is ~G, the negation of G, so that TNT is inconsistent...[and so on...Go over the rest of the deductions from Gödel's proof]...The problem is created by the assumption that theoremhood is represented by some formula of TNT, and therefore we must backtrack and erase that assumption. This forces us also to conclude that no FlooP program can tell the Gödel numbers of theorems from those of nontheorems. Finally, if we accept the artificial intelligence version of the Church-Turing thesis, then we must backtrack further, and conclude that no method whatsoever could exist by which humans could reliably tell theorems from nontheorems..."

"Tarski's theorem...Tarski asked whether there could be a way of expressing in TNT the concept of number-theoretical truth...he wished to determine whether there is any TNT-formula with a single free variable a which can be translated thus: `The formula whose Gödel number is a expresses a truth'...Let us suppose there is... True{a}. Now what we'll do is use the diagonalization method to produce a sentence which asserts about itself that it is untrue. We copy the Gödel method exactly, beginning with...:

InvEa:<~TRUE{a}^SELFSUB{a'',a}>=t"

[This statement is true even though it says that there is an a such that a is not true, because it is a statement of a metalanguage about an object language, specifically, of TNT about NT.]

[To derive the value of a'', we substitute t into itself, and we get T=InvEa:<~TRUE{a}^{<InvEa:<~TRUE{a}^SELFSUB{a'',a}>,a>, which means that the selfsub of t yields T, which is the Gödel number of a false statement, "But since the selfsub of t is T's own Gödel number", then T says of itelf that it is a falsity...this leads to the conclusion that it must be simultaneopusly true and false (or simultaneously neither)...If the Tarski formula actually existed, then it would be a statement about natural numbers that is both true and false at once...While we can always sweep the English-language Epimenides paradox under the rug, saying that its subject matter (its own truth) is abstract, this is not so when it becomes a concrete statement about numbers...then we must undo our assumption that the formula TRUE{a} exists. Thus, there is no way of expressing the notion of truth inside TNT. Notice that this makes truth a far more elusive property than theoremhood, for the latter is expressible."]

A.Tarski, "The Semantic Conception of Truth" (Philosophy and Phenomenological Research, vol.iv, 1944)

"...Tarski construes the predicate `true' as being applicable to sentences; it forms part of a so-called `metalanguage' in which statements are made about the sentences of an `object-language'... He then introduces the technical notions of a `sentential function' and `satisfaction' of a sentential function by objects; defines a sentence as `a sentential function which contains no free variables'; and concludes that `a sentence is true if it is satisfied by all objects, and false otherwise'. This definition he declares to be `formally correct' and `materially adequate'--the test of material adequacy being that it should imply all equivalences of the form `The sentence "snow is white" is true if, and only if, snow is white'.

"It should be particularly observed that this definition of truth is offered as applying only to languages having a `specified structure', in the author's sense of that expression; and that `at the present time the only languages with a specified structure are the formalized languages of various systems of deductive logic...He insists that all that his own definition requires is that, whenever for instance we assert or deny that snow is white, we must also be ready to assert or deny that the sentence `snow is white' is true...There appear to be two cases in which we might say that a sentence is true or false: first, where a context of utterance is understood; and second, where the context of utterance does not matter [logic]...It seems clear, partly from Tarski's observation that strictly we ought always to say `true in' a particular lamguage and partly from his account of `formalized' languages of `specified structure', that his definition of truth was framed with an eye to cases of this latter kind; i.e., cases where the context of utterance of a sentence may be neglected."

Fundamentally, though, what we have in Tarski is a meaningless definition of truth: it means nothing, it defines nothing, at most it singles out the expression of perception and sense-impressions as truth, and this can hardly do.]

Deductions and arguments

First exposition

The successive propositions here are:

--TNT expresses but does not represent theorems (if it did, from Gödel's proof, number theory could not exist; or, since it does exist, its results would have to be taken purely on faith).

--No program can tell theorems from nontheorems.

--There is no method to tell theorems from nontheorems.

--Finally (Tarski), there is no way to express the notion of truth in TNT.

Second exposition

The basis of all the above is the distinction between expression and representation. This says that it is possible, from the axioms and rules of predicate logic, to have a well formed formula which is invalid. Why so? Well, Church's theorem is a derivation of Gödel's proof and Gödel's proof cannot be realized without the distinction between expression and representation. This distinction admits as wff the formula P v ~P. But this formula goes against intuitive logic!

Again, Gödel's proof goes against intuitive logic, for how can a "logical" statement which purports to make a claim be interpreted as making the denial of that claim?

[CRF's only axiom: Nothing under or above the heavens can pretend to logical validity if it contravenes intuitive logic. How are the cases above to be dealt with from CRF's only axiom? The distinction expression/representation is invalid. If something can be expressed in a system of inference, then it must also be capable of being represented. Gödel numbers must be flawed since they produce Gödel's paradox.]

Third Exposition

There is no Church-Turing thesis. Church's thesis is as stated above. Apparently, as I said, it is based on Gödel. Turing's thesis was that a machine could replicate thought on the reasonable assumption that all thought is recursive, i.e. consists of logical, sequential, repeatable operations. I have read that Turing was initially opposed to Church's thesis, but later accepted it. His change of mind had to emanate also from his acceptance of Gödel's proof. Hofstadter creates a Church-Turing thesis on the common denominator for both logicians of Gödel's proof.

Fourth exposition

The argument in Hofstadter follows this order:

--Gödel's proof (concerning a deductive system)

--From Gödel's proof, Church's theorem (concerning a deductive system)

--Turing's thesis (concerning mind)

--From Turing's thesis, assuming mind/machine isomorphism, extension of Church's theorem in the sense that not only does there not exist a procedure for distinguishing theorems from nontheorems but there can exist no such procedure (concerning mind).

The last step is putting the cart before the horse. It posits the limitations of machines and systems. Then it equates machines and minds. Then it applies to minds the limitations of machines and systems. But how do we know that minds are as limited as machines and systems?

Putnam's principle: mind can go beyond anything that it can formalize. Together with CRF's only axiom, this means that intuitive logic is more powerful than any formal system and that it is impossible to devise a system powerful enough to encompass it.

Logical rules

Logical rules are:

(1) Specification: "If the string InvAu:x is a theorem [for all u it is the case that x], then so is x, and so are any strings mader from x by replacing u, wherever it occurs, by one and the same term."

"The rule of specification allows the desired string to be extracted from Axiom 1. It is a one-step derivation:

InvAa:~Sa=O (axiom 1) --> ~SO=O (specification).

[It is not clear to me why axiom one does not already contain this derivation, i.e. why the rule of specification is necessary.]

"Notice that the rule of specification will allow some formulas which contain free variables...to become theorems. For example, the following strings could also be derived from axiom 1 by specification: ~Sa=O --> ~S(c+SSO)=O.

(2) "...[T]he rule of generalization...allows us to put back the universal quantifier on theorems which contain variables that become free as a result of usage of specification. Acting on the [previous string]...: InvAc:~S(c+SSO)=O.

"Generalization undoes the action of specification, and vice versa." Hofstadter expresses it in this manner: "Suppose x is a theorem in which u, a variable, occurs free. Then InvAu:x is a theorem."

(3) Interchange

"Suppose u is a variable. Then thestring InvAu:~ and ~InvE: are interchangeable anywhere inside any theorem" as in

InvAa:~Sa=O (axiom 1) --> ~InvEa:Sa=O.

(4) Existence: InvAa:~Sa=O (axiom 1) --> InvEb:InvAa:~Sa=b, or ~InvAb:InvEa:Sa=b.

(5) Equality and its subordinates: symmetry and transitivty (syllogism):

"If r=s is atheorem, then so is s=r";

"If r=s and s=t are theorems, then so is r=t".

(6) Succesorship and its subordinates: addition and dropping out:

"If r=t is a theorem, then Sr=St is a theorem."

"If Sr=St is a theorem, then r=t is a theorem."

(7) Induction

"Suppose u is a variable, and X{u} is a well-formed formula in which u occurs free. If both InvAu:<X{u}-->X{Su/u}> and X{O/u} are theorems, then InvAu:X{u} is also a theorem.

"This is about as close we we can come to putting Peano's fifth postulate into TNT. Now let us use it to show that InvAa:(O+a)=a is indeed a theorem in TNT..."

<(O+b)=b-->(O+Sb)=Sb>

InvAb:<(O+_b)=b-->(O+Sb)=Sb>

This is the first of the two input theorems required by the induction rule. The other requirement is the first line of the pyramid, which we have. Therefore, we can apply the rule of induction to deduce what we wanted:

InvAb:(O+b)=b

Specification and generalization will allow us to change the variable from b to a: thus InvAa:(O+a)=a is no longer an undecidable string of TNT."

The axioms and rules of predicate logic are derived primitively from intuitive logic. However, it is possible to derive the axioms, or at least, the second axiom, from the rules of inference. Is this latter derivation intuitive or formal? Since the rules are ultimately intuitive, then the derivation is also intuitive, but the derivation itself is done with the use of the rules, hence it is through the operation of formal logic.

Un sistema deductivo, ej.. TNT, sería inconsistente si incluyera el teorema `x' y la negación de `x'. El mismo sistema estaría incompleto si no pudiera eliminar su propia inconsistencia. Dentro de TNT el procedimiento decisorio para determinar si una cuerda numérica `x' es un teorema es el siguiente:

(1) N-x debe tener un correspondiente TNT-x

(2) Si dentro de TNT se puede derivar TNT-x

(3) entonces, TNT-x prueba la validez de N-x

¿Existe un procedimiento decisorio para demostrar que TNT es un sistema consistente y completo?

La demostración tendría que hacerse dentro de TNT mismo, o sea, aproximadamente TNT --> [(TNT>TNT)>x], donde x = consistente/completo. Esto implica la circularidad de que TNT --> x, pero a la misma vez se está suponiendo que TNT>x, o sea, que [(TNT>TNT)-->TNT]. Esta circularidad significa que no hay un procedimiento para demostrar que TNT es consistente y completo.

Circularity

If all can be reduced to meaning, then we find ourselves in a problematical situation. If representation is the meaning of reality and reality is codependent with representation--not by this asserting the phenomenalist position--then, insofar as reality encompasses representation, representation is self-representation and the knowledge of reality consists in reality knowing itself. If knowledge is reality knowing itself, then we can only have knowledge as knowledge. We cannot escape from the circle of reality or meaning or representation referring to themselves in each individual mind.

Arthur C. Danto on Leszek Kolakowski, Metaphysical horror (1989), TLS

"Pragmatic thinking, including the utilitarian notion of truth, was supposed to free us from the fetters of metaphysical speculation, by measuring validity by usefulness. But it is easy to see that the concept of usefulness, however conceived--narrowly or generously, psychologically or socially--opens a wide gate through which the same metaphysics and theology can triumphantly return and assert their legitimacy, for one need only argue that they might be at the service of some human needs." (p.52-3)

Pascal Engel on J. Christopher Maloney, The mundane matter of mental language (CUP), TLS, August 17-23 990, p. 880

"The qualia typical of a mood are very likely the summation of the qualia occurrent in the sensory states caused by the nonsensuous representations constituting the propositional attitudes characteristic of the mood".

This sounds fishily circular: the mood is the product of the feelings or sensations produced by the mood.

Philosophy would not be possible if we became hopelessly entangled in the trap of circularity. In order to continue we recur to foundationalism, which consists in the systematic appeal to foundational statements. Foundationalism has its justification in the pervasiveness of circular thought. The concept of circularity is itself foundational and therefore foundationalism cannot escape the siege of circularity. However, foundational statements--which are to foundationalism as the rational is to reason--provide the basis on which thought can proceed.

A foundational statement is one into whose expression the issue of ultimacy tends to creep in. It constitutes a strong rational basis on which it is possible to found other epistemic claims. In brief, the foundational bottom-line is the rational containment of circular thought. The fundamental circularity of philosophic thought means that all attempts at defining abstract concepts are inevitably circular. It warrants that we continue and in this manner it permits us to posit as many derivations as epistemic criteria will allow.

We can compare the ordinary reliance on our everyday beliefs to a foundational denial of solipsism, or the foundational defense of fixity of meaning from the inconsistency of its denial to the formal truth that we normally communicate succesfully through the use of language.

The circularity of thought collides with the exigencies of practical existence, but it is contained in philosophy through the epistemic practice of foundationalism, by which foundational statements ensue upon the rational exploration of circular propositions.

Foundational claims are the expression of strong belief. It can legitimately be said that to philosophize consists in the coherent concatenation of foundational claims whose cut-off point cannot be determined beforehand. A necessary foundational statement in philosophy is that despite the temptation of radical scepticism, philosophy in the end proceeds on the assumption that universal doubt is incoherent and as if certainty were a viable objective of its exertions.

An example of a proposition that might involve foundationalism is the denial of the scepticism involved in circularity itself.

We are prevented by circularity, itself the primary font of scepticism, from radical scepticism, because universal doubt must include doubt itself, which means that we are justified in thinking that it is possible not to doubt.

From a bottom-line, epistemic point of view, circularity is the unavoidable recurrence of doubt.

Classes and properties

Properties are intensional. Classes are logical and precise. Classes therefore are to be used in lieu of properties.

To start with, there is the problem that extensionality hardly does justice to the concept of property or attribute. It is posssible because of shading that an attribute could gradually turn to its contrary, like say "porque te quiero te apórreo" or being generous and mean at the same time. There is the problem of coextensionality (large round eyes and owls, e.g. he is an owl means he has large round eyes). So Quine defines properties as classes minus coextensives. And there is also the problem that the class of all classes NMOTS confutes the platitude that classes are defined by membership conditions. So you are not even left with a valid unassailable definition of class. But so what says Quine. Even if logic and ordinary language disqualify the equivalence classes/properties, mathematics uses it, needs, and justifies it.

Codependence

Codependence is the same as reciprocal entailment or mutual entailment

Cognition

Cognition is the operation of cognitive processes such as perception, memory, and logic. The cog-processes that specify and make cognition possible are specified and determined by basic cognitive propositions (basic-cogs). There is nothing to cog-processes beyond basic-cogs. It is from the the fact that basic-cog's are the processes themselves that we can speak of sensation et al as basic-cog's.

Cognition is the interaction between basic-cog's and experience, but since experience is also the result of basic-cog's, it is the interaction of basic-cog's. The application of basic-cog's to experience or to themselves results in inferences. Some inferences are valid, some are invalid, and some are probabilistic. The validity of propositions is determined by the types of cog-processes involved. We can individually recognize which cog-processes are involved in inferences, hence we can individually say which propositions are valid, invalid, or probabilistic. We can generally do this. There may be cases in which we cannot be certain about the validity of propositions.

According to Josef Perner, in Understanding the representational mind , The Higher (October 25 1991), children acquire a "theory of mind" around the age of four. James Russell, reviewing Perner's book, describes the experiment thus: "For example, some chocolate is hidden at a place A by Susan, after which she departs and her mother moves the object to place B in her absence. Where will Susan look for the chocolate when she returns?" Children who answer A have "some understanding that behaviour can be driven by mental representation...but three-year-olds typically say that Susan will look where the object really is (at place B)."

Cognition and propositionality

The propositional theory of cognition makes these claims: (1) cognition is the application of propositions to propositions; (2) cognitive processes are innate; (3) cognitive processes are interactive. Basic-cog's have exactly the same meaning as cognitive processes. The fundamental cognitive process consists in the application of propositions to propositions to derive other propositions. In this process some propositions are more basic than others. These are the basic cognitive propositions, which describe and determine the processes whereby propositions are derived from propositions. When we mention basic-cog's it is implicit that they are cognitive processes. They are aspects of the same phenomenon, as, analogously, mental symbols are both faculties and means. All propositions are either basic-cog's or inferences. Inferences become inputs for basic-cog's, but basic-cog's can also be inputs to themselves. The elaboration of propositions implies their justification and/or validation. The grasping of propositions also involves their qualification as either valid or invalid. This validation could involve a process of "tracking" a previous process of justification. We know that we know. We do not see incoherent, unconnected bundles of sensations. Nor do we deduce that someone was smoking in a room out of thin air. Cognitive processes take place according to rules. These processes yield specific results but they all follow the same rules in all cases and in all human beings.

So-called criteria of knowledge are implicit in the means of knowledge. Since it is with the means of knowledge that we justify and validate propositions, this process consists in the "application" of certain propositions to other propositions. The propositions we apply to other propositions--epistemic or cognitive propositions--are not different from the means of knowledge, they are in fact the means of knowledge. Hence, means and criteria are the same. Epistemic propositions raise the issue that they are also subject to cognitive processes. In other words, in explaining how we elaborate propositions, we fall into regress. The propositionality of mind refers to the fundamental cognitive propositions that we described as the means of knowledge. Such propositions are the bottom line of cognition, and this is where regress stops. We cannot go beyond the fundamental propositions we have called the means of knowledge, but which are more adequately described as basic-cog's or cognitive processes. If we consider cognition as the subconscious processing of propositions, we do not find grounds for the distinction between justification and validation. When we perceive, we are both justifying and validating propositions, if not simultaneously at least without a noticeable cæsura. This does not mean that there are no such things as justification or validation, but only that we cannot adequately distinguish between them in our awareness of a clearly productive cognitive process such as perception. And this takes us back to our specification of cognition as a process, and now specifically a process in which justification and validation are indistinguishable. One of the fundamental tasks here is to identify and describe basic-cog's. The question is how do we go about doing this? And how do we know that our examination is exhaustive? Is it meant to be exhaustive? And if not, why not and what is it meant to be?

Let us consolidate: what am I after and what am I not after? I am looking for the propositional bases of cognition. I am not at this stage interested in belief, which is also a propositional base but not indispensable for the understanding of cognition. What I believe or do not believe, although undoubtedly related to cognition, has nothing to do with what is and what is not knowledge. I want to show how it is possible to specify cognition in sentences. I want to demonstrate how my public-language description of cognition grasps or at least approximates the processes of cognition. I expect to derive from these sentences further inferences about the processes of cognition. And I also want to discover what types or sets of propositions are necessary to give a thorough account of cognition. This account must include among its basic features the interactiveness of basic-cog's. What I am not after is a complete expression of all the propositions that make cognition possible. I am interested in the possibility of the basic-cog's of perception expressed in the public language, but I am not interested in stating all the basic-cog's involved in perception.

Since basic-cog's are innate and interactive, the beginning of cognition is comparable to a big bang of all cognitive processes. This implies that we cannot establish precedences. Basic-cog's cannot derive from other basic-cog's. But if what we have at birth are basic-cog's, how can we derive other propositions? Obviously, we must have input, but input is inferential. It is to be assumed that all basic-cog's simultaneously produce inferences. Since perception is not part of the big bang, the conclusion has to be that not all basic-cog's are active at once in the cognitive big bang, but this contradicts the claim of innateness for all basic-cog's. The solution to this conundrum is that we have an input which is itself a basic-cog. That input is constituted by sensations. Shortly after having sensations, the rules of perception start operating. There is an infinitesimal lag. But a lag nonetheless. If the no-precedences rule is to hold, the cognitive big bang must include all basic-cog's, but with the proviso that at first not all basic-cog's are fully operative. Basic-cog's are innate. Inputs do not add to or subtract from basic-cog's. Inputs are like "cues" for basic-cog's. There must exist a "first cue" and that is the function of sensation. But this does not imply precedence. Perception is implicit in sensation, but there must be perception for the big bang to proceed.

Alternatively, there is the possibility of "prelogical implicatives". Before anything occurs, we must have the symbols of the mental language, because they are implicit in the innateness of basic-cog's. The rules of the mental language describe what the mental symbols do. Another possible implicative is ascription. At the big bang we have no memory, hence no self. Therefore, we must have ascription to self. Beyond this, all experience implies the specific self, in which ascription is implicit. Still another necessary implicative is intuitive logic. However, if we include logic at the start of cognition, as we must, then we cannot speak of "prelogical" implicatives. And since we have said that perception is implicit in sensation, we are back to the no-precedences thesis. There are no prelogical implicatives and no precedences. The big bang holds. The only assumption we must make is that sensations in themselves are basic-cog's intimately linked to the basic-cog's perception. The development of cognitive processes is determined by genetics. The process is analogous to the formation of clusters, galaxies, and stars. All cognitive processes begin to develop at a basic level according to universal patterns but in ways specific to each individual.

Within the framework of cognitive innateness, can we speak of some kind of sequential order in basic-cog's taking birth as the starting point? We could argue for self as a kind of basic basic-cog, but in a theory of cognition the self entailed would be the object-self, which does not exist except as a theoretical entity. And in any event, is self anterior to sensation? Since sensation involves specification and generalization, can there be sensation without intuitive logic? And can there be sensation or logic without memory? Nevertheless, perception and language certainly do come later. But how large is the lag between sensation in relation to perception? Doesn't the process of perception commence with the first sensation? Sight may be a laggard, but isn't sound-recognition perceptual from the start? The sensation/perception distinction is hypothetical and precarious. And does language-learning not start from the first input, for, tout dit, is grasping meaning in things different from grasping meaning in words? So basically birth is a big bang in which all the laws and rules of cognition suddenly appear not in dribs and drabs but as a cohesive, explosive whole. The only "singularity" is birth itself and after birth there are no precedences among basic-cog's. Just as the universe developed from what the astrophysical big bag entails, and not one iota more, so the cognitive big bang leads to the formation of all cognitive processes, like the formation of clusters, galaxies, and stars, and not a single basic-cog more.

Cognitive processes

Cognition is the sum of basic-cog's and cog-processes. The crucial characteristic of cog-processes is their interactiveness. Withing a convetionally delimited "present", we can, e.g., "parcelize" perception and simultaneous count the units in the parcelized area. We can do this with a surface divided into squares with the same design or representation in all, like pop-art multiple photography.

Cognitivism

Stephen P. Stich on John R. Searle, The Rediscovery of Mind (MIT) in the TLS March 5 1993

"Cognitive science is an interdisciplinary approach to the study of the mind that emerged in the 1960s."

"At about the same time, Noam Chomsky was revolutionizing linguistics by producing grammars for natural languages that were as formal and explicit as the grammars logicians constructed for artificial languages. Indeed, Chomsky's grammars were so explicit that they could be programmed on to a computer. Chomsky went on to argue that our linguistic skills are best explained if we suppose that we have tacit or unconscious knowledge of one of those program-like grammars."

Anthony Kenny, The Metaphysics of Mind (Clarendon 1989)

"...Chomsky reintroduced the notion of faculty and gave it an importance in psychology which it had not had for many centuries. He distinguished, for example, between the language-faculty and the number-faculty, and claimed that the phenomena of human language acquisition showed that there must be a species-specific language-faculty quite distinct from a capacity for mathematical computation which might be common not only to human beings but to other species on other planets who would be baffled by anything similar to human language. Descartes, on the other hand, regarded the notion of faculties as an Aristotelian anachronism which stood in the way of genuine scientific progress."

Coherence

Since much philosophical thought cannot be validated in the full sense of the term, what is the most that can be achieved with it? One important objective is coherence. The development of philosophical propositions must be such at the very least that it does not permit inconsistency, not to mention contradiction, to creep in. But this is self-justification, or just plain justification, and nowhere near validation.

Coherence entails the principle of non-contradiction, i.e., if a and b are reciprocally contradictory propositions, they cannot both be valid.

Setting aside the logical aspect of coherence, can we really describe it as a criterion of knowledge? Criteria allude to operations of the propositionality of mind. Since mind does not contemplate specific criteria for specific disciplines, there cannot be a philosophical criterion. A proposition is not a criterion but a yield of the propositionality of mind. Therefore, strictly speaking, coherence is a proposition emanating from the mechanisms of the propositionality of mind which are called criteria of knowledge. What criteria do we apply in elaborating a proposition about the coherence of propositions? Basically, the same that we would apply to perception or to probability, e.g., are these propositions logical? Since we make valid logical propositions, evidently logic is a criterion of knowledge. And if coherence involves not infringing a logical principle, then one of the criteria that we apply in coherence, or one of the operations of the propositionality of mind involved in propositions about coherence, is logic.

Are other propositional processes involved? It is nearly inconceivable for a philosophical treatise or any philosphical work not to include experience and probabilistic statements. Therefore, when we make a coherence judgement about philosophy, all we are doing is elaborating a proposition which is just like any other proposition in involving the epistemic processes of the propositionality of mind. Coherence, then, is nothing at all like an independent criterion of knowledge. It is more like a theory or a process of reasoning such as foundationalism or contrastive thought.

We admit that we are theorizing, even though we also claim that our arguments are sound. But we know that our arguments on one issue require the reinforcement and the correlation of other arguments on other issues. We shall perhaps never be able to claim for our ideas more than the status of theory, but the denser the web of issues and arguments the stronger the over-all theoretical construct.

Coherence becomes manifest in its elaboration and at the end it is nothing and can mean nothing beyond its own elaboration. The main problem that it presents as a means to validate belief is that, like the proverbial chain, it is as strong as its weakest link: it will not take a debatable proposition any closer to truth than it would be if it stood by itself. A coherent set of valid beliefs cannot make another belief valid in the absence of a stronger demonstration of its validity.

Collective awareness

If we admit the concept of collective awareness, then we can also conceive the concept of the totality of being, and beyond this, the concept of absolute being. This is a natural progression of thought, related to meaning and language rather than to logic. The totality of being is the totality of knowledge and the totality of events. But these totalities do not exist and cannot be. They can only serve as illustrative or corrective or epistemic concepts, like metaphors or thought experiments. It is useful to understand history as a form of collective awareness in terms of the totality of being and of absolute being. These concepts suggest a linkage between events and principles of interpretation. It is useful also to have the concept of knowledge which transcends the individual for only thus can we understand the intersubjectivity of knowledge.

The concept of collective awareness is an inference from two propositions: (1) things are for the individual from the individual's awareness of them, and (2) each individual awareness only encompasses a part of reality. Therefore, the only way to describe all of reality is through the concept of collective awareness, which does imply the concept of the totality of being. The collective awareness of humanity is the totality of being, from which alone it is possible to infer absolute being. Absolute being is the final and total negation of nihilism.

In sum, the concept of collective awareness sustains or complements the following ideas:

--totality of being, and by inference: absolute being;
--history and the becoming of history;
--vox historiæ;

Common-sense psychology

See Dualism

Compatibilism

The feeling that we are powerless to determine the course of our lives does not seem to absolve us from the apparent responsibilities implicit in the awareness of the unity of self. It certainly does not diminish the feeling of uncertainty about the future. The distinction between past and future subsists only in abstraction and for an instant. Yet from what we think we know today we can never be sure of what we shall think and know tomorrow. Our conscious desires and intentions were of little consequence in determining events in our past. Yet in the present we do not, and cannot, renounce trying to act so as to affect outcome in the future. Hard as we try, we cannot escape the quandary between the feeling of being determined and the feeling that somehow we are not really devoid of choice.

I am absolutely and totally determined. But in my thoughts and acts it will always seem to me as if I weren't. I will always use the conventional vocabulary implying free will
I will be plagued by feelings of failure and regret. And I will always entertain possible alternatives to satisfy my hopes and desires.

Computation

Computers exist to realize tasks for humans with efficiciency and speed resulting in the compression of time normally or optimally consumed by humans in achieving such tasks. To check out by mail what books Barnes & Noble have in stock would take a very high multiple of the time it can be done through the internet. Instances are rife. Mind instructs computers to do these things methodically through programs which include or have instructions to carry out all the steps necessary to the completion of tasks. In order for programs to function computers must have a master program. This simply reflects the fact that in humans themselves tasks are pyramided in such way that tasks are needed to accomplish other tasks. Is there a basic human task? Probably just living and being able to think, but this in turn requires fine-graining for living and thinking involve an infinite multitude of other tasks. In computers, the master program, e.g., Windows, makes available to the user all applications. It does not account for all tasks--for, e.g., computers do things, like coming on and lighting monitors, that do not require the master program--but it does account for all of the mind-like tasks. And this infinite multiplicity of tasks means that the master program of computers like mind itself and its different cognitive processes makes possible the interaction of programs. Among interactive computer functions are alternability, conversion, transference, and a host of others, but of course the master program is constantly interactive in itself. The basic concept is that computers were invented and have been developed and will go on being developed to facilitate human tasks, and at the stage of tehcnological advance at which computation has arrived it can even be claimed quite accurately that they not only serve to achieve tasks but also to realize the desires, hopes, aspirations, and ambitions of mankind. It could even be that this is what was at stake from the beginning.

If the so-called quantum chip (an atomic nano-processor) is made operational, it should be possible to construct an artificial replica of the human brain. So far the greatest achievement of artificial intelligence has been to make chess obsolete: no more championships between human players, no riddles or goals to be solved or achieved, as if some one had run a zero-time mile, or an all-strikes, no-balls shut out.

See also Connectionism

Conation

Volition, as distinct from cognition and affections, conation (e. 17th century) is the desire to perform an action. Volition is the actual performing of an action according to intention. Conation is volition without the action. Conation is what Dennett describes as what-to-do-next.

Concept

Prima facie, a concept is the mental equivalent of a word. A concept is a slice of meaning. But words per se have only meaning as propositions. A word is an arbitrary sound. The association of words and meanings is arbitrary. Propositions are the context that bond words and their meanings. Mind is constituted by non-verbal, "squiggly" propositions. "Squiggles" have rules which are not the rules of grammar. Yet in the end the expression of squiggles is necessarily linguistic. From the above then a concept is a squiggly proposition which can be expressed as a word and consequently in a linguistic proposition.

The simplest form of the linguistic expression of the concept is the word and the existential predicate, e.g., table is, justice exists, non-existence exists, and so on. However, as in "red herring", the concept is also the word or phrase and the meaning predicate. This implies at least two things: (1) that an elementary concept is just a label for many other propositions, such as the definitions of table, justice, non-existence, and so on; and (2) that a concept is a general proposition. If a concept is a general proposition, then it is the same thing as a sortal and a type. Since types are classes, concepts must also be classes and sets. A concept is a label, linguistic or squiggly, for sets and classes. Since these are generated by predicates, concepts are also predicates. Since terms refer to general entities, concepts then are also terms.

Paradoxes are propositional and the concept of concepts is particularly paradoxical. But propositionality per se is not the source of paradoxes. The concept of concept is merely the mental representation of the expression "concept is or exists or means". On the paradox of the concept of concept (see Theory of types).

A concept is the mental equivalent of a noun. Since thought is mind and all thought is propositional, then concept must be propositional. In what sense are concepts propositions? A concept is a proposition of the form "something is or exists or means". The simplest definition of concept is a noun with the predicate "is" or "exists" or "means" attached to it. In other words, a concept is the propositional version of noun. It can even be argued that there is no such thing as the concept of concept, if by concept we mean a single word or a single representation without the existential predicate. The concept of concept merely says "concepts are" or "concepts mean". Outside of the set of specific concepts, there is no concept as such. We cannot say the concept of concepts in the same sense in which we cannot say the class of all classes.

But there is also the concept "my philosophy", and this has to go beyond the proposition "my philosophy exists". In this case a concept is merely a label for a vast and complex "file" filled with many interconnected propositions. In itself "my philosophy" means nothing whatever. It is a mere label. Now, even for simple concepts such a "cat" or "dog" the concept has a labeling function, for we do not exhaust all there is to know about cats and dogs by merely having the respective concepts. Concepts therefore are (1) the propositional versions of noun and (2) a label for all sorts of additional propositions.

Concepts are (1) something akin to "atomic facts", i.e., existents, and (2) "atomic facts" as labels for hosts of related propositions. A concept is a representation. Its expression is a proposition. A proposition is the unit of meaning and of representation. A concept is the representation of a proposition. Word is an expression. If concept is propositional, all representation must be propositional. Word is the expression of a concept. Word too is propositional. The basic units of language and of thought are propositions. This is the essence of the propositional thesis. This means that the only argument that we have so far for the propositionality of language is the analogy of words with concepts. However, it is also possible to argue directly for the propositionality of language. Cognition is propositional. Concepts are propositional. Concepts are the units of thought. Squiggles and thought are reciprocally dependent. Therefore, squiggles are propositional. Thought is propositional. Since we grasp thought with language we must argue for the propositionality of language.

Concept is the name for the label of the propositions that constitute inferences from perception, just as squiggles and system of squiggles are the names that we are using to designate the mental representation of perception. When we recall, we are recalling a label, and this means that we are recalling a complex of propositions. A concept is also the squiggles equivalent of a noun. Squiggly equivalence implies that a concept is a proposition.

Flew: "The extension of a general term, predicate, or concept is made up of all those entities to which the term or predicate correctly applies, or which fall under the concept"

Connectionism

William Ramsey, Stephen P. Stich, and David E. Rumelhart, eds., Philosophy and Connectionist Theory (1991)

"Until the early 1980s, almost all cognitive models viewed the mind as what Allen Newell has called a `physical symbol system'. Models that adopt this perspective treat cognitive processes--processes like problem solving, language comprehension, and higher visual processing--as rule-governed symbol manipulation...This situation has changed very dramatically since 1984."

Ramsey, Stich, and Joseph Garon, "Connectionism, eliminativism, and the future of folk psychology"

"For the present purpose we will assume that common sense psychology can plausibly be regarded as a theory, and that beliefs, desires, and the rest of the propositional attitudes are plausibly viewed as posits of that theory."

"...the crucial FP tenets in forging the link between connectionism and eliminativism are the claims that propositional attitudes are functionally discrete, semantically interpretable, states that play a causal role in the production of other propositional attitudes, and ultimately in the production of behavior. Following the suggestion in Stich (1983), we'll call this cluster of claims propositional modularity."

"Some of these models [compatible with propositional modularity] represent individual beliefs as sentence-like structures--strings of symbols which can be individually activated by transferring them from long-term memory to the more limited memory of a CPU. Other models represent beliefs as a network of labeled nodes and labeled links through which patterns of activation may spread. Still other models represent beliefs as sets of production rules."

In a "`semantic network' representation of memory" (Collins and Quillian 1972) "each proposition is encoded in a functionally discrete way, [and] it is a straightforward matter to add or subtract a single proposition from memory, while leaving the rest of the network unchanged."

[It is to be doubted that propositions are stored in that way or that they come to mind in such a precise, discrete manner. And who does the adding and subtracting?]

"Second, the model treats predicates expresing the semantic properties of belief or memories as projectable. They are treated as the sorts of predicates that pick out scientifically genuine kinds, rather than mere accidental conglomerates, and thus are suitable for inclusion in the statement of lawlike regularities."

"...we want to describe a class of connectionist models which...are not readily compatible with propositional modularity. The connectionist models we have in mind share these properties: (1) their encoding of information in the connection weights and in the biases on units is widely distributed, rather than being localist; (2) individual hidden units in the network have no comfortable symbolic interpretation; they are subsymbolic...; (3) the models are intended as cognitive models, not merely as implementations of cognitive models."

Paul Smolensky (1988): "Connectionist models are large networks of simple, parallel computing elements...The network elements or units influence each other's values through connections that carry a numerical strength or weight...In a typical...model, input to the system is provided by imposing activation values on the input units of the network; these numerical values represent some encoding or representation of the input. The activation of the input units propagates along the connections until some set of activation values emerges on the output units; these activation values encode the output the system has computed from the input. In between the input and the output units there may be other units, often called hidden units, that participate in representing neither the input nor the output.

"The computation performed by the network in transforming the input pattern of activity to th eoutput pattern depends on the set of connection strengths; these weights are usually regarded as encoding the system's knowledge. In this sense, the connection strengths play the role of the program in a conventional computer. Much of the allure of the connectionist approach is that many connectionist networks program themselves, that is, they have autonomous procedures for tuning their weights to eventually perform some specific computation."

[If encoding is necessary for a connectionst model to function, then there must be decoding on the output side. If connectionist models decode, then the decoding cannot be done with the same means that need themselves decoding. Decoders must be attached to connectionist models, so connectionism per se does not explain the results of the cognitive process. Suppose by coding and encoding I am referring to ordinary psychological processes which have a connectionist description? It may simply be a question of adaptation to a theory which does not posit representation in conventional terms.]

"One point must be added to Smolenky's portrait. In many connectionist models the hidden units and the output units are assigned a numerical `bias' which is added into the calculation determining the unit's activation level. The learning procedures for such networks typically set both the connection strengths and the biases. Thus in these networks the system's knowledge is usually regarded as encoded in both the connection strengths and the biases."

"...in many connectionist networks it is not possible to localize propositional representation beyond the input layer..."

"Because of their obvious, though in may ways very partial, similarity to real neural architecture, it is tempting to view connectionist models as models of the implementation of psychological processes...A very different view that connectionist model builders can and often do take is that their models are at the psychological level, not at the level of implementation. So construed, the models are in competition with other psychological models of the same phenomena."

"In the connectionist network...there is no dictinct state or part of the network that serves to represent any particular proposition...Whenever information is extracted from a network, by giving it an input string and seeing whether it computes a high or a low value for the output unit, many connection strengths, many biases and many hidden units play a role in the computation...It simply makes no sense to ask whether or not the representation of a particular proposition plays a causal role in the network's computation. It is in just this respect that our connectionist model of memory seems radically incongruent with the propositional modularity of FP...[which] seems to presuppose that there is generally some answer to the question of whether a particular belief or memory played a causal role in a specific cognitive episode. But if belief and memory are subserved by a connectionist network like ours, such questions seem to have no clear meaning...the system lacks functionally distinct, identifiable substructures that are semantically interpretable as representations of individual propositions...though there are are indefinitely many connectionist networks that represent the information that dogs have fur...these networks have no projectable features in common that are describable in the language of connectionist theory."

"The propositional modularity presupposed by common sense psychology requires that belief tokens be functionally discrete states capable of interacting with one another in some cognitive episodes and remaining causally inert in other cognitive episodes. However, in a distributed connectionist network...the dispositional state which produces one activation pattern is functionally inseparable from the dispositional state which produces another."

Kim Sterelny, The Representational Theory of Mind: An Introduction (1990)

"Connectionists see the mind (or subdomains of the mind) as networks. These networks consist of large numbers of multiply interconnected nodes. The nodes are simple, numerous, and interact without supervision from a central processing unit. In the limit, all the nodes are connected; even if the limit is not reached each node is connected with many others...[T]he node is under local control. What it does depends only on its state and its immediate environment, not on any global properties of the system.

"The network's information is encoded in the weights between the nodes. Typically these weights are modifiable. The network's capacity to learn (and, in effect, it's memory) depends on this modification process. Learning proceeds by slight modifications of the weights between nodes. This is known as `training' a network...Let me give an intuitive sketch of training the mine/rock recognizer. Initially, the connection's strengths are set at random. The input nodes are then represented with a series of teaching stimuli...Some of the input nodes will fire strongly, others weakly, others still, not at all. In the next cycle, these reach the hidden nodes; stimulating some, inhibiting others. These begin to inhibit or excite both other hidden nodes and the output nodes. Many nodes will get and give both excitatiry and inhibitory signals, as will the output nodes. Gradually, as these stimuli are transmitted back and forth, the network will begin to settle into a stable state: it's a striking fact about these networks that, though they have an enormous number of states, only few are stable. Eventually the network will settle into a stable state with `yes mine' node or on the `yes rock' node...There is no automatic commitment to the view that particular intermediate nodes in the network stand for any identifiable element or feature of the environment...Hence it's often claimed that representation in these systems is distributed. The representational properties are carried by the networks as a whole (or some part of the network) rather than by individual nodes representing particular features of the environment...The connections between the nodes are understood causally rather than as a system following a sequence of rules...There is no control or executive orchestrating thye network's behaviour. There is no homuncular breakdown of a connectionist network after the style of Lycan and Dennett."

Super computer speed can be achieved thorugh a huge network of massive parallel processing involving several processors
NYT , 6/15/92

With such speed it is possible to have a connectionist replication of brain processes such as pattern-recognition and the transformation of optical signals. In pattern-recognition decisions involve total information. The problem is broken into parts. The processing of the parts is done simultaneously. The input into the processors produces changeable connections. A variant on this process is the conversion of optical signals into electronic ones. The entire connectionist process deemphasizes logical reasoning. Work of this sort in artificial intelligence should be able to result in a general-purpose real-world intelligence. The objective is to solve the "frame problem". NYT , 8/25/92

Connective

"Connective. A word or group of words that can be regarded as joining two or more sentences to form a single complex sentence. Examples are `either...or...', `and', `because', `since'. Most common are connectives joining two sentences; these are termed binary connectives. Although there are many expressions that function grammatically as connectives, the term is often, in the context of logic, restricted to the logical connectives: `and', `or', `if...then...', and `if and only if'." (Flew)

Consciousness and self

Starting from the proposition--taken from David Hodgson's Mind matters (1991)--that consciousness of sensations amounts to having evidence for the material basis of thought, we can develop the following chain of questions and arguments. Are we to start with conscious of sensations? That we have perceptions cannot be denied. But are sensations perceptions and vice versa? In normal language-use, sensations are components: pain, colours, forms, etc. Perception is the recognition of compounded sensations. If perception is a complex, "holistic" event, we can only "abstract" sensation from perception, not have sensation separately. In fact the notion of "being conscious" is itself problematical. When we say we are conscious of something what we actually mean is that we remember an instant ago. Whatever it is I do, I am conscious of it in recall, but not usually in doing it, for this means two actions at once, which is only possible to the detriment of both, or perhaps doing only one distractedly, so normally we do one thing of which we are conscious of in recall.

Awareness is a complex of faculties--the result of interactive cognitive processes--by which we perceive, have thoughts, and distinguish between perceiving and having thoughts. Is writing conscious? If consciousness is having a display in front of me and being aware of options and so on, writing isn't even awareness. How about Surrealist automatic writing in which critical or rational awareness supposedly does not accompany wakefulness? It is a total myth. It is seeming to distract the mind in the act of writing and no less subject to cognitive processes than normal writing.

Let us return to the ordinary act of writing. I am concentrated on my work. In which sense am I conscious at all? I am conscious each instant of doing something: writing one specific letter, putting letters into words, reading what I wrote, and so on. But I am not conscious of writing as such for all the previous moments were all part of writing and not writing itself. And I am not conscious of making rational choices, although I know that reason is making possible what I am writing. In sum, being conscious of the act of writing cannot be an occasional awareness of this or that, but of the entire act itself, which, for one, is not complete, and, for two, is never present as such to me. Therefore, if consciousness is consciousness of writing, then I am not conscious at all.

But there is something there of which I am conscious at every instant and that is the self. If consciousness is to be something other than recall, if it is to be a constant and not just an occasional event, then the only sense that consciousness can have is the awareness of self. I am conscious at every moment of my specific self. Therefore, consciousness is equivalent to my specific self. But it is not possible to think and be aware of anything other than my thought. Consciousness cannot be different from awareness, although all awareness is specific and it therefore doubles as self-awareness. But I am not even aware of my specificity. It is just a trait of my thought. Consciousness in sum is nothing.

It is obvious that Beckett's L'innomable is about thought. But it is a peculiar sort of thought. It can exist divorced from quotidian reality: in fact, since it is not certain about its own context, it virtually generates its own world. Words constitute the underlying reality or the substance of this thought. Words relate among themselves in a formal rational way, so that thought can proceed without reference to any reality beyond the reality of words. Since language is syntax and syntax is the rationalization of the relation between words, thought in Beckett is linguistic. It is also abstract and circular. And thought, in addition to all the above, is aware of itself and can even try to "reject" itself as words that are imposed on it by "others". What all the above indicates is consciousness.

Consciousness is the awareness of awareness. It is cognition probing itself, the dog chasing its own tail, the snake swallowing itself.

One of the specific neurotic forms is fixation on thought to the exclusion of its relation to reality, hence upon itself. The thought in L'innomable also exhibits fixation upon itself: it is in fact fixation upon itself more than it is anything else. Neurosis seems to be a feature of awareness in Beckett.

In fixation (the vacant-look state) the mind tries to control mental states. It produces anxiety because mental states are not physical. Hence, the awareness of awareness when the mind realizes it can do nothing about its own mental states. Anxiety is the mental equivalent of pain. Anxiety is characteristic of neurosis. It is one of the effects of L'innomable. Besides being the most finished literary representation of consciousness, L'innomable is also a representation of the anxiety component in awareness. It is easy to find lines of affinity between the concept of neurosis and the representation of awareness in L'innomable , even if we cannot claim that it was Beckett's specific intention in that work was to represent neurosis. There is the implication in all this thought of an equivalence or a very close relation between neurosis and consciousness.

Neurosis can be useful as a touchstone to test the validity of the propositional theory of affects. To do this it is necessary to disentangle it from the web of myths and nonsense in which it was bound by Freud, who virtually "disovered" it. This is not contradictory. Columbus discovered America yet he believed he had reached India . Why bring in neurosis at all? For its argumentative value, basically, but also because there is at least literary "evidence"--specifically in Samuel Beckett's L'innomable and others of his works--that neurosis evinces paradigmatically the awareness-of-awareness circularity that is the elementary specification of consciousness. Beckett's greatest achievement may indeed have been the "reification" of epiphenomenalism.

Consciousness and paradox

Consciousness as the awareness of awareness is a rich source of paradox. Since the awareness of awareness is still only awareness, then consciousness is the awareness of nothing. Consciousness is the same as the class of all classes of mental events. But if so, it is not a mental event itself. Since we can disarm paradoxes with reason, this would mean that one of our tenuous holds on consciousness simply vanishes. Could we not argue however that since formal logic is the source of paradoxes, consciousness is somehow the process whereby intuitive logic draws formal logic from itself? Or that it is embodied in the process through which Gödel obtained his famous proofs? But isn't this just giving reason another name? Consciousness is reason??? Beyond awareness there seems to be nothing that can really and truly be qualified as consciousness.

Consensuality and transactionality

Perhaps consensuality can give us a more reliable version of what knowledge is. We have had occasion to describe language, scientific hypotheses, even perception, as consensual. Let us try to further specify consensuality.

In which sense is language consensual? It is consensual, in a very elementary sense, in that we find the definition of words in dictionaries. Dictionaries are an expression/reification of collective, historical experience, in the sense of being constituted by "agreed-upon" definitions. This consensus about definitions is the product again of the complex processses of the propositionality of mind, e.g., just think of Samuel Johnson writing his dictionary or Diderot compiling his encyclopedia.

An evident part of of these processes is transactionality. The transactionality of knowledge produces consensus, although of course it is not the only product of transactionality. The definitions of language are transactional and consensual.

In which sense are scientific hypotheses consensual? Science always starts with the justification of hypotheses, which implies transactionality/consensuality, e.g., the process of being published in, say, Nature , or the upshot of the Bones of Contention controversy.

In which sense, finally, is perception consensual? In part, it is consensual from language, as when two persons are trying to get together on which term to use for an object of perception. But it is also implicitly transactional/consensual, as when we drive a car in traffic or when at work different persons are doing the same task.

Transactionality is implicit in perception: it is not a process to which we must appeal at each instant of perception. But transactionality is explicit in the case of writing a dictionary or of being published in a scientific journal. In other words, transactionality, or something akin to it, is an indispensable cognitive expedient for certain types of propositions, but it can be dispensed with in the case of other propositions, mainly factual propositions. In this case it is implicit. In general, the more probability enters into propositions, the stronger the need for transactionality.

Let us be more precise about the differences between transactionality and consensus. Transactionality is a cognitive process. It is a property of propositionality. It can be both individual, i.e., when I compare my beliefs to those of others, and collective, e.g., when different beliefs meet "in the market place of ideas". This "meeting" can be described as the externalization of individual transactional processes.

Now, it would hardly do to say that the individual transactional process is consensual. Our epistemic transactions with the world can produce changes in our beliefs, but these are not consensuses. But the collective transactional process can produce consensus. Consensus is the result of the collective transactional process. It is a possible, even a probable, but not a necessary result.

Let us now recap transactionality. From what perspective do we or can we speak of the transactionality of knowledge? Evidently, the external perspective on knowledge is only possible from individual awareness, for which all is belief in, denial of, 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 intersubjectivity 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, transactional perspective. 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.

Knowledge is a transaction between the subject and the world. Since knowledge cannot avoid being of a subject, i.e., the ascribability of all propositions to specific minds, the transactionality of knowledge cannot prevent the formation of false belief. And if such is the case I cannot have an accurate final version of the extent of my knowledge. How do we get out of this cul de sac? We do not!!!

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 vague and imprecise, 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. Their precision is imaginary. This applies even to science and to mathematics, e.g., the genome debate and meta-mathematical thought. The most that can be said is that the historical tendency is towards their continuous expansion.

Consensual theory of knowledge

How do we know that what we perceive is true?
Certainly not from any criterion external to the act of perceiving, nor because we consult with others about what we are seeing. We simply know that perception is reliable, and we know this not because we do a course on perception but because we know it from shortly after birth, assuming there is a brief phase during which we only infer and generalize about sensations. However, even though we do not consult with others about what we perceive, we are sure that others see what we see. We are agreed among each other that perception is reliable. It is somewhat as if we had taken a vote. But we never actually voted, we never actually reached a compact about the reliability of perception. In fact, it is perfectly possible to think of someone who may be disinclined to believe in the reliability of perception, e.g., a feather fluttering down and a plane taking off are both under the influence of the same physical laws. What this actually means is that there is a consensus about ordinary perception and about other reliable cog-processes.

Where did this consensus come from?
The answer must lie in the history of life. At some point a microbe of some sort acquired the ability to sense the external world and to act according to this knowledge. Other microbes from this original sensitive microbe also began to act in accordance with the information they had from the outside, including the presence of the other microbes and their behaviour. An interaction was established between these animalcules. They did not compare notes or speak or communicate in other than a rudimentary way but their communicative interaction resulted in more survival-efficient behaviour. It was from this interaction that the consensus arose that the sensitivity experienced by these microbes was reliable and useful. This behaviour increased their chances of survival, so that just by being alive and reproducing and besting other non-sensitive forms of life these microbes established a consensus about knowing, including that knowledge consists in knowing how to sense and how to use sensation.

Quine says something to the same effect ( TLS , July 3 1992) in connection with his wonder at the complexity of scientific elaborations from what he considers to be the meagre inputs of experience: "The answer, at the level of natural science itself, is that evolution by natural selection has rendered us attentive to certain features of our perceptions that tend to mesh with the regularities of nature." However, the regularity of gravity is observable in the orbits of planets, but on Earth it would be difficult to conceive of more irregular occurrences than falling objects.

Knowledge is the use of basic-cog's. There is a general consensus that basic-cog's work, i.e., no one can actually prove the reliability of perception. There is therefore a general consensus about what is knowledge.

Constative

Constative is affirmative mood.

Constraints

Conditions to be satisfied for something to fit a definition or specification.

Constructivism

"Constructivism. The view that mathematical entities exist only if they can be constructed (or, intuitively, shown to exist), and that mathematical statements are true only if a constructive proof can be given. It is thus opposed to any view of mathematics--for example, platonism--that sees mathematical objects and truths existing or being true independently of (our) apprehension. Constructivism encompasses intuitionism, finitism, and formalism." (Flew)

The distinction is useless. Constructivism entails platonism. Who would undertake long and complex mathematical computations without the belief in their efficacy? It would be like taking to a stormy ocean on a ship taking water. Conversely, no one can pretend to see another sea strand without undertaking a sea voyage.

Context

See Definition

Contextualism

See Holism

Contingency and necessity

John Leslie on P.W. Atkins, Creation revisited (OUP), TLS, January 29, 1993

"One of his most intriguing suggestions is that there exist up to many universes, their characters varying randomly. Our universe may then be very special in how its character permits observers to evolve. Atkins argues that balances between the strengths of natural forces--gravity, electromagnetism, and the nuclear strong and weak forces--may well need to be `exactly right' if living intelligence is to emerge. (Imagine strengthening electromagnetism just a little. Chemically based life becomes near to impossible: `prods like nuclear explosions' would be needed to produce chemical changes. Slightly increase the range of the nuclear strong force, and the entire universe is quickly `wound down into a blob'. Etcetera.) The same applies to the combination of three dimensions of space with one dimension of time: anything else would be incompatible with stability and with a complexity which was neither too great nor too small. `Chance might have stumbled on fortune' in the case of our universe. `Alien and unknown universes may litter the void', but `necessarily we are awake amid benevolence'--or rather, in a universe in which observers could evolve, a universe looking just like a product of benevolence...Why, however, is Peter Atkins so hostile to the idea that our universe genuinely is a product of benevolence?...[He] delights in the idea that no creator exists."

Zygmunt Bauman on Geoffrey Hawthorne, Plausible worlds: possibility and understanding in history and the social sciences (CUP) in TLS October 11 1991

"The fact that past events happened to be what they were is shown to be nothing but contingent [sic]; what actually happened was just one of the possibilities that (through a concatenation of actions impossible to predict with any certainty) prevailed over many (how many? and how to count them?) virtual turns of events. But our explanations of the events that have taken place are in no better condition than the events themselves. However hard we try, explanations do not make past events, retrospectively, any less contingent than they were at the time they happened."

This involves modal logic. The argument I think goes like this: if it is logical it can be and, therefore, "because of the infinity of possible human actions, and the virtual infinity of the possibilities the inquisitive human mind can conceive of, a scientific theory of history or, indeed, of anything social, is impossible.

Contradiction

"Contradiction, principle (or law) of. `It is not the case both that p and not p' (where p is any proposition)." (Flew)

Contrastive thought

What is "contrastive thought"? Propositional processes produce propositions of different types. The propositional process involves perception and appercetion, intuitive logic, and so on, in constant interaction between them from the beginning. There is no specific area of mental process to which contrastive thought itself can be justifiably attributed. Is contrastive thought a rational principles? Only if it were a constant operation of mind, which is not the case as concepts do not necessarily involve contrast between concepts, e.g., we can understand "shoe" without having to think of "shoelessness". So where does that leave us? It is a rational operation not involving any specific propositional process. Ultimately, contrastive thought is an aid to speculative thought.

Some believe that contrastive thought is indispensable for explanation. However, this is not true. In areas of interpretation, contrastive thought is perhaps indispensable, precisely because you can not draw necessary conclusions in such areas. In science, contrastive thought may be important, perhaps even crucial, at the stage of hypothesis building, but prima facie contrastive thought would be superfluous once theories have become laws of nature and can be used to explain different phenomena, e.g., the tides. In historiography, contrastive thought amounts to counterfactuals. But counterfactuals have a special meaning in philosophical debates.

The demonstration of the space/time indissolubility is made from contrastive thought, i.e., in order to understand space we need to think of what reality would be like without space and in order to understand time we have to think of what reality would be like without time.

Correspondence

See Truth

Cosmology

There are two opposing cosmologies. In one, God is the guiding hand. In the other, chance rules the universe. But there is a third which claims that it is reason that determines events and their linkages and successions. The universe is suffused by logic.

Selfishness and lying and success are the trimurthi of politics. No country can help another develop because each country is responsible for its own underdevelopment. Once an injustice is committed it is irreparable; consequently, the concept of justice is an absurd. Closure is revenge. Equality is a dog's fart. Individualism, worse than a dog's fart, is a dangerous delusion. Yet history is perfectly and totally rational. Science and technology advance. Truth is a lost child though: it needs parents; it is not loved per se. Democracy and economic freedom are accepted as universal goals. There is a tendency to cultural sameness the world over. The making of money and the accumulation of wealth are universal constants.

Counterfactual

Counterfactuality is to argue assuming that something might have happened instead of what actually happened. This would seem to be a very precarious, in-conducive method. However, certain historical events are of such a nature, e.g., Michael Collins' assassination or Stalin's death, that it is inevitable that they should have had immediate ad hoc consequences in which case it is also inescapable to fall into counterfactual speculation. What would have happened had Collins met De Valera on his ill-planned, ill-fated tour of West Cork ? What course would the USSR have taken had Beria emerged victorious? Of course, in the long run, conventionally defined--not in Keynes' comic sense--such events are smothered in the powerful undercurrents of history, e.g., the collapse of the USSR was probably inevitable--Malcolm Lowry, e.g., foresaw it as early as 1952 or thereabouts, i.e., it was hardly unthinkable--but history is written not just about the long-haul, on which Keynes was right, but also on the short-term evolution of events.

Philosophically counterfactuals are a means of arguing about the logicality of thought. They are, consequently, a philosophy-of-mind version of modal logic, in which what is logical is necessary in the world, or something to that effect. In the case of philosophy of mind, counterfactuals refer to the necessity of inferences based on subjunctive premises. If thought is a form of behaviour or at least the cause of behaviour, counterfactuals would then function as an actual cause of behaviour, and it could be argued that mental life is as subject to laws as natural phenomena.

A counterfactual is a strong deduction built on a weak premise: if this, then that. But if is nothing. If it is, however, the deducted proposition is inevitable.

The bottom-line to counterfactuality and contrastive thought is that they are strong cognitive maneuvers. They are not probatory in any way. There are of course countless cognitive maneuvers, e.g., enumeration of alternatives, mnemonic devices, etc. "Maneuvers" may not be the best term. They are patterns of cognition. Counterfactuality and contrastive thought are strong patterns.

Covariance

One sense at least of covariance is identity: any change in mind must be accompanied by a change in the brain and vice versa. In fact, all relations of equivalence, be they identity, similarity, synonymy, or what have you, are or can be based on covariance: if things vary simultaneously in the same way, then they are equivalent, identical, similar, synonymous, or what have you.