Languages fall into two general categories: public, communicative languages and all other languages. But all languages, sooner or later, end up as instruments of communication. The cognitive system, of which languages are a part, is not for knowledge as knowledge but for the communication of knowledge. Perhaps it is for the use of knowledge, e.g., for survival? But in surviving we are communicating, are we not? If there were no movement, there would not be the need to survive, and there would not arise cognition; so cognition, which requires a language, arises with movement, and since movement entails communication, cognition and language are for communicating. There is no communication without meaning. Therefore, the "essence" of language is meaning.
The basic physical unit of public, communicative languages are words. But words are arbitrary associations between sounds and references. This is bottom-line conventional meaning. Words are in arbitrary association with sets of things like chairs.
A word in a strictly formal sense of utterable combinations of letters need not have meaning, e.g., lili bulero. These are nonsense words. Yet "Lili
Bulero" has meaning: it is the title of a tune. This is a specific arbitrary association.
Can real nonsense be a word, e.g., batruvnu? Well, there is a line to be crossed here, but we have as yet no reason either to cross it or not cross it.
There are combinations of letters that seem to be words but are not, e.g., unpossible. In this case we have an utterance that not only sounds like a word and has an intended meaning, but which is not in any dictionary of English. Is it a word? According to the rules, e.g., hear or read a word, go to the dictionary, etc., it is not a word. But in all other respects it is a word. Here then is a case of an utterance that has meaning, functions as a word, has the form of a word, and is not a word. Therefore, words are meaningful and conventional combinations of letters. Since no dictionary includes "batruvnu" and it means nothing, it is a "nonsense" word.
Limericks, incidentally are not nonsensical, e.g.,
there was an old man from Perú/ who dreamed he was eating a shoe.
/He woke in a fright in the middle of the night /and found it was perfectly true.
There is not one nonsensical sound in that rhyme.
It is logical and impeccably grammatical.
If language consisted in the conventional definition of words, its
use would be circular and obtuse. A word means what it does because it does. Word substitution gets us out of and into circularity again, e.g., in defining "reason" we can say "intelligence" or "logic", but we immediately find ourselves again in difficulties, for "intelligence" and "logic" by decree or convention are synonymous with "reason", which is what we wanted to define in the first place. But of course words are propositions and we are soon out of circularity. We can, e.g., use "syllogism" to break the circularity. The indeterminacy of terms in philosophy, e.g., "Platonism" in ontology and in math, is an example of a conventional definition in terms of propositions.
Sentences are combinations of meanings put together with rules of grammar. Words are units of language but generally speaking languages are for communicating--mental languages are for thinking and communicating--and communicating is usually done with sentences and not with single words. The expressions of a language are sentences. Sentences are propositions. Propositions theoretically can also exist without public, communicative language. A dog's recognition of his master is like assenting to a proposition, but dogs can only bark and make other rudimentary communicative sounds.
There can be
But we can in no way assume is a meaningless sentence. A sentence must necessarily have meaning. You cannot make a sentence that says "batruvnu kiuku nag garrigan". The latter is a meaningless combination of word-like but nonsensical sounds. You can make "batruvnu" mean anything. Or you can leave it alone, not even think of it. If you do think of it, you have a word-like meaningless combination of sounds. A sentence or a proposition must have meaning. The essence of a word is sound. The essence of a sentence or a proposition is meaning. Therefore, meaning comes in sentences, hence in propositions, and as language is meaningful by essence it is composed of propositions. Since the essence of languages is meaning, then the real unit of meaning in language are sentences or propositions.
Dummett wrote of
Strawson: "According to him, it is only of sentences that we can say that they are meaningful or meaningless, whereas it is of assertions or of particular uses of sentences that we can say that they are true or false". L. Jonathan Cohen also makes a comparable distinction.
Since words imply a language and the units of meaning of languages are propositions, where words really operate as meaningful entities, then human concepts are propositions of a mental language. This could be true of canines, but we are not interested in their psychology.
Let us get our ducks in a row here. Words are meaningful and conventional combination of letters. Therefore, we can have combinations of letters which are not words, i.e., combinations of letters which mean nothing and combinations of letters which mean something but are not in any dictionary. What we cannot have is a meaningless proposition. A proposition can give meaning to a non-word or to a meaningless word.
"Unpossible" is not a word even though it means, but a meaningful combination of words such as "unpossible", e.g., unpossible rain
under not wet be, is a proposition. "Batruvnu" means "thing". Insofar as words are meanings, they are propositions.
"Batruvnu" defined, it immediately becomes "Batruvnu exists and means thing".
Specification and categorization or the
linguistic structuring of reality
Specification is done with words and words are meaningful. Specification is meaning. Meaning has two values: an
"intrinsic value" and a "relational value". Words label and mean something specific. But words also relate to other words, they evoke other words, as concepts they combine with other words. Language is a self-multiplying, self-generating existent. It is true it only grows on the margins, although margins can travel to the core, but over time this growth has been considerable. All of this is a result of the relational value of the meaning of words. The relational value of the meaning of words is the basis of the categorization of reality. Of course, the intrinsic value is itself the basis for the relational value so that it cannot be avoided that the intrinsic value also categorizes.
There was reality before human language came to be. But the categorization of reality is the result of a long historical process. Even though undoubtedly reality determined the primitive categories of language, the use of language has subsequently expanded the categorization of reality. Reality therefore determined language and language in turn "determines reality". But in determining reality, does language follow the "guidelines" of reality? This cannot be denied. It can be said that the process of language and of knowledge consists in the wresting of knowledge from reality.
We know reality directly but we also know it as expressed linguistically, i.e., our awareness of reality includes language per se and language as the means to specify and categorize reality. Our knowledge of the world and of the contents of mind includes the words by which we designate such knowledge. We specify things in reality with their specific names and in designating things by their names we also recognize that things belong in categories, e.g., "bird" is a specific bird but it is also "all birds", and when we say something about "bird" we can be saying it of "all birds". It can be said that this specification and categorization of experience constitutes a structuring of reality.
The linguistic structuring of reality embraces all the parts of language: the names for things, the verbs that refer to actions, and the qualifiers of things and verbs, but as well the parts of language, such as conjunctions and prepositions, that express relations between the other parts of language, e.g., between simple, conceptual propositions such as "birds exist", and between complex propositions, e.g., all birds have wings, but not all birds fly
The structuring of reality is not a one-off, definitive "event". It goes on through life on the linguistic base we acquire. There are many examples of how reality is further structured from the linguistic base that we acquire. School learning gives us explanations, new names with which to designate phenomena of all sorts. Even in ordinary everyday life we are constantly learning new things, from others, from news media, at work, even at home. The basis for this expansion of our knowledge is language. The structuring of reality consist in its "subjection" to linguistic specification and categorization.
A philosophico-historical illustration of this process can be found in the Aristotelian synthesis. Today we do not need to start from scratch concerning physical events. We gradually learn that there exists a vast accumulation of knowledge about the physical world, that the work of explaining how the physical world functions has been done in the past by multiple disciplines and subdisciplines. That knowledge is there for us to acquire. No one has to elaborate it anew. Some problems in the past have been solved, e.g., we do not have to discover and reformulate the laws of gravity. But when Aristotle started philosophizing the knowledge of the physical world was rudimentary and unsystematic. His philosophy, in the starkest terms, consisted in giving names to things and events, in finding relations between them, and in providing explanations. In this sense, his philosophy consisted in the structuring of reality for his time on the basis of the knowledge "contained" in the language that he inherited. The fact that his physical theories and explanations were wholly off base does not disqualify what he achieved as a coherent structuring of reality. The problems that he dealt with are no longer with us and therefore the study of his structuring synthesis of the physical world is of merely historical interest. His concept of philosophy is still central to what philosophy is about, but it has been worn down from the edges inwards to the fundamentals. This means that the structuring of reality is a historical process and that it consists in the expansion of knowledge. In this sense, then, knowledge is the progressive subjection of "brute" reality to a linguistic structure encompassing concepts and explanations, their relations, and their application. This process is what we are describing as the specification and categorization of reality. Specification means identifying and circumscribing the things, the events, and the connections between them. Categorization means grouping these specifications, generalizing from them, and in so doing, discovering possible explanations.
Austin in Hacker (p.175): "...our common stock of words embodies all the distinctions men have found worth drawing, and the connections they have found worth marking, in the lifetime of many generations..."
Language is knowledge as reification, as communication, as grammar and lexicon, but it is knowledge, especially for our purpose of defining knowledge, as the specification and formalization of reality. However, within the structuring of reality that is in language and that becomes part of our cognitive system, there is plenty of room for error. Language has the categories, but what we do with them is our business. Language has no "business" other than to function as a map of reality. But even with such an splendid map it is the easiest thing in the world to go astray.
Language is formed of specifics, i.e., words, with sortal value. It is a self-generating system of categories, and that in this respect it is neither a program nor an algorithm. In a sense, language does the work of knowing for mind. Language will not take you to the end of the road, but it will light the way. However, this raises the issue of possible knowledge: is this too knowledge since it has to be unstructured reality? Here we have to draw a line: we do not know what is not known, or what is only adumbrated as potential knowledge. This then would be the only area of reality that is unstructured, but this is an area that is constantly ceding ground to the probing of mind.
In its most elemental, material sense, language is a system of symbols with a syntax for combining them.
On a functional level, language is the principal means of human communication. The basic components of language are words and the trait common to all words is meaning. Language is meaningful because words mean something to us, although this does not mean that the meaning of language can be restricted to the meaning of words, for the syntactical ordering of words gives rise to complex meanings which affect the individual meaning of words.
In a historical sense, language is a reification of the awareness of humanity. Reality does not come to be in a certain way through language. It determines and contains language. Reality and language are reciprocally dependent, but they are not identical or equivalent. From the idea of the biconditionality of language and philosophy, it may be possible to argue, using the definition of language as an accumulation of categorized experience, that philosophy is an expansion of awareness.
Language--whether we call it the historical reification of awareness or the reified foundation of knowledge as the specification and categorization of reality or in any other way--is a product of human experience and as such it does not come with logical as opposed to historical explanations, e.g., the use of agricultural, chemical, or physical metaphors; and so on. Linguistics consists in the search for the explanations of language.
Language and logic
Simon Blackburn on Crispin Wright,
Realism, Meaning and Truth (Oxford: Blackwell), in TLS, February 27 1987, p. 221-2
"It is fruitless, [P. F. Strawson] argued [in 1976], to try to wash away the rock of truth that our concepts enable us to understand ourselves as in a world which extends boundlessly beyond the fragments of which we have experience."
[According to Blackburn truth and "truth conditions" are concepts in the theory of language.
I would have thought that they are epistemological concepts.]
"One of the most central, beautiful and difficult disputes in analytical philosophy for (at least) the past twenty-five years has concerned the role of truth and `truth conditions' in the theory of language. An extreme position holds that a proper view of the way sentences of a language have their `truth condition' is the first thing that we need to know if we are to understand language. The focus in this view is upon the connection of language with the world: the connection effected because names refer to things, predicates delimit sets of things, and sentences are true or false in determinate circumstances. Compared to the technical problem of properly charting the structures whereby sentences obtain their meaning, other issues are secondary.
"To most philosophers this view would seem at best complacent. It is a way of entering during Act Two of the drama, of failing to engage with the problems of how reference, predication, assertion and truth are even possible. It neglects the connection of the meaning of language with its use--with experience, activity, and with the responses and purposes of human beings in their societies."
Language of thought
That there is a language of thought, different from natural language, can be shown through certain experiences. For instance: I have thoughts--as in understanding the cladistic or molecular genetics theory on the African origins of humanity--before I can express them linguistically. In Book XI of his
Confessions , St Augustine says that he knows perfectly well what time is until someone asks him what it is. This, however, is not to say that I do not also think in words and in images. Sententialism constitutes a multiple ablation.
From Robert Cummins, Meaning and
mental representation (1989)
"Haugeland (1985) credits Hobbes with
being the first to have an inkling that mental representations might be
Pascal Engel on J. Christopher Maloney,
The Mundane Matter of Mental Language (Cambridge University Press),
TLS, August 17-23 1990, p. 880
"That mental terms do have meaning must,
if computers are not to be genuinely intelligent, be a function of what
differentiates the naturally and (merely) artificially intelligent. Holding
fast to this, we may find warrant in hypothesizing that the difference here
is a material, physical difference. Cognitive agents must be made of stuff
that allows their mental terms to be meaningful. Computers, as we now know
them, must simply be made of the wrong stuff."
1) Here again Maloney parts ways with
standard functionalism. But why go to matter for differences? Thought itself
could be different in the mind and the computer. Mind has a faculty that
computers lack: the faculty of awareness. Maloney goes for an easy
observable "solution": if mind has a grasp of itself, it is because it
"inhabits" a brain. This is begging the question!
2) Maloney characterizes his work as
philosophical psychology and he injects himself into the mainstream of
debate from the mid-70s.
"Internal mental representations seem to
entail an infinite regress of embedded cognitive agents. Appreciation of the
representational powers of artificially intelligent programs serves to
illustrate that representations do not require embedded agents."
Some of the fundamental philosophical
ideas and contributions of Leibniz are:
(1) indiscernibility of identicals
(2) best of all possible worlds
(3) perception is not necessarily
(4) salva veritate.
Quine says: "Unlike Russell's paradox and the heterological...the liar calls for some tinkering to secure it against scoffers." But I can't see how you can get away from the paradox involved in saying I am a liar.
Quine goes sideways: he prefers the statement:
"this statement is false", which is absolutely meaningless, because there is no statement involved to make true or false.
So he comes up with his version of the liar's paradox, which is: "'Does not yield a truth when appended to its own quotation' does not yield a truth when appended to its own quotation", of which Hofstadter makes a great deal in his exposition of Gödel's theorem.
"`Does not yield a truth when appended to its own quotation' does not yield a truth when appended to its own quotation", is an undecidable proposition, which is the case of Gödel's proof. Of course, Quine's phrase means nothing whatever. And Gödel's proof means that no formal system can be both complete and consistent. But so far no
mathematician has given up on mathematics because of Gödel's theorem. The point is the limitations of deductive concepts and systems. However, even the proposition that "identity statements are paradoxical" is itself a paradox. If identities are paradoxes, then identities are not possible, and the paradoxes disappear.
Alternatively you can use predicate logic and the quantifier.
Although both Frege and Russell were mistrustful of thought, they did not actually find a satisfactory substitute for the mental thing. Frege could never shake the belief that thought determines meaning. Russell went a little further by reducing thought to propositional attitudes. It was in fact Wittgenstein who went all the way and declared that outside of language and grammar there is no thought and there is no logic.
Linguistics is the study of language, but, as some one said, in what language has of contingent and accidental. Linguistics is about specific languages and about their origins and their inter-relations or categorization by families. If so, then, philosophy of language is about what language has that is necessary and universal, e.g., that language is the principal means to express thought. In other words, philosophy of language tries to specify the relation between representation and expression at its most fundamental level.
Linguistics, philosophy of language, and the archaeology of language
Linguistics is the study of language as a means of communication. Linguistics = semantics + grammar. Philosophy of language = knowledge + language.
Philosophy of language is the study of what all languages have in common as tokening more than their grammars or specific sentences. Archaeology of language = philology.
Intuitive logic is the knowledge of logic that we are born with. We apply logic without taking courses on logic. In fact, we know logic from birth. This doesn't mean that we are as adept at using logic at birth as we become in time. What it means is that we have at birth all the conceivable and possible axioms and principles of logic, but they become available to us only by degrees determined genetically in general and specifically within the general pattern or mode of genetic development. The most potent argument for intuitive logic is the existence of formal logic in itself and as part of history. We derive formal logic from intuitive logic. We could not use formal logic without intuitive logic.
Formal logic is the logic of textbooks. It has a history. It can be presented in different ways. Formal logic is what intuitive logic derives about itself from itself. It is in sum a derivation from intuitive logic. It can be assumed then that intuitive logic is more powerful and more "extensive" than formal logical. Given that formal logic has a history and can be presented in different manners, it is not possible to say whether it exhausts or can ever exhaust intuitive logic. However, it can be argued that formal logic is all that we actually know of logic. This means that to prove that there is such a thing as intuitive logic it is necessary to argue for "logical" differences between the two
~The problem is that if we can actually have that then we are transforming intuitive logic into formal logic. Ultimately, the only proof we have that intuitive logic is more "extensive" and more powerful than formal logic is that formal logic has a history. If formal logic was all there was to intuitive logic, then it could be argued that intuitive logic would have been totally formalized by now.
It is possible to argue for the existence of intuitive logic from a version of consciousness. Consciousness is the awareness of awareness. It is basically the source of paradox. Aside from this it is merely epiphenomenal, for it implies no epistemic function different from those that result in awareness itself. However, it can be argued that, since awareness is the tip of cognition, the awareness of awareness is the awareness of our cognitive abilities. It is from the awareness of cognitive processes that Putnam derives his claim that reason goes beyond anything that it can formalize. Loosely this is something that characterizes mind. More precisely, this ability is expressed in Gödel's theorems about numbers. In these mathematical propositions Gödel has arguments to the effect that no formal system can be both complete and consistent, for if it is consistent it is incomplete and if it is complete it must be inconsistent. Since logic is a formal system and all formal system assume their consistency and completeness, then the disproval of a formal system has to be some reasoning ability superior to all formal systems, and that can only be intuitive logic. Gödel only used formal logic, you say? Then his own proof is invalid. You can argue about this in circles, but if Gödel did demonstrate something, he demonstrated that thought is more complex than any formal system.
If you separate mind and cognition, you get "disembodied" logic which is the myth that mind can encompass itself entirely. Intuitive logic can deal effortlessly with paradoxes. In the process I ask: does Quine
really believe that disembodied formal logic corresponds to anything at
all? It certainly doesn't to the way we think. Is it possible to claim that we think in terms of formal logic? It is hard to sustain the idea that when we think we are using the rules of formal logic. To start with, which are the rules of formal logic? We have seen that logic is historical and that it can be presented in different ways. Everyone reasons but few would claim that when they reason they have formal-logical formulas in their heads. The claim that we think in formal logic is nearly absurd. However, Hume's causality argument is based on strict formal logic and many assume that it is valid. And Quine does not even contemplate the possible existence of a logic other than formal logic. Quine in fact assumes that we think in terms of the empty formulas of formal logic.
Mind contains intuitive logic from birth. Intuitive logic applied to itself yields formal logic. Intuitive logic and formal logic are equivalent. Formal logic is the source of all formal systems. The contents of formal logic are empty. However, intuitive logic is never empty. The logical forms that conform formal logic are always operative in mind either interactively or turned towards reality. The empty formulas of logical form can be the source of error. Wittgenstein realized this, but he was never actually concerned as Frege and Russell were by the paradoxes of awareness. This probably was because he never gave thought much thought. Thought was either imagic or verbal. Since images are by definition faithful and since language is objective, there could not be an awareness paradox for him.
Wittgenstein's concept of grammar can be read as the equivalent of our concept of intuitive logic. Wittgenstein distinguishes between formal logic and grammar, and he uses grammar and not intuitive logic because of his anti-mentalistic prejudices. Transposing logic to natural language, we can make the following specifications: nouns denote or refer; verbs relate; adjectives and adverbs qualify. Hence, nouns are represented as variables, verbs as functions or connectives, and adjectives and adverbs as predicates.
La lógica está presente cuando reconocemos una señal que puede disparar una reacción afectiva. La reacción puede ser racional: buscar protección si vemos a alguien con una pistola haciendo disparos. La reacción puede ser irracional: si no nos atrevemos a salir a la calle al oir un estallido por temor a vernos enfrentados a alguien con una pistola haciendo disparos. Por irracional que sea una deducción en la práctica, la deducción en sí obedece a las formas deductivas de la lógica intuitiva.
Since a logician must produce apodictic inferences, shehe needs to be precise in the rules that shehe applies and in that sense shehe must be stickler about the rules of herhis trade, i.e., he must know them perfectly, he must invoke them constantly, and so on, yet in herhis work formal and intuitive logic coincide totally. The logician cannot, e.g., bother with the problems of the identity relation in reality, i.e., he must accept it tacitly, but his reasoning will generally flow smoothly along the course that intuitive logic indicates. In practice the distinction between formal and intuitive logic tends to collapse, and this is the origin of Quine's fallacy, for even though in the practice of the logician intuitive and formal logic are nearly indistinguishable, in his dealings with the rest of reality, not excluding philosophical problems different from those proper to logic, the distinction is not only valid but inevitable. Quine's fallacy consists in not making the distinction, e.g., in connection to language-use.
Intuitive logic is used in the functioning of formal logic. Formal logic proves its propositions. Intuitive logic both proves and validates. To the extent that validation can involve probabilities, formal logic does not validate. Even though formal logic derives from intuitive logic, it is not possible to apply formal logic to history without obtaining absurdities. This can be made more explicit from the opposition or at least the radical disjunction between Newtonian physics and quantum mechanics.
If we applied formal logic in this situation, we would have to disqualify
one or the other, but in fact both systems appear to work! The intuitive
logic/formal logic interaction is as subject to history as any other
aspect or field of reality!
Let us just assume formal logic, also called predicate calculus. Formal logic applied to language, as in Frege's
Beggrifchifst, is predicate logic. Logic and calculus are germane, so predicate calculus and predicate logic are not dissimilar, and both are ultimately formal logic. Propositional calculus is associated with truth tables, a reduction of formal logic. Propositional calculus embraces or means the same thing as propositional logic and predicate calculus. Therefore, since predicate calculus is formal logic, propositional logic is about the same thing as formal logic. There is an area where we seem to get away from the hold of formal logic. If we apply formal logic to mathematics, we get number theory, but this is in essence mathematical logic. We are still back in formal logic. Predicate calculus, predicate logic, propositional calculus, truth tables, propositional logic, number theory, and mathematical logic all mean the same thing. They are variants of formal logic.
Is formal logic knowledge? Bertrand Russell seemed to believe it was a science. I think there are fundamental differences between logic and science. However, there are fundamental differences between physics and history and both are knowledge. Therefore, we can believe that logic is knowledge without having to subscribe to Russell's belief. At the opposite extreme of these beliefs is Wittgenstein's claim that logic is tautological. How do we argue for logic as knowledge? For one thing, formal logic has a history. It has evolved like any science or like the knowledge of history. And second and crucially, formal logic is a derivation from intuitive logic. Intuitive logic entails basic-cog's. Since knowledge is knowing how to use basic-cog's, then formal logic, which is derived from our knowlegde of intuitive logic, must itself be knowledge.
IS REALITY LOGICAL?
Does reality engender intuitive logic? Reality is the perception of things. If different things occupied exactly the same area of space, they would necessarily be identical and indistinguishable. Since no two things can ever occupy the same space, then we must assume that reality necessarily obeys or submits to the principle of the indiscernibility of identicals. Alternatively, the indiscernibility of identicals reveals the existence of things. Since no two things can be identical, then it follows that all things are different. If two propositions were identical, they would be merely the repetition of the same proposition. If there are no identical propositions, then all propositions are specific.
Does this mean there are no basic-cog's?
Basic-cog's are like laws of nature. They apply in the same circumstances for all individuals. A theory of cognition must try to formulate the ideal or type of all basic-cog's. But this does not mean that the yields of basic-cog's can be identical between two individuals. No rocket launch is identical to another. There is no flight path that does not have its specificities. Basic-cog's are the same for all of humanity in the sense in which the laws of physics should be the same for all planets and all galaxies.
The identity relation is not observed in experience. The relation of equivalence (double equality sign) between two variables means that either x is a property of y or y is a property of x, e.g., philosophy is equivalent to x or x is equivalent to philosophy. Propositions which are alike in all possible respects are identical. Propositions which are conceptually alike in all significant respects but whose tokens are never alike in all possible ways are equivalent. Identity is the likeness relation in respect to numbers and logical terms (abstract concepts). Equivalence is the likeness relation in respect to all entities except numbers and logical terms. Equivalence is an intuitive-logic relation. Identity is a formal-logic relation, possibly the fundamental axiom in formal logic. It is the formal-logic derivation of the equivalence relation of intuitive logic. But formal logic cannot work without intuitive logic, so it cannot be said that identity is not an intuitive-logic relation also.
Is equivalence validating? Or is equivalence always implicative? A building implies walls, but it is not solely walls. Implication is certainly equivalence. Equivalence relations can be probabilistic and probabilities are not necessarily valid. There are similarities between all revolutions and the French Revolution, but it would be foolhardy to make deductions about any specific revolution from the knowledge of the French Revolution.
We have made the distinction between identity and equivalence in respect to abstracts such as numbers and logical terms. Is equivalence valid in respect of abstract concepts and representations? Self-evidently, identity is not applicable to the concept of justice. Is equivalence? Justice is a representation. All definitions of justice are specific including all definitions that the same person may elaborate or entertain at different times. But all definitions of justice also belong to a type. All specific definitions of justice are equivalent though they differ in significant respects. The distinction between identity and equivalence seems to be valid not only for abstract concepts but also for historical concepts such as justice and for representations. But abstract concepts are also historical and they cannot as such be the basis for a distinction between identity and equivalence. History contains both types and tokens. Insofar as abstracts include types, intuitive logic is as much about abstracts as formal logic.
Equivalence being a non-exact fit it could lead to contradiction by degrees. If grey is a shade of white and black is a shade of grey, then white and back are equivalent. But such a development entails sorites, hence a basic syllogistic relation, and the syllogism cannot be contradictory. In physics, white is the absence of color, but in painting white pigments exist. A white pigment makes a white mark and a black pigment makes a black mark. Mixing white pigment with black pigment produces grey. But once the two pigments are mixed, they cannot be unmixed. Hence, white and black are different.
Reality contains the denial of equivalence. It is necessary for things to exist independently of other things in order for categories and relations to exist. The denial of equivalence is the possibility of all categories including relations which are not equivalence. Alternatively, the being of things is the basis of equivalence.
Exactly the same reasoning can apply to inclusion and dependency. It is the absence of equivalence that makes possible inclusion, dependency, and all other non-equivalence relations. Intuitive logic transforms equivalence into identity and identity furnishes the grounds for the principle that no proposition can be both true and false. It is from the transformation of equivalence into identity that formal logic is born from intuitive logic.
If a proposition cannot be both true and false, although it needn't be one or the other, then we have grounds from the principle of identity for the principle of excluded middle. In physical terms, an object cannot invade the space of another object. We can get genetic mixes of all sorts, but we cannot infringe the physical occupation of space by objects.
Equivalence within things makes induction possible. The function of induction is generalization. It is from reality therefore that perception creates types. As it is from types that we recognize tokens, reality also involves the logical principle of specification.
Not only do different things occupy different spaces, but they also occur in different lapses of time. Now, this is not quite the same as the indiscernibility of identicals because whereas it is impossible for two objects to occupy exactly the same place, there is the possibility of simultaneity. However, if all objects occupy different spaces, it is highly unlikely that they would also occur in exactly simultaneous times. But "highly unlikely" does not really cut it in logic. We need a stronger argument than that. The specificity of things and propositions implies their non-simultaneity. Specific things cannot be simultaneous. Can we derive non-simultaneity from the principle of identity? We can certainly derive successiveness from the temporality of things, but this is cloth of another weave. Now, supposing that we did manage to derive all these propositions from the principle of identity, would we have proved that reality is logical? In what sense would we be saying that reality is logical? One possibility is that these derivations and arguments are made from intuitive logic. Intuitive logic is innate. Consequently, there is codependence between intuitive logic and reality. It is reality, i.e., the impossibility of things being identical, that ultimately instilled intuitive logic in the species. With the influx of experience and starting from the principle of identity, it was possible for life gradually to derive the full panoply of intuitive-logic axioms, principles, and rules of derivation.
Can one derive the syllogism from the identity principle of intuitive logic? The same space necessarily implies a space of time. A different space entails a different space of time. A different space of time involves the sequence or successiveness of time. That objects occupy different spaces means that time is successive. It is the successiveness of time that not only makes the syllogism possible but is actually the basis of the syllogism itself. We have to reason at some time like this: instant b is the continuation of instant a and instant c must be the continuation of instant b. For c to be, a and b must be related in some logical manner.
To illustrate the determination of successiveness take lamps a and b. Lamp a occupies specific space a and lamp b occupies specific space b. Could lamp a occupy the same space as lamp b? Only if the time that lamp a occupies is the same as the time that lamp b occupies. But this is not possible if lamp a and lamp b are different since they would the result of two different times in the process of manufacture. If the exactly same spatio/temporal process that manufactured a manufactured b, then a and b would be identical and indistinguishable, in sum there would be only a or only b.
Intuitive logic contains the principles of identity and of equivalence. It also contains the relation of equivalence from which it derives or refines the formal-logic relation of identity. Reason or logic applied to reality distinguishes between the possible applications of the relations of identity and of equivalence. It knows that the relation of identity is incompatible with physical reality but it also knows that it is only through the identity relation that science can make sense of physical reality.
Equivalence would be the basic relation in intuitive logic and identity then would be a derivation from the application of intuitive logic to itself. Identity is a formal-logic refinement of the fundamental intuitive-logic relation of equivalence.
syllogism is necessarily codependent with equivalence.
It would also seem to be codependent with identity, yet identity and
equivalence are different and there cannot be two types of syllogisms! The syllogism self-evidently is compatible with two different basic relations: with identity as the basic relation in formal logic and with equivalence as the basic relation in intuitive logic. It is through the relation of equivalence that the syllogism first arises. But it is through the identity relation that we formalize the syllogism. The principles of equivalence and of identity are valid for time as well as for space. They are the source of successiveness which, with the relation of principle of identity, are the necessary condition for formalization of the syllogism. The syllogism is not necessarily dependent on the identity relation. Its formalization does not affect the validity of necessary inferences and the possible validity of probabilistic inferences. Attained from equivalence and temporality, the syllogism gives grounds for the logical concepts of symmetry and transitivity.
We can invert the argument and derive equivalence from the assumption of the syllogism. If it is impossible for things and propositions to be identical, then in order to mediate relations between unrelated terms, as in the syllogism, we must have relations, such as equivalence, ~which derive from the identity principle and the principle of excluded middle. The same argument applies to modus ponens. However, as the separateness of things had to occur before logic came into being, the principle of equivalence must have anteceded the syllogism.
The syllogism validates but whereas in formal logic it validates apodictically, in intuitive logic it yields necessary inferences. We must keep in mind that not necessarily valid does not necessarily mean not valid and that not necessarily valid could mean valid. It would seem that intuitive logic and equivalence are the same as formal logic except that its inferences can be valid but are not necessarily valid. Since not necessarily valid can allow thought to proceed to valid--which is not possible in formal logic--this implies that intuitive logic is formal logic plus, e.g., Schliemann discovered Troy on a mere hunch, and so on. It is this "plus" that we are trying to identify.
Besides the distinction between equivalence and identity to differentiate between intuitive and formal logic, we can also use the distinction between validation and proof. Intuitive logic used in formal logic produces proof. Proof is tantamount to apodictic inference. The inputs for proof are either axioms or apodictic inferences. Validation is a wider concept which does not have to involve apodictic inference. Validation works with empirical inputs to intuitive logic.
Another possible distinction is between implication and
entailment. Entailment signifies necessity, i.e., if a, necessarily b. Implication is less constraining. That a implies b does not mean that a entails b. We have can have all sorts of implications that in the end turn out to be false. That someone offers me money for my porpety implies that he is interested in buying it, but it does not follow that he will buy it. Or that someone expressed an interest in my property implies that he might make me an offer, but it doesn't follow from his interest that he will make me an offer.
Through induction we have generalization and types. Through generalization we have induction and types. Generalization and induction are based on the equivalences within reality. The equivalences of certain tokens make the types. The relation type/token permits interchange, as in using a stump as a seat. Reality is imbued by logical principles. There is a constant interaction between logic and reality. Can we say that it is logic that begat reality or reality that begat logic? The world had in it the constraints that man absorbed as intuitive logic. The world had logic in it. I do not know how reality became imbued by logic. I can surmise that nature constrained life towards logic.
INTUITIVE LOGIC TO LANGUAGE
Is language the repository of logic? Wittgenstein seemed to think so. Often semantic relations are meant to signify logical relations and semantics is supposed to include logic. But the rules of language do not coincide with the axioms and principles of formal logic. If language were logical then it would not be quite as flexible nor quite as equivocal as it is. However, language probably started with grunting and squawking and all sorts of other noises and it was finally applied logic, i.e., reason, that organized the noises of language to make them more expressive and communicative. This organization is called syntax. Syntax is the part of grammar dealing with the manner words are strung together. Grammar is of course about all the aspects of the use of language.
"Logic. In its broadest sense logic is
the study of the structures and principles of reasoning or of sound
argument. Hence it is also the study of those relations in virtue of which
one thing may be said to follow from or be a consequence of
another...Within the study of reasoning which aims to establish the truth
of propositions, the major distinciton is between deductive and inductive
logic." (Antony Flew, A Dictionary of Philosophy (NY, 1984)
"The aim [of logic] is to make explicit
the rules which are implicitly recognized as rules according to which
arguments ought to be constructed, at the same time pointing out any
anomalies that may appear in the process...[T]he fact that a given inference
is regarded as legitimate (reasonable) is not sufficient for it to be
logically valid: the inference must also be such that conformity to it is a
requirement of reason...If knowledge is knowledge of an independent reality,
and if the truth of a proposition consists in its presenting a picture that
is an accurate representation of this reality, then laws of logic, as
regulative principles governing the pursuit of knowledge and the
construction of scientific theories, will appear as laws founded in the
nature of reality we seek to know...A theory of logic thus involves (a) a
discussion of the principles for formalizing ordinary language in order to
reveal its logical structure, and (b) the development of a formal system of
rules for the construction of valid forms of argument." (Flew)
"Thus Leibniz claimed that by the
provision of a lingua characteristica (a logical notation together
with rules for its use), `the mind will be freed from having to think
directly of things themselves, and yet everything will turn out
correctly'...The pursuit of knowledge through rational debate is an ideal
presented in the dialogues of Plato, but it was Aristotle who first engaged
in a systematic and theoretical study of the principles according to which
such debates should be conducted...To this end one must consider (a) how any
two terms can be related and the nature of the proposition in which these
relations are expressed and (b) how the information conveyed in such
propositions can be combined to give further relations between the terms
mentioned. Aristotle's answer to (a) is that, given any two terms A and B,
there are four possible relations that could hold between them. These find
expression in four kinds of categorical proposition (see syllogism). His
answer to (b) is contained in the theory of the syllogism, presented in the
Prior Analytics...It was only with the work of Frege...whose approach
was adopted by Russell and Whitehead in the writing of Principia
Mathematica, that the focus of attention was shifted firmly away from
terms to propositions and their relations. The advance made in Frege's
system (set out in Begriffschrift ) is the introduction
of quantifiers and of the treatment of concepts by analogy with mathematical
functions. This enabled him to unify the logic of propositions
(propositional calculus) with the study of those logical relationships which
had previously been treated in the theory of the syllogism...Even prior to
the Fregean innovations, the study of logic had become increasingly
mathematical, since it is possible to treat a formal logical system as just
another system of algebra giving rise to algebraic structure that can be
studied using mathematical techniques." (Flew)
Logical atomism is the proposition that knowledge can be brought down to basic, non-reducible statements about reality, such as perception.
Logical axioms and principles
Logical axioms and principles are elementary, non-reductive propositions of logic. The rules of deduction or inference are derivations from axioms and principles. The categorization of rules of deduction as axioms leads to infinite regress. Axioms are the ground-floor of logic. Without axioms different from rules of inference, it would necessary to go into an endless search for the grounds of the rules of inference.
Logical constants are symbols which are used to express the logical structure of linguistic propositions. They include logical operators such as quantifiers and the existential predicate. The formal system that includes logical constants is called predicate logic or predicate calculus. It was Frege who devised predicate calculus, but the symbols he used were not generally adopted. The purpose of a predicate calculus is to discover the truth-value of sentences through the analysis of their logical structure. However, it soon became obvious that predicate logic and logical constants, which were supposed to permit valid inferences without reference to specific contents, could yield absurd propositions and inferences.
"Logical constants...The logical
symbols...introduced to represent the logical structure of sentences are
what are known as the logical constants. Those most commonly employed are
`-', `&', `v', `-->', or `tumled U' [inference], `inverted A', `turned
around E'...etc." (Flew)
Logical empiricism is the doctrine that the only sources of knowledge are sense-data and logical inferences.
It usually refers to the philosophy of Ayer, a disciple of the Vienna Circle.
Logical forms are the purely abstract and content-less expression of inferential processes. Terms in logical forms are represented as variables. Variables are abstract symbols for contents. Logical forms can yield necessary, apodictic, and probable inferences. In other words, the input to logical forms need not be valid propositions. Logical forms merely allow certain steps either in thought or on paper. Hence, reality instilled logic which imbues history which engendered Nazism.
Logical positivism is the cover-all name for the set of doctrines held by the Vienna Circle, including verificationism, logical atomism, and so on.
Logical relations license inferences. If I am six-foot tall and my brother is five foot nine, it is licit to infer that I am taller than my brother. But this inference does not licit inference about the relationship between us. Practically any relation can licit inference as long as the relation is logical. The relation between relative sizes and consanguinity is not a logical relation.
In logics and in mathematics the most common relation is equality, because equality is the basis of the syllogism. However, when the syllogism is applied to reality, the relation it works with is never equality--because of the indiscernibility of identicals--but equivalence. Both equality and equivalence license substitution, but whereas the equality relation yields apodictic inferences, the equivalence relation yields necessary inferences. Depending on the strength of the equivalence, inferences can be necessary or probable.
Premises that yield necessary inferences through equivalences are said to have an entailment relation with their inferences. Premise or proposition x entails y. Entailment is also a logical relation. Other logical relations between x and y are implication and involvement. Implication is as strong as entailment. Involvement or inclusion is a more general relation that does not involve necessary inferences. That x involves or include y does not necessarily imply modus ponens. This issue, e.g., involves or includes another issue, but the first may not need the involvement or inclusion of the other issue for its resolution. The relation of involvement or inclusion is like the relation of containment. Because my body contains a liver, it doesn't follow that it also contains an appendix. However, entailmente and implication do imply or entail modus ponens. When two terms imply or entail each other there is a relation of reciprocity. Reciprocity, mutual or reciprocal dependence, mutual or reciprocal inclusion, all mean the same thing. This relation is as strong as entailmente or implication because it posits the necessity for each other of two terms in an inferential process, i.e., I cannot infer something about x that cannot be inferred about y. Involvement, inclusion, and containment merely indicate that a proposition among many possible propositions is embedded in another proposition. Therefore, we could have an inference about the inclusive proposition that is not necessary for the embedded propositions.
Exclusion is the opposite of inclusion, involvement, and containment. It is a strong logical relation in that what applies to an excluded proposition cannot apply to the proposition from which it is excluded. This contrasts with inclusion where what applies to the inclusive proposition need not but could apply to the included proposition. Reciprocal exclusion is a very strong logical relation almost tantamount to the principle of identity, i.e., ~(q v ~q). The principle of identity entails reciprocal exclusion, e.g., a tree x that is not planted in the spot where tree y is planted is not tree y, and vice versa.
Logical rules are the steps for making derivations from axioms and from principles.
Logical tachygraphy is a personal system for the short-hand expression of thought. It is not necessarily a system for making apodicitic or necessary deductions. It comprises symbols for propositions and for relations. It also includes a symbol for negation, since every proposition and every relation imply their negations. Propositions are about things, properties, and relations. The relations between symbols yield propositions. Logical tachygraphy contributes to the continuity of thought. It is a formal derivation from intuitive logic.
We are not talking science or replicability. We are talking here of non-repetitive human experience, not necessarily perception of course. Since formal logic is not necessarily applicable in these situations but logic necessarily is, then we are saying that logical tachygraphy is intuitive logic.
Why logical tachygraphy? In reasoning, language is too cumbersome, too slow. Also it cannot be converted easily or accurately into formal logical expressions and it does not justify apodictic inferences. In fact, conversions from natural language to formal language are distorting, but the expression of arguments in natural languages is justified by intuitive logic. How can we differentiate between formal and intuitive logic using logical tachygraphy as a starting point?
The self has intuitive logic. The self-exploration of intuitive logic yields formal logic. The interaction between intuitive logic and formal logic leads to apodictic inferences. The interaction between intuitive and formal logic applied to experiences can result in necessary or in probabilistic inferences. There is an input difference between these types of inferences. The input for necessary inferences is replicable and "natural"--although admittedly some science is non-replicable--and the input into probabilities is non-replicable. What does probability tell us about the interaction between intuitive and formal logic? The basic conclusion would seem to be that they are equivalent but not identical. One implication of this is the distorting character of formal logic as applied to inputs which are non-replicable and "human". From this we could infer that it is intuitive logic that necessarily applies to such inputs.
Logical and mathematical propositions have in common that they are apodictic inferences. However, they are not identical because whereas logic is innate math is learned. There are no logico-mathematical propositions.