In traditional psychology, imagination is the ability of mind to associate or combine images. Knowledge, like reality, being, and the totality of awareness, are imaginary. concepts. They are not in the world, not even in the sense in which my affects are not in the world. They do not exist period, except insofar as I can imagine them, although they exist in the world as language. The fact that there are terms for these imaginary concepts means, however, that it is not only myself that can imagine them.
Impredicativity refers to the specific claim that there are properties or predicates that do not define classes. Russell's paradox showed that there is such a property, i.e., non-self-membership. In order to plug the hole he banned from set theory talk of self-reference, i.e., classes of classes.
Inclusion defines set and set implies similarity but inclusion can embrace entirely dissimilar things.
Inclusion therefore is hardly a concept that would yield apodictic and only apodictic inferences.
See also Co-dependence.
Indiscernibility of identicals
Leibniz used this expression to indicate
that in "reality" the mathematical relation of identity does not hold. If
two objects are identical, they cannot be distinguished from one and
another. Alternatively, it is an expression of the identity principle: a
cannot be b or c or d and so on ad infinitum. The indiscernibility of
identicals entails that formal logic, where the relation of identify is
currently used, is not adequate to grasp "reality". Logic applied to
"reality" can only work with the relation of equivalence.
No factual proposition can be transferred to the inferential, apodictic domain, i.e., logic per se cannot provide explanations of events in reality, although this is not to say that intuitive logic is not always involved in such explanations. We could not function in any domain without logic. But the necessary recourse to experience means that induction or inductive reasoning is involved. This is not a different cognitive process, just as predictability is not a specific cognitive process: it is not different from factual or probabilistic propositions and, as in the case of all acts of cognition, it does not involve only one cognitive process.
Induction is frequently taken to refer to a specifically scientific method, but it is wider than that. In experience we are constantly elaborating hypotheses, e.g., this happened because of that; or, if that happened, it is because something else must have happened before; and so on and on. This is what a scientist does, if in a vastly more complex manner. Both in science and in our everyday lives we elaborate hypothetical explanations from experience. From a hypothesis we go back to experience, e.g., we ask, or we wait and see, and so on, and we discover that either our hypothesis was correct or that it was incorrect. In no conceivable situation could we elaborate a hypothesis first and then go to experience to have it factually confirmed. Presumably in science the search for explanations involves a more profound or a more comprehensive quest for related factual propositions and the hypotheses rely on mathematical means to a greater extent than in everydayness, but the pattern "experience to hypothesis to experience" is invariable. Induction is universal.
Since experience is always "partial", i.e., no one can have total knowledge of any phenomenon, on the trip from hypothesis back to experience, science can find itself in error. How does science escape the danger of error from the partialness of experience? This is probably somewhat like the problem that Quine calls the underdetermination of theory. The only way to escape the circularity implicit in the partialness of experience, as every disciplined scientist knows, is merely to go back to experience and elaborate another hypothesis until in the course of justifying propositions from experience, the scientific effort comes up with a hypothesis such that, when applied once again to experience, it permits the elaboration of predictive propositions, e.g., a body with a certain mass at a certain speed will either fall towards another body with a certain mass or will drift away from it.
Induction is a form of inference.
We know three types of inference: apodictic, necessary, and probabilistic. Since induction is the method whereby science develops hypotheses and hypotheses are probabilities, induction is of the type of probabilistic inferences. According to G.Harman and Peter Lipton induction is
"inference to the best explanation." (See Lipton, Inference to the best explanation , The Higher , September 13 1991.) Assuming then other explanations, induction is the inferential process that leads to the most probable explanation. "Causal explanations, [Lipton] argues, typically answer contrastive questions: a different cause may be relevant to explaining why someone went to the cinema rather than going to the theatre than is relevant to explaining why he went to the cinema rather than staying at home." Admittedly, contrastive thought is pervasive, but is it inevitable? I would certainly not feel comfortable with one philosophical view on a certain problem. On the other hand, I do not need to contrast my belief in subconscious cognitive processes with other views in order to consider that I have made a necessary inference.
Does nature have only specific explanations or does it admit of different laws for the same event? The macro/micro distinction would seem to be in favour of the latter. But in fact the micro does not explain the macro and macro has no answers for micro-events. How they relate is a physics issue of its own, close to the speculative
(the universal theory). The point is that they are not different theories for the same events. Consequently, nature admits of only one set of laws for each series of events and induction cannot be "inference to the best explanation", a definition that only applies to hypotheses. But it can never apply to actual scientific or descriptive laws. Scientific induction is inference to the only explanation, with the necessary proviso that valid explanations go through a probabilistic stage before they give rise to necessary inferences.
Aunque no se trata necesariamente de una norma deductiva, puesto que la lógica es inconcebible sin la experiencia, inducción es una forma de deducción, y a la inversa. De hecho, en el mundo, la lógica siempre es inductiva, siempre es razón. Por lo tanto, si el mundo es racional, si en el universo todo tiene sus razones, también se puede decir del mundo que siempre es lógico.
Inference is the fundamental logical operation. Inference is derivation from premises. An inference yields propositions. It does not transform propositions. Abstract inference is the logical form of inference. All logical forms are inferential. Logical forms are abstract expressions of inferences.
Inferences are of three types:
(1) apodictic, when the derivations or conclusions or deductions are inescapable, i.e., they cannot be otherwise than as they are, regardless of the material circumstances;
(2) necessary, when inferences yields necessary truths such as perception or scientific calculations, or when they are based on empirical premises and allow only one conclusion;
(3) probabilistic, when inferences are neither apodictic nor necessary, which means that they are not necessarily true, i.e., they can be true or false.
The logical form of inference applies to all types of inferences. The difference is in the premises. However, the logical form of inference is virtually the same thing as apodictic inference. It is because such inferences are, so to speak, preordained, that Wittgenstein held that logic is tautological. But to restrict logic to its logical forms is to deny it to the rest of reality, including experience, and there is reason to believe that everything is necessarily logical, e.g., that perception is logical and that even irrational behaviour is also logical.
Induction is as inferential and logical as any cognitive operation. However, induction does not necessarily yield valid propositions. Induction initially yields hypotheticals. If these hypotheticals then yield necessary inferences, we can say that induction is necessary inference. Therefore, induction covers both necessary and probabilistic inferences. Probabilistic inferences can also be called hypothetical.
Inferences are also about one, some, and all. Terms function under the umbrella of the quantifier
"all". "All" is implicit in terms. But "all" is hardly ever a component of inference. It is possible to go from all to one in deduction and retain truth on the assumption of true premises. It is possible to go from any of these quantifiers to another provided certain conditions are met. It is even possible to go from one to all, if the syllogism is attached to a qualifier to the effect that one is a valid representative of all. But the syllogism or inference hardly ever comes singly. Reasoning involves concatenations of syllogisms (sorites), from the first of all which is that if inference worked once before it should be able to work repeatedly, to the final event in a chain involving main and subsidiary syllogism, ex ante and post hoc syllogisms, straight sequences of syllogisms, and so on.
Christopher Hookway on Peter Lipton,
Inference To The Best Explanation (Routlegde) The Higher,
September 13 1991
"He follows a number of philosophers,
notably Gilbert Harman, in arguing that inductive reasoning is `inference to
the best explanation': we should accept hypothesis which provide the best
explanations of the experiences that serve as `evidence' for them...Causal
explanations, he argues, typically answer contrastive questions: a different
cause may be relevant to explaining why someone went to the cinema rather
than going to the theater than is relevant to explaining why he went to the
cinema rather than staying at work." Nonsense: explaining, e.g. tides, does
not always involve contrastive considerations.
"Inference, rule of. A rule for the
construction of arguments which says what may be inferred from one or more
statements whose logical structure is specified...The attempt to embody
all rules of inference in axioms leads to an infinite regress, as was
observed by Lewis Carroll in his `What the Tortoise said to Achilles'."
Infinity is a derivation from numbers. It does not exist and cannot be shown. Infinity could be a derivation of eternity, which is a religious concept. The axiom of infinity means that there is a set with an infinite number of members. It also entails that there are more sets than numbers. If every object is a class and there is a class of non-objects, then there are more classes than objects.
"In the 19th century, Cantor and
Dedekind dispelled much confusion surrounding the infinite by noting that
talk of an infinite property, substance, etc., can be reduced to talk of
an infinite number, numbers themselves being regarded as certain classes.
Thus Cantor's theory of the actual infinite was a theory of infinite
Mind is intensional, which can mean different things but which basically refers to the variability of meaning from the subjectivity of
the use of language. Would mind be less intensional or not intensional at all without affects? It is to be doubted that the intensionality of mind is only a result of its affectivity--there is, e.g., the intellective strength of each person, the extent of knowledge, associative powers, and so on--but undoubtedly affects do play a part, do have some influence on the way we recall, reason, understand, communicate, and so on.
The analytical specifiction of the intensionality of mind is its propensity to error. This is demonstrated in the work of Frege, Russell, Quine and others, through logico-linguistic acts which yield erroneous inferences. These errors underlie the analytical and proto-analytical distrust of psychologism. They also serve to set the agenda of analyticity in the sense of placing knowledge and the recognition and correction of error at the top of its concerns. The intensionality of mind is therefore the maninstay of the analytical disqualification of mentalism. Intensionality defines mind. Intensionality produces error. Hence, mind is error-prone and unreliable.
"Intensional" means connotative and connotative is ambiguous and subjective. Intensionality is related to the opacity of mind. Flew defines opacity and transparency in these terms: "Terms used in theories of reference...and modal logic, which are used to explain cases where the principle of the substitutivity of identicals apparently breaks down."
It may be best to start by defining intensionality ostensively or illustratively. The evening star is the morning star. Sir Walter Scott is the author of Waverly. Tully is Cicero. But poor old John might not know any of these equivalences and with this in mind it is possible to express a series of errors and paradoxes, such as that Tully did not denounce Catillina or that George the III knew and did not know Sir Walter Scott. These exercises are supposed to show either that (1) mind is opaque or (2) language is unreliable as a cognitive instrument. Another instance of intensionality is "Copernicus believed that the planetary orbits were round", which is both true and false. The transparent absurdity of these arguments makes them almost laughable. Searle took them so seriously that he went about refuting them. His argument is that intensional propositions are extensional to the extent that they refer to beliefs, i.e., other propositions. However, how can you make belief extensional in the sense of measurable and demonstrable? On the question of belief you go blind. It can be said though that whether someone does or does not believe in something any belief statement is necessarily true because if he is not lying it is true that he believes and if he is lying since belief is necessarily true it doesn't make any difference what he really believes.
Ultimately, intensionality refers to the paradox of awareness. Supposedly intensionality is the illusion of mind that accepts what it knows to be real knowledge. How can it be that what I know as well or as better than anything else can be not knowledge but error? Searle takes care of intensionality by explaining that so-called intensional propositions are those that refer to other propositions and as such are as susceptible to verification as extensional propositions. My own solution is that all mental propositions have bases and contents. The bases are necessarily true, i.e., no one can demonstrate that what I believe is false. The contents of propositions can be true or false. Russell's word games refer to propositional bases. They have no relevance at all to the knowledge of the world.
Extensional sentences or expressions involve truth-value.
Intensional sentences or expressions involve probability or matters of opinion. Belief and opinion are different.
You can believe a valid proposition, but all opinions are probabilities.
Flew posits an extensional proposition to the effect that "The author of Mysticism and Logic was a Cambridge don" and an intensional proposition to the effect that "Tycho Brahe believed that the Earth was the center of the Universe". But how about a proposition that expresses this thought: "The concept of justice is utilitarian" and one that says: "J.S.Mill believed that the concept of justice is utilitarian"? No amount of tinkering will confer a truth-value on the first proposition. Hence, it is not the form of the proposition that defines intensionality and extensionality, but its contents. Consequently, as Searle claimed, there is no reason not to suppose that the proposition about Tycho Brahe can be just as extensional as the proposition about whoever wrote Mysticism and Logic [was it Russell?].
Let us assume that mind is intensional because we cannot verify all our beliefs. Let us use again the proposition "The concept of justice is utilitarian". This is an interpretation. All propositions are ascribable. As an ascribable belief it can be expressed as "Someone believes that justice is utilitarian". This does not mean that all beliefs are necessarily interpretations. And it does not mean either that all propositions are necessarily beliefs. Thus it is possible to just say that "someone has the proposition that justice is utilitarian", in fact, myself and any one who reads the proposition. The having the proposition is in itself true. There is nothing intensional about my having such a proposition. And as to the contents of the proposition they are debatable, but not intensional if by intensional is meant a belief. You can of course have such a belief, but it would not be intensional. Whether as a belief or as just meaning no debateable or controversial proposition is intensional. Consequently, intensionality, except as connotation, does not exist.
Mind is not intensional. Propositions are not intensional or extensional. Propositions can be classified according to a typology. The extension/intension distinction is spurious.
Intention and action
The relation of intention to behaviour is like the relation of cause to effect, in which however the cause can be a background condition or just a possible cause. In sum, an intention need not become an act, but if it does, it is the cause of the act. Intention is mental. Behaviour is physical. But it is difficult to establish the limit between the intention and the act. Consequently, the physical "imbricates" on the mental. The mental partakes of the physicality of the act. The squiggles shade off into neurons and vice versa. To explain the intention I appeal to the squiggles but to translate the intention into action I must involve the neurons. But where do squiggles end and neurons begin and vice versa? Were neurons not active when I was appealing to squiggles and did squiggles not continue operating even as neurons produced physical action?
Now, let us suppose the intention is obstructed and there is a reaction which can be a thought or an act. My intention can become or not become an action. If the action is behaviour, why should the inaction not also be a form of behaviour? And if inaction can be behaviour, then why should thought be thought of as non-behaviour because it is not visible? In reaction even though no action has taken place, it is exactly as if it had. If the reaction is another intention, then in the process from intention to action, intentions can be indistinctly causes and effects, and if effects are actions, then the causes too are actions. The point is that the physicality of action does not disqualify intention as action because it is not physical or at least visible. We do not see intentions as we see actions, but we know that intentions are there as sure as we can see actions.
The thought/action dichotomy presupposes a separation between awareness and action. We are aware one moment of our intention and we act the next moment. But in fact there is never a separation between mental events, there is no discontinuity between the intention and the action. We have the intention and when we carry out the intention the mind knows what is going on. The mental processes are as present in intending as in acting. The action is qualitatively not different from the thought of the action. Since regret is about what might have been, when we regret we necessarily imagine thought as behaviou.
Similarly, when we inhibit a thought about an action, we are in fact acting upon a possible action.
The mental state of intending to act or not act results in another mental state. Acting and not acting are equivalent. The difference lies in that we went from one mental state to another. Not acting produced a mental state. Not acting is a happening and the mental state it produced is also a happening. Since a happening is an act, a mental state is an act.
The claim that thought is a form of action or behaviour has implications for:
--the specification of awareness
--the bridging of mind/matter dualism
--the attitude of analytical philosophy to mind
--the cause/effect relation in the mind.
Everything in the mind is a caused cause. However, mental events are not necessarily causes of overt behaviour. This leaves a lot of dark matter to account for. It makes it difficult to argue for mental laws, even as hypothesis. But if we assume that every mental event is a cause, whether it is translated into action or not, then we at least have theoretical grounds for mental laws.
Language of thought
We cannot know what another mind contains except through what we are told. We know the contents of our own mind. By comparing what we are told, sometimes what we see, with what we know of our own mind, we can make reliable and probable propositions, e.g., he is experiencing pain. This is the essence of intersubjectivity. It does not involve any criteria of knowledge different from those we can infer from propositions not involving intersubjectivity. It does not involve anything different from perception, reason, and logic.
If we say that there is an equivalence between self and world, e.g., somewhat like the correspondence relation, we assume a realist position. If we say that S confers being on the world through perception, we run the risk of solipsism. But it is not necessary to choose between these extremes. We can presume that just as we perceive the world others too perceive the world. But we can actually do more than presume. We could not communicate if we did not have language and we know that the use of language implies many minds. It is from this awareness of other minds that we derive the concept of intersubjectivity. When we say that something emerges from the mind/world interaction, we actually mean a process that takes place entirely within the possibilities of the propositionallity of mind.
No thesis about mind is possible at all without introspection. Wundt, considered one of the founders if not the founder of experimental psychology, made no bones about using introspection in his research into mind. Presumably, control lay in the comparison of data. Frege's antipsychologistic attitude is probably the source of the contemporary rejection of introspection as a philosophical method. Initially Husserl shared Frege's antipsychologistic stance, but in the end he could not philosophize without appealing to introspection. His dilemmatic situation led him to steer clear of traditional psychological categories and to concentrate on the mind's cognitive abilities for which he built an abstruse set of categories.
Whether these were expressions of real mental processes or merely verbal fireworks is a question on which opinions diverge, but he certainly seemed to believe that his thought was not debilitated by the actual use of introspection, a term he did not use preferring interpreted words, such as epoké , which meant the same thing without supposedly the taint of psychologism.
Husserl's method, known as phenomenology, ultimately rests on the principle of those-in-the-know. This is also the basis of Wundtian experimental psychology. It is assumed and sometimes overtly affirmed that some individuals, usually affiliated to schools or other groups, have a more disciplined access to mental data than the run of humanity. Heidegger relied on invented words to express his privileged understanding of existence. Most phenomenological philosophers simply assume that their readers will recognize and admit their exceptionality.
The those-in-the-know stance was expressed at length by Nicholas Everitt in a review of the centenary issue of Mind: A review of philosophy ( The Higher , October 11 1991): "Is there anything in this collection for the intelligent man (or woman) in the street? The answer to that is a definite `no'. I doubt whether all of the papers would really be accessible even to someone who has just completed a first degree in philosophy. But that is probably in the nature of progress in philosophy, or any other discipline. Large vague questions can be raised which the layman finds intelligible and interesting, such as `How is it possible for what is in our minds to represent the world around us? Might our ideas simply fail to match what the real world is like? How is it that what goes on in our minds can cause our bodies to move, and to move, moreover, in ways that are appropriate to the content of our beliefs, intentions, etc?' But by the time these questions have been made precise enough to be answerable, and a detailed and intellectually satisfying answer has emerged, the limits of understanding of non-professionals has long been passed."
There is much to be said for this view, but there is always the risk of philosophers donning the emperor's new clothes, especially since the claim that philosophy is a science is a demonstrable myth
The Origins of Analytical Philosophy
"In the case of perception, too, Husserl thought that we can, by an act of reflection, make the noema the object of our attention: but he held in this case that this is an extraordinarily difficult thing to do, which only the philosopher can achieve, and that it is the fundamental task of philosophy to fasten its attention on noemata and attain a characterization of them."
Willy-nilly, in the end all philosophy of mind must rely on introspection. The vaunted reliability of folk-psychology underlies this claim. Descartes saw this and said so. The empiricists knew it also but they did not try as Descartes had to provide a method to introspect reliably. They merely assumed that they were better at it than the rest of mankind. This is also the way contemporary British philosophy of mind sees it, but it makes the superiority claim explicit. Kant proposed that introspection was a form of transcendental deduction. Husserl called it phenomenology, Dennett heterophenomenology. We incline to the empiricist point of view, but we also argue that, because of the temporality of all existents, "logically" introspection is as reliable as perception. Nevertheless, it is legitimate to ask: how can we discipline introspection? Basically, we try to keep loans to a minimum. We know that awareness is but an instant.
"Squiggles" are a non-introspective deduction from introspection.
Since perception is always past perception, e.g., did I just see some one enter and leave this room?, although it can be claimed that my recent perception is very reliable, in a fundamental epistemic sense it is as reliable as factual propositions, e.g., Paris is the capital of France, for which we may have no other evidence than the perceptions of others. From this it follows that we can validate propositions other than our perceptions.
It can also be said that perception is probabilistic. But we can circumvent this characterization--and its threat to validity--from the existence of memory as a reliable source of knowledge. If we did not accept this argument, then we might as well forget about explaining cognition. Cognition necessarily implies memory. There is no knowledge without memory. Factuality entails the reliability of memory. If we assume that the direct,
"intuitive" knowledge of thought, affects, and so on, is not reliable or is not really knowledge, i.e., is not valid in the sense in which perception is valid, then evidently we will not try to define meaning from what it is for something, anything, to mean something to us
"intuitively" and directly.
Meaning is that we perceive rather than just register different, disparate sensations. Or it is to be able to know the difference between affects and logical thought, it doesn't matter that we may not be able to say in so many exact words what it is exactly that we feel or what it is that we are thinking. It is to be able to understand that perception can be expressed or understood as a proposition, i.e., that we can if we want to put what we perceive into words and affirm that such a proposition is valid.
To someone who accepts a version of meaning based on our direct grasp of reality, including language itself, then a theory of meaning will not be so much about language as about what underlies the grasp of reality, the use of language, and the processes of thought. The bottom-line on introspection is that if we can characterize thought as a form of behaviour--and arguments about--then introspection would be of behaviour in the same epistemological level as perception.
In mathematics it means the gradual discovery of the field. It probably usually means just very quickly deductive. But this would make perception intuitionistic. More likely it refers to the ideas that cognition throws to the tip of cognition.
Si bien la lógica intuitiva es un fenómeno mental del cual emerge la lógica formal, esta última se independiza de la lógica intuitiva, y aunque es un fenómeno mental, lo es sólo en el sentido en que la razón es un fenómeno mental y lo es inclusive en el sentido de ser un fenómeno subjetivo y no sólo en el sentido de tener siempre un sujeto, sino también en el sentido de no ser un conocimiento estrictamente objetivo, desprovisto de las desviaciones y de las pequeñas imperfecciones que introduce el sujeto al conocimiento, de las que ni siquiera la ciencia y la tecnología más rigurosas están exentas.
La lógica intuitiva es la lógica que usamos a diario: la lógica que utilizamos sin necesidad de leer textos o seguir cursos de lógica. La razón es la aplicación de las formas deductivas de la lógica intuitiva a la realidad. La lógica formal es la que está en los textos y se aprende y se enseña en las aulas.
Podría acaso decirse que la lógica formal es un pardo reflejo de la lógica intuitiva? El ser humano, aunque la lleva adentro desde que nace, no puede asirla plenamente. En otras palabras, la razón en el mejor de los casos tiene la limitación de que no puede abarcarse a sí misma.
Puesto que nadie aprende lógica intuitiva, es de suponerse que élla nace con el ser humano y es por lo tanto un contenido de la mente. Y puesto que no hay ab origine ninguna lógica distinta a la lógica intuitiva, entonces la lógica formal tiene que ser un producto de la lógica intuitiva.
Formal logic is a form of knowledge. But by which criteria do we judge it? Only by the criteria of intuitive logic which is itself the source of formal logic. That we can speak of intuitive logic has the implication that logic is not exhausted by its historicity.