Logic and Psychology

The survival of the human group precedes in evolutionary terms any other symbolic action, which will always have to assume such a survival as a fundamental final referent. If the content of the organism’s categorizations are the successful processes of adaptation, the valuation referents would be such processes, and the meaning of all other actions would be derived after these. For this reason, basic emotions provide the fundamental semantics of our language, and are cognitive processes that evolutionarily precede what philosophy has called rationality. Both the system of seeking and that of fear perform cognitive functions of induction, after pattern recognition, based on the memory of experiences, which are selectively strengthened by fear.[1] Fear functions as a social regulator when it is coupled with rage, as can be observed in the hierarchical formations of animal communities as well as in the repression that the law in human communities entails. On the other hand, rage communicates states of frustration in which individual instabilities that affect the group are expressed, some homeostatic loses that are regulated by means of the violent repression of unwanted behaviors. Likewise, the impulse for seeking, from which an individual organism benefits, also occurs at a collective level, and prospers according to its degree of symbolization, in fact reaching its maximum power when it is accomplished by the group, due to the concurrence of greater energies and to the multiplying effect of the ordering structures which allow specialization. For its part, sex establishes basic human relationships of association that structure the group, besides offering epistemological analogies for the general processes of generation, a strategy which has served (even today it serves at the core of some of the great religions) for a simple ordering of the universe. The emotion of maternity embraces the entire initial process of social learning, and serves epistemologically, like sex, to elaborate primitive cognitive schemas in which the universe is understood through a maternal or paternal link with it. The social emotion is mainly communicative, and therefore cognitive; in fact, it is this emotion the one which (modified by the others) makes relevant the semantic content that is being transmitted, i.e. the group is the final referent of meaning. For its part, the ludic emotion has at the same time a cognitive and a social dimension, strengthening the bonds of the group. Play, by enclosing the vital experience and self-containing its actions, allows the creation of simulacra in which the actions of direct relevance for survival can be anticipated and rehearsed. To sum up, all the emotions have a cognitive function, and by having evolved from the relationships between the live organism and the environment allow a flexible and adaptive behavior that we have called intelligent.

According to the model of Neural Darwinism, the global mappings generated perceptual categorizations -or of first order- and conceptual categorizations -or of second order- in which the frequency of certain actions which successfully related the organism with the environment produced permanent circuits or memorizations (understood as re-categorizations), that conditioned the future behavior of the organism. Such categorizations imply a first type of valuation which follow an inertial impulse for the preservation of life, to which we can hardly call intentional or conscious, but which, nonetheless, generates a frame of reference for basically syntactic processes that can be considered like a proto-semantic system. These circuits –analogous in all mammals- to the extent that they systematize pairs of internal and external stimuli with motor responses, index representational scenarios from the categorical valuations, a process of valuation of second order which takes as objects the global categorizations linked to their scenarios, in which it is configured a rudimentary, diffused, consciousness, that is linked to the emotional protocols, and it is active insofar as these are active as well. There is primary consciousness as long as there is emotion, and such a consciousness is nothing more than its protocol of action. This second order valuation is the basic emotional valuation that serves as semantic referent for the actions of survival, and it is more complex depending on the type of perceptual and conceptual categorizations that may enter in the determinations of the emotional neural circuits. To the extent that the different neural systems, with their different tempos, interact amongst each other, processes of anticipation and delay will be produced, to which we could call of deferred valuation, in which the protocols of respond become more flexible, whether anticipating or delaying them in order to complete a successful action of survival that is better adapted to the scenario in question. The emotions of longer duration will condition those of shorter duration, in the sense that they must adjust to the general program of action for the organism. If the emotional core is composed by the emotion of seeking and the reproductive emotion, and the first one has an intermittent functioning, then it must be the mammalian maternal emotion the one that agglutinates around itself the rest of the emotional system. In fact, the physiological maternal bond in mammals can be extended for decades, because fetal cells cross the placental barrier and the blood-brain barrier,[2] something which seems to indicate that the maternal emotional conditioning occurs at an even more basic level than that of the neural systems, a fact that would support the idea that it is this emotion the one that centralizes the mammalian social behavior. The emotional system on the whole supposes a valuation of third order whose objects are the valuations of the primary emotions, and unlike the two previous valuations, the endomorphic component of the action of response is greater, in the sense of being, relatively, less conditioned by the environment, of requiring a less urgent validation and molding the scenario according to the internal conditions. These three valuations, to which we could call vital liminal valuations, or valuations of the Unterlebenswelt, make up the basic semantics for the actions of the organism. On them are grounded the neocortical symbolic developments of the human being, whose valuations have to be in harmony with these vital liminal valuations, as a kind of lower bound which conditions them. Nihilist symbolic valuations of life have subverted the most basic values of survival proclaiming the unreality of human existence in favor of the unconditioned reality of a supernatural world, though -despite negating the existence on this earth- they have transferred the world of the emotional valuations to that ideal world, they have projected basic emotional contents into those other worlds. Of course, it could not be otherwise, for if it were not so, if the gods were not fathers and mothers, and the positive and negative experiences on the other worlds were not to have an emotional content, it would make no sense for the biological organism of the mammal. 

Vital valuations are evolutionarily previous to the higher symbolic ones and have priority over them in their own scenarios. The neocortical control over the subcortical systems is effective only in non-stressful situations.[3] Emotions involve a processing of maximum efficiency of the memories of the species in extreme situations. In these cases, the amygdala is in charge of producing a higher quantity of dopamine and norepinephrine, interrupting the functioning of the prefrontal cortex, in which it is located the so called working memory or blackboard memory -indispensable for abstract thinking-, thus being activated the emotional protocols.[4] The emotional neural systems are superposed with the systems that are in charge of somatic activation, as well as with others in which are processed the personal judgments that are adopted in decision making. These latter systems are different from the systems that correspond to a more specific cognitive intelligence,[5] however, the constrictions exerted by the emotional systems over learning during the long evolutionary periods of behavioral adaptation, have made the emotional experience, in humans, inseparable from cognitive ones, even so in merely logical processes.[6] Neuro-scientific studies about deductive reasoning have shown that a process that may seem isolated from emotions, like in the case of deduction, is conditioned by them in neurological terms: inference is emotionally modulated.[7] Emotions can affect deduction in two possible ways: due to the presence of semantic content in logical reasoning, which activates the linguistic neural systems and long term memory –which in turn activates the emotional systems-, or directly due to the emotional content of the scene in which the reasoning occurs, that is, the emotions of the reasoning subjects.[8] As the experimentation undertaken by Vinod Goel has shown, the purely symbolic reasoning, like the syllogisms in which the premises are represented by letters, involves an activation of the visual parietal system, which is not activated in syllogisms in which there is a semantic content. When our propositions have a semantic content, beyond their interpretation as formal symbols of a calculus, such semanticity resonates emotionally in the subject, activating memories and emotions that neuro-chemically condition the functionality of the blackboard memory, introducing external factors into the merely formal game. The easiness by which argumentative fallacies are produced –formal and informal- is grounded on this phenomenon of emotional conditioning. The influence of the emotional elements in the argumentation has been known since ancient times,[9] and it is normally used, inadvertently or deliberately, in social communication, even though, it was superstitiously considered that the most formalized deductive reasoning was immune to emotional influence.

On the other hand, as Roland Friedrich has shown using fMRI, formal and natural reasoning are processed differently at a neural level, for they correspond to different evolutionary areas despite their structural analogies.[10] There are different neural processes for different reasoning actions: the deductions of mathematical logic and those of everyday life -which are imbricated in the mythological inheritances of the natural languages- are applied to their corresponding scenarios, and it is not clear yet if there would be some of these scenarios in which these neocortical activities could be harmonized with one another. The differences between natural and formal reasoning are much greater than it would be expected at first glance, and if we judge the patterns of everyday life from the reasoning structures of science, we find ourselves with a surprising abyss between them, whose explanation has the evolutionary content that Friedrich pointed out in relation to syntax. We could speak of at least two kinds of symbolic reasoning with their corresponding types of valuation, although both conditioned, ultimately, by the emotional processes. Both operate with an added mutual tension due to the inevitable interaction that they maintain as a result of the demands of the vital processes of the modern human being, who lives following the patterns of formal reasoning -in which his most n-ary techniques are based-, as well as those of natural reasoning which, being nearer to the basic emotions, serves as a link with the praxis of such a technique in everyday life.

The tension between these two reasoning ways is basic in order to understand modern man psychology and the processes of emotional valuation. Let us take as a comparative tool for natural and formal reasoning a common structure to both, the material conditional. Bertrand Russell and the logicians characterized pure mathematics as a class of all the propositions of the type p implies q,[11] which, aside from the validity of the declaration, gives us an idea of the importance of the structure of the material conditional within a field so unequivocally rational in its proceedings (not always in its ontology). The structure of the conditional occurs in all human natural languages,[12] and in the last fifty years it has been as exhaustively studied by psychology as it had been by philosophy -and in a very problematic manner- since Aristotle.[13] It is not my intention to treat this discussion in detail, but simply to show what are the bases that make the material conditional such a problematic question, in order to illustrate the difference between natural and formal reasoning, and the place that both occupy in relation to the processes of emotional valuation and later in myth construction.

As William and Martha Kneale pointed out, some classical authors tried to formulate the conditional as a necessary connection between statements, and these were defined as constructions in which it is not possible that simultaneously the consequent may be false (apodosis) and the antecedent true (protasis), even though the contradictions appeared everywhere. For the Megarians Philo the Dialectician, and his master Diodorus Cronus, well-formed conditionals cannot begin with the truth of the antecedent and finish with the falsity of the consequent, being their construction correct in the rest of cases of truth valuation of protasis and apodosis. Philo argues in relation to the material conditional some questions which even though they were left aside by the logic of the 20^th Century, appear in natural reasoning. I refer to the problematic of the temporality in relation to antecedent and consequent, as in the case in which a conditional may be true during a moment of the day and not so during another: If it is daytime then I am reading this sentence. According to Philo’s framework, it would be logically true both during the day and at night, because the falsity of the antecedent does not make false the construction of the material conditional, but it is intuitively contradictory. The problematic is not only due to the possible divergences between a syntactic conditional structure and the self-referential semantic content of a proposition, from which are derived well known paradoxes, but we find ourselves with more general semantic problems in relation to the conditional when the temporal dimension is introduced, a tension that occurs between logic’s ambition of timelessness, inheritor of the Parmenidean thought that studies the immutable essences that relate among each other in syntactic games, and the directional mutability of experience. With an example: Let there be P and Q two past events that are not made true simultaneously. P became factually true (in the sense that the semantic content of the sentence P corresponded with a set of physical actions) first, and later Q. Let us now construct the material conditional Q→P. Such a conditional is well formed, for it never happened the case True→False, and when afterwards it occurred True→True, it continued to be in accordance with the definition of truth of the conditional. We are postulating a connection between something that has not been yet, and something that has already been.[14] Let us suppose now that P and Q are two future events that are not true simultaneously, and that P will become factually false first, and later Q. Let us now construct P→Q. The conditional is well formed, for it would never occur True→False, and when False→True, or False→False may occur, it will be equally well formed, although we are postulating some relations whose epistemological content is irrelevant (at best) and paradoxical, because we are affirming a link which is non-existent from the present point of view and that it occurs for all conditions of truth and falsity of the antecedent and the consequent. In the case that P may become factually true first and then Q, in order for the conditional to be always true, we must formulate it as Q→P. On the other hand, any pair of propositions that became true simultaneously in the past, or will become true simultaneously in the future, will form -in any order- well-formed conditionals.

The use of the material conditional as a necessary connection between antecedent and consequent has not been the most common, neither in the sphere of logic nor in ordinary thinking. In the logic after Russell, the role of the material implication is better understood when it is considered in a wider context, like the one provided by the axiomatic system of number theory. (x) A(x) → B(x)[15] expresses the relationship between variable propositions, or propositional functions, that we call formal implication. The formal conditional represents implication, not in an a priori sense, but in the sense defined by the formal system.[16] On the other hand, in ordinary language, the primary goal of a conditional statement is not to maintain the notion of a necessary connection between protasis and apodosis, but to call the attention about a possibility whose fulfilment is somewhat uncertain to the speaker, and whose consequent has only meaning in relation to the antecedent.[17] This phenomenon has been studied by the psychological Mental Model Theory,[18] which, from the syllogistic schema that takes the conditional as major premise and as minor the affirmation or negation of the antecedent or the consequent, has characterized ideal reasoning by means of a three-step process. The first one involves the representation of the reasoning process through a set of mental models compatible with the major and minor premises. In the second, a conclusion is obtained which is innovative and true for all the models of application of the syllogism. Lastly, counterexamples are sought for, additional models that may be compatible with the premises but not with the conclusion.[19]

However, in practice, the reasoning accomplished is a different one. Experimental psychology has shown that the difficulties that formal logic has had with the conditional since its very beginnings are rooted in our spontaneous way of thinking the sequences of phenomena and the propositions that verbalize them. Thus, for instance, in a syllogism in which the major premise is the conditional and the minor Q, or ¬P, which formal logic would solve in uncertainties, are solved in the scenarios of natural reasoning with the acceptance of the consequent and the negation of the antecedent.[20]

       Table 1: Syllogisms of natural reasoning.

Major premise: P→Q

Name of the inferential process	Minor premise	Conclusion
Modus Ponens	P	Q
Modus Tollens	¬Q	¬P
Fallacy of Accepting the Consequent	Q	P
Fallacy of Negating the Antecedent	¬P	¬Q

In natural reasoning we find two limitations with respect to formal reasoning: the two spontaneous deviations noted (the acceptance of the consequent and the negation of the antecedent) and the openness of the system of natural reasoning. Both matters are related, for the deviations are partly produced due to the confusions generated by the semantic content in relation to the sequential content of the material conditional. If we accept the thesis that emotions establish a proto-semantic root for symbolic communications, and that the processes undertaken in a protocolary manner by the basic emotional systems constitute a unity of meaning for the organism, the natural forms of inference make sense as chains of actions (or propositions) not analyzable into individual actions or propositions. If an stimulus (internal or external) activates an emotional protocol E formed by a sequence P⟹Q (read as, Q follows necessarily from P), the synthetic unity of meaning is the pair (P, Q), that is, the protocol E, which distinguishes two temporal irreversible moments, in which it cannot be the case that action P may occur without occurring also action Q. If I find myself in a dangerous situation, my organism activates the physiological changes that we call the emotion of fear, and if the protocol is to have the effectiveness that evolutionarily has shown, has to activate the entire sequence, so that by finding ourselves in any of the elements of that chain of actions we can ensure that it has been preceded by some specific actions and will be succeeded by others, as the antecedents of the cascade progressively unfold. It is a question, then, of a reasoning schema in which the two fallacies of accepting the consequent and negating the antecedent make sense. The difficulty that natural reasoning has with the acceptance of the Modus Tollens happens because in the elements of the sequence P⟹Q, the minor premise, ¬Q, does not negate P but the synthesis of signification that forms the sequence E, which, when it occurs, has emotional meaning, of survival, whereas when E does not occur, we find ourselves in a natural process that corresponds to another type of characterization, speculative and neocortical in this case, which we could call an scenario of formal reasoning. Suppose that we construct the following material conditional: If a raging dog would attack you and you were near a tree that you could climb to, it would be reasonable to climb to that tree. Let us suppose, to simplify, that we assign to the propositional conjunction of the antecedent a single formula P, and that we will only consider the cases in which simultaneously occurs the attack and the fortunate presence of the tree, or none of these two occurrences. Within a scenario of natural reasoning, we would be dealing with a sequence E formed by P⟹Q, in which is posed a dangerous scenario with a possible way out: the action of climbing the tree. Suppose now that P occurs as minor hypothesis. To conclude that Q will occur is unproblematic, a Modus Ponens, although if the person doing the reasoning is someone who goes usually armed, can change the scenario and offer an alternative R: forget the tree and kill the animal. If on the contrary, we affirm the consequent Q, to climb the tree, the synthetic unity of E makes us infer P (fallaciously), and in the same way, if we negate P, we will be also negating Q fallaciously. Natural reasoning is occupied with elaborating scenarios with minor premises that function as a sequence pair E(P,Q), with a unified meaning, a unification which if it is not achieved by some of the values of the antecedent or the consequent, it will be attained by substituting the consequent for R, that is E’(P,R), but without touching the antecedent, for it is the condition that defined the reasoning scenario in the first place, and without which it makes no sense to continue thinking. Within an emotional scenario the need for sequence is even stronger, and although the response to fear is conditioned to the experiences of the individual in similar stressful (liminal) situations, the initiated sequence will be completed, and in such a context neither the minor premises like ¬P, ¬Q, make sense, nor to try to deduce the truth or falsity of P once Q has been produced, these are considerations that find their place perfectly in reasoning processes in which the blackboard memory intervenes. The scenarios of natural reasoning are found half way between those of emotional liminal reasoning and those of formal liminoid reasoning. In fact, we could consider natural reasoning as a delimitation of the processes of basic emotions in non-urgent situations, in which n-ary emotions process sequences in a sequential manner E(P,Q/R), which only become P⟹Q in formalized liminoid scenarios, in which the dominant emotion is that of knowledge (an n-ary emotion).

On the other hand, the models of natural reasoning, as different from formal models, are open, that is, additional information can enter the system altering the former logical structure (called non-monotonic systems). Thus, for instance, in relation to the myth of Oedipus, since we know that Oedipus was a man and all men are mortal, we conclude that Oedipus died, however, knowing that later he disappeared at the entrance of Athens, because the gods took him away, we are not so sure anymore if we could conclude his mortality. Another similar case would be that of a friend who tells us that he has a mammal as pet, to which he has named Fred. By having such information we simply infer that Fred is not poisonous, but later on we find out that Fred is a platypus, one of the rare venomous mammals, and so we change our conclusion. The opening of natural reasoning does not only occur from the side of the reasoning scenario, in which not all the information is determined a priori as part of a calculus and new data can continually enter, but also from the opening of the reasoning subject, who will interpret the scenarios following specific mythic (ideological) structures, which condition both the formulation of hypotheses that may be plausible with the scenarios and the rejections of those logical assumptions that may suppose a basic contradiction with the axiological core of its mythology. The interpretations of natural reasoning usually lead to assign a truth-functional value to the propositions, according to the scenarios and times in which these occur, or lead directly to accept the paradox as a condition of some specific epistemological scenarios, especially those that refer to exomorphic representations. However, the most complex types of natural reasoning do not operate by a simple acceptance of the paradox, but by means of non-monotonic adjustments. If we observe natural reasoning, the non-monotonicity expresses itself according to this schema: (P ∧ ¬T) → (Q ∨ R), in which T represents the adverse conditions that will impede the occurrence of Q regardless of the occurrence of P, and R represents the additional information that enters the system. While T destroys the scenario logically, since in the Modus Ponens ¬(P ∧ ¬T) blocks the deductive certainty, R safeguards the whole scenario, for its acceptance as truth makes true the scenario described by the formula, an R which can be either a corroborated fact by social experience or a hallucinatory personal belief.[21] With an example: If Fred is a mammal, and not a virtual mammal, then Fred is not poisonous, or Fred is a platypus. The proposition: Fred is a platypus, is late information that by being thus added saves the first scenario. Another example in which beliefs intervene: If the gods have created the universe, then the universe is proof of our perfection in all its actions. Here the first belief, P (the gods have created the universe) is expressed as a necessary condition for the whole argument, and it is not contemplated either ¬P, or a possible T that may contradict it. The point is to prove the consequent by means of the Modus Ponens, and when a negation of the consequent is produced by means of a Modus Tollens, like in a proposition that contradicts the beliefs by affirming: hunger, war and emotional misery, in which the better part of humanity lives and which are actions of the universe, do not show any perfection or grandeur, therefore, the gods, if there were any, either are not perfect or have not created the universe, the most common answer is to produce a disjunctive premise to be added to the consequent that saves the argument: human suffering is part of a divine plan whose perfection escapes the ordinary human, as, for example, do the Hinduism and the three religions of the Book. In sum, the ability of human reasoning does not operate equally in liminal scenarios than in the liminoid scenarios of experience. Formalized thought is a late evolutionary development that is limited by the most basic inferential operations that take place in the emotional processes. When propositions have semantic contents, they are processed in different neural areas than when they do not, and with the semantic content a whole valuation system of the subject enters the scenario. For its part, the greater liminal weight of the scenarios of natural reasoning determines absolutely the reasoning action, and the syllogisms work spontaneously with the fallacies of accepting the consequent and negating the antecedent, moreover, such fallacies obey a need from the part of the emotional protocols that is perfectly intelligible. In most reasoning scenarios of human vital experience, rationality is inseparable from emotionality.

It has not only been proven the emotional conditioning of natural and formal reasoning, but the alleged independence of moral judgments with respect to the emotions (and in fact, the independence of these judgments with respect to any human thing)[22] -which the philosophy of ontotheological grounds was inclined to think from Plato down to our times-, has been refuted as well by the neuro-scientific investigations. Moral decision-making is not independent from emotions[23] –despite the fact that both processes have a different topobiology-,[24] that is, our morality is biologically conditioned, something that we could simply derive from the understanding of the functionality of the emotional protocols, but which has been also confirmed by means of neurophysiological experimentation. Emotions condition even our perception of reality, for it has been observed that perception data are not even processed in a simple manner, but are re-elaborated from the combination of the emotional systems, from criteria such as that of group cohesion (belonging and not belonging to a particular group), something that can distort even the sizes of the objects perceived.[25] Some authors sustain that there is not a specific neural system for moral judgments, but that these are produced by means of a complex interaction between multiple neural systems which are not specific to this cognitive activity,[26] a postulate that seems to confirm the thesis of the emotional control of morality by proposing a decentralization of the natural processes that correspond to moral judgments into other neural systems. The resolution of these differences can only be empirical, even though (regardless of there being or not an exclusive system for morality) by being an activity that involves the emotional social neural systems, it makes no sense to consider it independently of them. However, there is a generalized agreement about the importance of the modulation that emotions exercise on moral judgments, and in fact, the frontier between the emotional and the social neuroscience is becoming increasingly vague. For this reason, human emotions can be considered the most complex neural processes, to the extent that they are mixed with all the other brain processes,[27] obviously, always considering that we speak of n-ary emotions, with scenarios of natural reasoning of the kind (P ∧ ¬T) → (Q ∨ R), dealt with earlier, and not of mere processes of basic emotions.

N-ary emotions can perfectly handle logically contradictory scenarios, introducing disjunctive hypotheses that express beliefs, although they are not capable of processing scenarios that are non-linkable to the basic emotional circuits in which the survival of the organism is based. What is relevant to the emotion is not the form of a given scenario, but the importance of such a scenario for the subject, its link to any of the specific emotions that guide the actions of survival. Let us suppose for a moment that in the future humans develop a new neural system to process new scenarios of survival. Let us call aesthetics to this new emotion, an emotion that we define as an exaptation of some part of the system of rage, within an imaginary society so civilized and reasonable that rage is already a marginal and sporadic emotion. Suppose that the aesthetic emotion solves situations in which rage functioned before, in such a manner that whoever has that emotion more developed will enjoy a higher social recognition and higher reproductive opportunities, both in relation to children and to ideas. If we are capable of imagining such emotion, is because we associate it with the other emotional systems. If we understand this hypothetical scenario, is because we connect it to scenarios of our current emotional experience. An intelligent living being who may not share with us anything more than the system of seeking, who is asexual, non-social, and who does not feel fear or rage, would be fundamentally incomprehensible in its actions, and it would only be comprehensible from the actions related to the seeking neural system. Unconsciously, when we speak of intelligence we talk about life, and when we talk about life we imply the process of development of all or at least some of the characteristics of the emotional systems. We consider as intelligence the adaptive ability of living beings, of which our most formalized and methodic reasoning is but an n-ary evolutionary development of the set of the emotive-communicative system, which functions more like a limiting regulative condition of cognitive processes in certain liminoid scenarios, than as a pragmatic condition of human action. The use of reason is conditioned to the emotional homeostatic contexts of the group’s survival, and for this reason its intervention in the narratives of identity is always restricted by the needs of the homeostasis.

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[1] Cf. Panksepp. Affective Neuroscience. Ed. Cit. p.48.

[2] See Bianchi, D. W. et al. Male fetal progenitor cells persist in maternal blood for as long as 27 years postpartum. In Proceedings of the National Academy of Science. U.S.A. 1996. January 23; 93(2): p.p.705-708. Web. And also Rei Sunami et al., Migration of michrochimeric fetal cells into maternal circulation before placenta formation. Landesbioscience.com. October, November, December. 2010. Web.

[3] Cf. Panksepp. Affective Neuroscience. Ed. Cit. p.301.

[4] Cf. Amy Arnsten, Carolyn M. Mazure and Rajita Sinha. El cerebro sometido a tensión. Investigación y Ciencia. Junio 2012. Prensa Científica. Barcelona. p.p.64-67.

[5] Cf. Reuven Bar-On, et al., Exploring the Neurological Substrate of Emotional and Social Intelligence. In Social Neuroscience. Ed. Cit. p.p.223-235.

[6] Cf. Gerald M. Edelman. Second Nature: Brain Science and Human Knowledge. Yale University Press. New Haven and London. 2006. p.65.

[7] See: Vinod Goel. Cognitive Neuroscience of Reasoning. Draft Nov. 27. 2003. Web. In the book, Cambridge Handbook of Thinking and Reasoning. Eds. K. Holyoak and R. Morrison. Cambridge University Press. 2003.

[8] Cf. Goel. Ibid. p.29.

[9] See the treatment of the enthymemes in Aristotle. Rhetoric. 1354a. 15.

[10] Cf. Roland Friedrich and Angela D. Friedrich. Mathematical Logic in the Human Brain: Syntax. p.p. 1-5. May 28, 2009. Plos ONE. Web.

[11] Cf. Bertrand Russell. Principles of Mathematics. W.W. Norton & Company. New York. 1964. p.3.

[12] Cf. Comrie, B. Conditionals: A Typology. Cited in Mike Oaksford and Nick Cater (eds.). Cognition and Conditionals. Probability and Logic in Human Thinking. Introduction. Oxford University Press. Oxford. 2010. p.3.

[13] In Sextus Empiricus, are found formulated the four main conceptions that are developed in classical logic about the conditional. Pyrrhoneiae Hypotyposes. ii.110-112. See the discussion of William and Martha Kneale in The Development of Logic. Oxford University Press. Oxford. 1984. p.p.128-138.

[14] Moreover, the acceptance of the consequent in the past carries the question of the validity of the reasoning to purely semantic terms, to the factual truth or falsity of the statements P and Q, which no longer belongs to formal logic.

[15] Read as: “For all x, if A is x then x is B.”

[16] Kleene, Stephen Cole. Introduction to Mathematics. North Holland Publishing Co. Amsterdam P. Noordhoff N.V. Groningen. 1964. p.p.138.139.

[17] Kneale. Op. Cit. p.135.

[18] Started by Phillip Johnson-Laird with Mental Models: Towards a Cognitive Science of Language, Inference and Consciousness. Cambridge University Press. Cambridge. 1983.

[19] Sonjia M. Geiger and Klaus Oberauer. Towards a reconciliation of mental model theory and probabilistic theories of conditionals. In Cognition and Conditionals. Ed. Cit. p.p.295-296.

[20] This is especially noticeable in children and people without an education in logic or mathematics. See Nilufa Ali et al. Causal discounting and conditional reasoning in children. In Cognition and Conditionals. Ed. Cit. p.p.117-134. And also David E. Over, Jonathan St. B. T. Evans, and Shira Elqayam. Conditionals and non-constructuve reasoning. In Ibid. p.p.135-151. As well as Henry Markovits, Semantic memory retrieval, mental models, and the development of conditional inferences in children. In Ibid. p.p.178-195.

[21] A distinction which is not always so simple to make when we deal with religious constructions.

[22] Analogous to the independence of mathematical objects with respect to the ordered space-time experience to which we call world. In moral judgments, we also deal with ideal objects whose necessity is formal (like that of the mathematical objects) from which its universality is derived.

[23] See Joshua D. Greene. The Cognitive Neuroscience of Moral Judgment. In The Cognitive Neuroscience IV. Department of Psychology. Harvard University. Web. 

[24] A neural net which comprises the orbitofrontal cortex, the temporal pole and the superior temporal sulcus of the left hemisphere, is specifically activated with moral judgments, whereas evocative emotional judgments, but not moral, activate the left amygdala, the lingual gyrus, and the lateral orbital gyrus. (Cf. Jorge Moll et al., Functional Networks in Emotional Moral and Nonmoral Social Judgments. In Social Neuroscience. Op. Cit. p.63.)

[25] See, J.T. Cacioppo and Gary G. Bernston. Social Neuroscience. Ed. Cit. p.p.97-98.

[26] See, J.D. Greene, The Cognitive Neuroscience of Moral Judgment. Ed. Cit. p.26.

[27] Cf. Gerald M. Edelman. Bright Air, Brilliant Fire. Ed. Cit. p.176.