THE PSYCHOLOGICAL MEANING OF THE CATEGORICAL SYLLOGISM ACAD. ALEXANDRU SURDU Romanian Academy, Institute of Philosophy and Psychology „Constantin Rădulescu-Motru”
1. THE PSYCHOLOGICAL MEANING OF THE LOGIC FORMS The beginnings of the mathematical logic (at the start of the last century) and its integration made by philosophers of the positive approach (especially by the representatives of the Vienna Circle) has determined a so-called anti-psychological reaction in logic. To a certain extent, this reaction was fair. It was obvious from a philosophical point a view as well. Ed. Husserl criticized psychologism, as methodological tendencies from logic, firstly, because it was impossible for pure logic to be elaborated, which implicitly meant abandoning logic as an independent area. For extremist psychologists like Theodor Lipps, logic was actually part of psychology (Die Logik ist eine psychologische Disziplin) and it appeared as such (as a chapter of psychology). Likewise, methodologists (such as Alexander Bain) made out of logic a simple preliminary presentation of what today would be called philosophy of science. Secondly, the mentioned tendencies, even though they do not deprived logic of any independence, they did not stimulate the researches aimed at contributing to its development either. However, this situation has caused, in the name of some representatives of mathematical logic, a totally exaggerated anti-psychological reaction. They did not stop at considering the whole classical period (psychological period) of logic as a “decadent”, “barbarian”, “dead” period (eine „tote Periode”) and they rejected the fundamental concept (for classical logic) of structure of thinking. Considering the fact that logic does not study the structures of thinking, it means that between logic and psychology there is nothing else in common. The same should be true for the connection between logic and other sciences but
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because of the fact that mathematical logic has appeared within mathematics, it has become, as it was natural, to be considered as part of mathematics (the logic is a part of mathematics). In addition, through mathematics, that kind of logic has become to acquire methodological significance as well. In this context, it can be considered that logic has gain nothing concerning its purity (before it was a part of psychology, then it became a part of mathematics), and the methodological tendencies (psychological or mathematical tendencies) prevent to the same extent the development of the researches concerning pure logic. However, it must not be forgotten that modern psychology has acquired the symbolic apparatus of mathematical logic. Genetically, it has been proved that the logical-mathematical operations (such as inclusion in the logic of class) are mental activities that can be detected in certain stages of development of intelligence in normal children without any previous instruction. From here to the idea of elaborating a psychological and mathematical logic is just a step. And it was made. Consequently, it is possible for mathematical logic such as the classical one in the past, to be part of psychology (from “psychology of intelligence” analogous to the old “psychology of thinking”- Denkpsychologie) because this is just a “real theory of the same operations” which logic studies as “formal theory”. The anti-psychological reaction, which is of logical-philosophical nature, it is subsequently proved exaggerated compared to classical and modern psychologism. In any kind of definition, logic is naturally proved to be related to the processes of thinking. But these are studied by psychology. Historically, it is also proved that the study of logic from the other sciences’ perspective (recently, from mathematical perspective) and even including logic in these sciences not only prejudices “pure logic”, but also considerably contributes to its enrichment even if, in certain periods, it can lead to extremes (disputing whether logic is an independent subject or not). The main issue is that of establishing a fair relation between logic and the sciences that tend to include it. The relation between logic and psychology, which is of main interest in this context, has been most of the times well understood by classical logicians. On an Aristotelian direction, the distinction between act and force has been made. Psychology studies thinking through act, actual thinking, which cannot be only individual. In what logic concerns, the interest is directed towards the possibilities of thinking, even though they are never achieved, and towards the general aspect of thinking. As an actual act, thinking is a process that develops in time, in certain circumstances, because of certain reasons, etc. Psychology studies the definite development of this process, whereas logic studies its abstract result. Classical logicians have considered as a task of psychology the study of genetic principles and of laws that determine the appearance and the development of thinking (conceived as a natural, material and definite process) - which is the modern objective of genetic psychology.
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Admitting these general theses makes possible the clear distinction between the objectives of the two areas. In reality, logic is not an object of psychology, whereas thinking is an object of psychology and also an object of logic but although it is about the same thinking, psychology studies the definite matter of its actual process, while logic studies only the abstract form of its potential result. It is obvious that, without being similar, the two areas complete each other. Modern psychology has integrated the results of mathematical logic but, through the psychological data analysis, it has highlighted previously adopted structures of logicians (the case of quaternary group INRC of inversions and reciprocations within the propositional combinations studied by J. Piaget). But the psychological study of thinking has not been made and it is not made especially for obtaining new logical results. There is a pure psychological interest for the study of thinking as it is the most important and the most complex psychological process. Consequently, the main interest is its phylogenetic and ontogenetic development but, moreover, it is its structure and detecting its creative components which are necessary both for educating and stimulating the creative activities and for their eventual symbolic modelling, essential to the modern technical attempts of designing “artificial thinking”.
2. THE TRADITIONAL LOGICAL AND PSYCHOLOGICAL INTERPRETATION OF THE SYLLOGISM Unfortunately, most psychologists who have studied the issues of thinking have introduced in the psychology of thinking elements of formal logic, even though they admitted that logic and psychology of thinking must not study the same thing. The most obvious example is the categorical syllogism which appears as an inference so, as a logical operation that is according to the syllogistic laws, even when it is illustrated through definite examples. The situation is maintained nowadays also when in psychology we meet definitions of the categorical syllogism as “a manner of rationalising from general to particular or, more precisely from established premises to a right conclusion”. But, psychological speaking, there are a few questions that are raised, firstly, who established the premises, then what they aim at and, especially, how their process of “establishment” has developed and, finally, who reaches the “right” conclusion, why the “right” conclusion has been reached and how the “right” conclusion was reached. The modern psychologists’ answers to the these questions are usually the following: the premises are established by the researcher; the aim is to test the intellectual capacities of a subject; the premises are established according to the syllogistic laws; the “right” conclusion is to be chosen from a few phrases previously mentioned, other times one has to state which is true and false according to the established premises; the subject chooses the conclusion aiming only at
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answering the test; the choice is generally made by coincidence (there are times when the cause of the mistaken choice is actually studied and it is revealed that there are disturbing factors which interfere, like the emotional ones, although more often the main cause is the difficulty of the premises). So, these syllogisms are composed by the researcher, the subject’s contribution being only a simple option. Other times, in a strictly formal manner, it is considered that the “psychological” activity connected to the syllogism would be the operation of substitution, the “replacing of some judicative elements with others that have a different content but the same value”. These schemes, with variables for words, are of such nature, that any nouns (usually common words) that would replace the variables the syllogism obtained is correct, regardless of the propositions’ meaning which results and their value. The method of offering meaningless premises is also used by the modern psychologists mentioned above. Obviously, in this case the subject’s contribution is also zero. In addition, the common thinking does never operate with nonsense words, which makes that kind of syllogisms to have no meaning in the psychology of thinking, apart from the fact that nobody thinks in syllogistic schemes, these being the abstract structure of the syllogisms. There are more special methods of defining the syllogism through the psychological approach by substitution. Considering that logical forms are illustrations of the law of thinking (so, of some psychological principles) the syllogism, for example, becomes “the operation through which the spirit shows the identity of two ideas, then the spirit compares each one of them with a third idea”, so an illustration of the law of identity, shown through the following scheme: “A = B, B = C, so A = C”. The syllogisms could be obtained by substitution through this scheme or by another one: “A ≠ B, B = C, so A ≠ C”. It is not surprising that the syllogism, analyzed which such methods (more or less formal) has become discredited in the modern psychology of intelligence. Le syllogisme est vigureaux mais n'est pas fécond, states J. Piaget. By the fact that the syllogism is the main method for rational thinking to be achieved, it also offers as a component to this kind of thinking the uncreative character; dividing thinking into divergent and convergent thinking, modern psychologists consider that deductive reasoning is convergent, that it does not accomplish the conditions necessary for creative thinking. The main reason is the method of interpretation previously mentioned and the use of the syllogism, the fact that its mechanism is only, at best, the “drawing of conclusions” from the given premises. When the result is correct it is the same for all subjects. In the rest of the cases (determining the values of a given conclusion or the choice of a conclusion), it is more about the ability of evaluation. By no surprise, the “logical thinking”, which is generally considered vertical, predictable, was opposed to creative thinking (“lateral” thinking). Another cause, which has determined similar conceptions, is gnoseologic. It is about the well-known argument which refers to the “sterile” aspect of the syllogism and that it was started in modern times by J. St. Mill and it was continued by H.
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Spencer but which had appeared since antiquity. Comparing, especially for figure one, the data offered by the conclusion with the ones stated in the premises, it can be considered that the conclusion brings nothing new, that the syllogism would be a tautological formula. The enemies of this point of view state that the tautological formula would appear only in the cases when the syllogistic terms refer to finite collections of objects or beings who can easily be numbered, whereas when talking about the whole collection means to previously check each component. Then, indeed, going from knowing the whole to knowing the parts means to previously go from knowing the parts to knowing the whole, which can be a vicious circle. Highlighting the fact that, generally, things do not happen this way, that syllogism is a fertile form which means extending the knowledge. It can be concluded that the syllogism is not sterile but this is not of psychological interest as it is not a special contribution of the subject who uses this kind of syllogism. The thesis which states that the syllogism would be a tautological form also appears in the mathematical logic. Irrespective of the manner in which it is treated, it appears as the formula: ((M a P) & (S a M)) —> (S a P), where a highlights that the premises and the conclusion are always universal affirmative. The formula is valid (always true irrespective of the substitutions which operate with it) or tautological when interpreted with different types of calculus (with classes or predicates). It is considered that this kind of formula does not express anything, that it is true in an unconditional way. Moreover, is lacking sense and any reflection. Obviously, this type of definition of the syllogism has nothing in common with thinking and it is of no interest for psychology. It does not mean that there is no possibility to transfer on a psychological level of some of the elements of the syllogism interpreted this way. The border of this possibility is, firstly, the psychological thesis which states that thinking means the basic form of thinking; the thesis is accepted both by psychologists (older or more modern), and by some classical logicians. Sometimes, the judgement is considered to be the only act of thinking, the notion becomes a judgement which is lacking subject, and the syllogism is considered, in its turn, as a type of judgement. The privileged role given to the judgement is based on linguistic and gnoseologic data (the phrase, which expresses the judgement, is considered as the only independent linguistic act that gnoseologically is true or false). The operational interpretation of the logic forms (à la Piaget) - “the class” psychologically corresponds to “classification”; “notion corresponds to “notification”, etc.- invalidate the psychological fairness of the previously mentioned thesis. But once admitted, irrespective of the method used, leads to considering the syllogism as an operation with judgements (or propositions). In this context, the main interest is, firstly, what kind of connection is being established between the premises and what kind of connection is being established between the premises and the conclusion. Therefore, a logical-mathematical interpretation can
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be reached, afterwards “the conjunction between the first and the second proposition implies the third”. Sometimes, from the same position, the relation between the premises and the conclusion is treated from a psychological perspective also. It is considered that a conclusion can be inferred or deduced from the premises (psychologically speaking) only if (logically speaking) the premises imply the conclusion. Therefore, the syllogism is conceived as a logical operation (implication) interpropositional, which would correspond on a psychological level to inference. The inference is considered a psychological process because it implies time so, a transfer from the premises to the conclusion (a sequence in time). But the inferences are not always considered as psychological acts, within the traditional logic, the syllogism is interpreted as a rule or inference scheme, the distinguished sign of this definition being the line which divides the premises from the conclusion or the word “so” which precedes the conclusion, as it is being considered that the truth of the premises results from the truth of the conclusion. Giving more importance to the connections between the syllogistic terms than to the ones between the premises and the conclusion, it has been considered, from both a classical and a modern perspective, that the base of the inference is the operation of the inclusion and subordination, without considering the inference a psychological process. These operations are defined in modern terms of inclusion of classes and even the traditional names of the syllogistic terms (major, medium, minor) have been given considering this operation. Aristotle defined the word “medium” from figure I as being the one “which is contained in major and also contains the minor”. But, starting from the operation of inclusion of the terms, the same dispute about the sterile aspect of the syllogism, from a classical point of view, can be reached. On the other hand, on the same logical-mathematical structure the same tautological implicated formulas can be achieved, fact which confirms the uncreative aspect of the syllogism.
3. CONDITIONS FOR THE PSYCHOLOGICAL STUDY OF THE SYLLOGISM The cause because of which all the interpretations from above come towards the thesis of the uncreative character of the syllogism is seeing it form neopsychological and logical-gnoseological perspective. The syllogism is considered a define form which will be used. But it is forgotten that Aristotle himself, who elaborated the first theory of the syllogism, did not applied as such the syllogistic deduction in none of his philosophical or scientific works. The natural thinking, common or scientific, more likely at first sight, does not confirm the fact that its structure is syllogistic-deductive. Aristotle’s merit consists exactly in the fact that he succeeded to detach the concrete thinking from its abstract forms, succeeded in simplifying them, in reducing them to perfect forms, to possible structures,
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irrespective if these have appeared or will ever appear in natural thinking. However, to reduce natural thinking to these kinds of forms would practically mean its abolition. As Spencer had already observed, the syllogism, as it is described in the papers of logic, “is a psychological impossibility because the mental procedure the syllogism wants to represent it is not the procedure through which the conclusion is obtained but the one through which the conclusion is justified”. The syllogism, as a logical form, is not an inference but a rule or a scheme of inference. It can explain why certain conclusion has been reached starting from certain premises, but not how the premises have been reached that conclusion because, besides the students who learn about the syllogism, nobody composes inferences based upon the syllogistic rules. Also, Spencer subtly transmits the fact that usually, there is no rule to make the premises known before the conclusion or the general case to be chosen before the particular one, the last one being easier to everybody. It is about the distinction between the logical and the psychological aspect of the forms of thinking, between the potential and the present aspect. The last one being the one which appears in natural, common or scientific, individual thinking. Here, the formal rules within the syllogistic area are rarely followed, therefore starting form the premises to the conclusion, in most cases, the conclusion is present in our minds before the premises. In addition, many times, only one premise is expressed. The cause is that the natural thinking does not feel the need of familiar truths to be stated. Most of the time, both premises are indirectly understood, fact which is highlighted by addition like “it is known that...” or “it is obvious that”. Usually, these additions are also lacking because the common truths do not necessitate expressing any justification, which is implicit. In addition to this, there is a great difference between the manner of thinking for oneself, which can be totally elliptic, the manner in which one communicates in a familiar environment, the manner of trying to convince a stranger or the manner of proving something that anyone would admit. Sometimes, especially in literature but also in usual talks, the premises are intentionally hidden or they are sustained without knowing what conclusion they will reach. The fact that both in writings as in conversations, syllogisms, which can be recognized as such, appear extremely rare, does not mean that they do not exist or that they cannot be detected, ordered and concisely expressed. However, this activity is useless and even damaging in certain fields. Generally speaking, the artificial aspect of any attempt to apply syllogistic in current thinking was highlighted. Considering all these, as long as current, individual thinking is the object of psychology, the psychological study of the syllogism must be done within this kind of thinking. This does not mean that finding definite methods adequate for syllogistic forms is sufficient and, eventually, reducing some of them to others. The analysis of the concrete syllogisms in the context of natural thinking is important.
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Concrete syllogisms appear contextually, whereas the syllogistic forms are independent; they subsist in and for themselves. The contextual analysis highlights the circumstances of creating a syllogism, more precisely who created it, how it was created and why. These circumstances have no importance for the syllogistic form but they are essential for the concrete syllogism.
4. THE SYLLOGISM AS DEMONSTRATION AND REASONING Ever since the beginning of Prior Analytics, Aristotle had specified that the aim of studying the syllogisms is demonstration. This means that the study of the syllogisms in and for themselves, their study as simple formal possibilities, as it is done in logic, do not represent an aim of natural thinking where nobody wants to just create syllogisms. Syllogistic offers only the formal aspect of the demonstration being also a method to practice the demonstrative abilities and a method of learning a few formal techniques for avoiding errors, of, consequently, making one familiar with the syllogistic models and figures. But, as Aristotle also stated, demonstration is a kind of syllogism but not any syllogism is a demonstration. The demonstration is the perfect method for sustaining a certain thesis, the demonstrative premises must be prior (to not necessitate demonstrations) and true. The syllogism itself guarantees only formal the production of a demonstration. Searching prior and true premises does not have any connection with logic; it assumes a proper scientific activity. Demonstration is one of the similarities of the syllogisms in natural scientific thinking. However, it needs to be highlighted that the syllogistic demonstration does not correspond to any logical interpretations of the syllogistic forms. As a logical-mathematical definition, the syllogism, considered as a tautological formula obtained through axiomatic deduction, cannot have a demonstrative significance. Within the syllogistic demonstration, the conclusion becomes a thesis which will be demonstrated, but in the logical-mathematical calculus there is no possibility of demonstrating the truth of a simple proposition such as “S is P”. In the case of the syllogism, which becomes an implicit formula, the conclusion can be detached (stated as being true) because the implication is true even in the case when the conclusion is false. Therefore, the syllogistic demonstration is characterized only by classical, inferential interpretations of the syllogistic form. The syllogistic demonstration appears in natural thinking both in the common form, with the premises followed by conclusion, and in a reverse form, with the conclusion as a thesis followed by the premises which justified it. The order of the syllogistic demonstration’s components depends on the gnoseological and psychological factors. Sometimes, the premises can be known before the conclusion; the difficulty is in reducing the previous knowledge to propositional
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forms which can act as premises so, to allow obtaining a conclusion. Other times, the start is a known thesis and the correspondent premises are searched for. But the order also depends on the intentions of the one who presents the demonstration: to highlight more the thesis or to highlight the premises. The syllogistic demonstration appears only in natural scientific thinking. But in common thinking concrete syllogisms similar to demonstration also appear. The difference is that, for the last ones, the premises do not need to be prior but only true. The syllogism created through this method is a reasoning. The reasoning frequently interferes in usual talking, being marked by specific linguistic particles and related to the common form with the premises at the beginning or it is related to the reverse form. “Due to the fact that...”, “admitting that...”, “because of...” are linguistic particles which announce the premise that can be expressed completely or elliptically. When the reasoning begins with the thesis, it is followed with articles such as: “...because...” etc. Unlike the reasoning, which it assumes a serious reflection over the syllogistic components and in order to be totally correct, it needs knowing the area of syllogistic, as Aristotle recommended, reasoning is spontaneous. Because of this, its common form is the reverse one, with the premises after the conclusion. In the case of reasoning, the errors are frequent and, in addition, aristotelically speaking, the premises are most of the times probable, which entitles their rejection by an eventual opponent. The rejection is made like reasoning, with the difference that it is made in favour of a proposition which is opposite to the reasoned thesis. The syllogism can appear in natural thinking as demonstration, reasoning or rejection. These are the forms of the natural rationale with its adequate motivations: in order to demonstrate, to reason or to reject a certain proposition. The syllogism as such does not assume this kind of motivation. Therefore, understood as a pure form (in classical logic) or even as an operation (in mathematical logic), it interests us as a formation which acts like a whole, which is abstract, schematic or symbolic. It is form, principle or rationalising rule and not rationalising in act. However, psychologists use in experiments syllogisms with variables of terms, asking subjects, with no special training (such as the thorough study of the syllogistic rules), to mark the conclusions they believe are valid. Obviously, there are many errors because the answers are given by chance. In these situations, they do not “reason syllogistically” and the syllogism itself becomes an object of rationale because it is given as such. But this metasyllogistic rationale can be made only by specialists. For the correct answer to be given, one it is supposed to know syllogistic figures, general and special rules of each figure, which is totally different than to “syllogistically reason” so to create a judgement in natural thinking. However, rationalising itself is often considered as being of logical nature, which means that thinking in act would be possible as “logical process”, as a process with no motivation and which also means that thinking with syllogistic schemes would be possible, indeed. This would be the “pure logical process” of
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rationalising which, however, in the case where variables are replaced with concrete terms would also be influenced by “psychological factors”. These “extralogical factors” intervene when the subject chooses the conclusions which he/she considers to be valid. The fact that the syllogisms, when interpreted as above, are elaborated by the researcher they exclude the psychological factors from the mechanism of the syllogisms’ composition. They become simple disturbing elements of the act of marking (of choosing despite of the lack of knowledge and within a record time of 30') of validating a syllogism. This means that using the syllogisms already designed cannot be viewed as a method of testing the psychological abilities for rationalising. On the contrary, if we start from natural thinking, the only one where syllogisms exist and they are produced, which cannot be concrete (demonstrations, reasoning or rejections), then it can be proved that the process of creating concrete syllogisms is of psychological nature and that syllogistic reasoning in act is itself a psychological process, which can be conceived as pure psychological process. This process can or cannot be influenced by logical factors, more precisely by the syllogistic knowledge of the subject who is rationalising. This is just the case of replacing the concrete terms with variables and the formal study of the syllogistic correctness, activity which is basically made within demonstrations so, within natural scientific thinking. But a person reasons even without knowing the laws of logic as he or she talks without knowing the grammar rules. The concrete rationalisation is not a logical act as the common talking is not a grammar act. Rationalization is considered a logical process due to the illicit transposition of the logical forms into the psychological plan, to the transposition of the possible into the real, of the abstract into the concrete. 5. DISCOVERING THE MEDIUM TERM The scholastic logicians of peripatetic influence used, like Aristotle, to ask themselves not only how many types of syllogisms can exist but also how (quomodo) concrete syllogisms are built when related to a given theme (ad propositum). It is interesting the fact that they never proposed, although they knew it very well, the method of substitution as a manner of obtaining the concrete syllogisms; for them it was clear that the syllogism ad propositum is not just a correct syllogism but one which aims at something. Being given a proposition such as “All S are P”, irrespective of what word would be chosen for M, the syllogism “All M are P, all S are M, so all S are P” is valid but this cannot be an ad propositum syllogism because it does not assume nothing besides its correctness therefore, it is not demonstration, nor reasoning or rejection and it cannot appear in the natural language as such.
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Starting from the conclusion and heading to the premises, leaving aside the possibility of working in the 4th figure and with the indirect methods of the 1st figures, it is proved that the universal affirmative (A) is obtained only in one way of the 1st figure, whereas the universal negative (E) in two figures and three methods, the particular negative (I) in two figures and four methods, and the particular negative (O) in all figures and in six methods but with the exception of (A), in the rest of the cases, one cannot know in what figure or in what way it will be worked. For this it is necessary the inventory or the discovery of the medium term (inventio medii). This activity has always been considered, especially for demonstration, very difficult; Aristotle himself named the capacity of discovering the medium term “sharpness of thinking” (agchinoia). This is a psychological capacity, which differs from individual to individual. Who cannot find the medium term cannot build an ad propositum syllogism or a concrete syllogism which can be used in natural thinking although it can perfectly answer to the usual syllogismstests so, the correct conclusion can be chosen from the shown multiple choices or it can even be drawn from the given premises. Others, on the other hand, can find more medium terms (through discovery or invention). Some people find the medium term, others do not. And the ones who find them can do it faster or slower. And taking into consideration the medium terms found, they can build syllogisms in one or in several methods from different figures. Discovering the medium term has no connection with logic. Logic is a material activity which in the exact sciences it is built only by a long and laborious research. Finding the medium term cannot be done based on any of the rules of logic. Even in the case of reasoning, where it is not about prior premises, finding the medium term is a work of original endeavour based upon previous knowledge but also upon inventiveness. Discovering the medium term needs a considerable effort from the spirit, it represents the inventive part of deduction. This can be proved, however, through an experimental method also.
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