1 Q-RATIONALITY (Q-RAȚIONALITATEA) Abstract The paper discusses some issues regarding the irrationality as an inherent ingredient of any effective (real) rationality model, and consequently, of any decision or action. To this end the ways (channels) through which the irrationality occurs are examined, establishing three categories of possible irrationality: 𝛼-irrationality, 𝛽-irrationality, and 𝛾-irrationality (containing a sub-category called 𝛾 ′ irrationality). The 𝛼-irrationality is analysed vs. Kuhn, Gödel, Heisenberg, and Nicolesco proposals. The standard rationality entered by the irrationality categories is called q-rationality, and is analysed vs. three essays to adjust the genuine rationality model of homo œconomicus (Smith): bounded rationality (Simon), anticipations, and expectations. JEL Classification: B41, C00, E17 Key-words: irrationality, rationality, q-rationality, para-rationality, rationality model 1. Introduction As discussed in previous articles, by rationality we understand a necessary property of a deliberation device able to deliver a kind of justification for a decision or action. Such a justification must verify, however, some accepted or acceptable logic. In other words, the rationality must be discursive only. Being a necessary property of a deliberation device means that such a deliberation device (or rationality model) that has not the property of rationality doesn’t exist. Irrationality signifies, of course, the lack of rationality. So, the irrationality cannot be associated with a rationality model, whatever it would be. As consequence, the irrationality must be seen as a negative property, i.e., a property obtained by logical negation of the property of rationality. However, from a logical point of view also, we can still talk about an irrational rationality1, because there are many rationality models which confront each other in taking decisions, justifying actions, or even choosing the dominant rationality model in a social group. So, there are many contemporary benchmarks of rationality and, as consequence, many cases of identifying irrationalities although they are associated with rationality models, but different. In this paper we will debate the ways (and their signification) in which the rationality and irrationality can be associated. 2. How the irrationality arises We think the irrationality could arise through two channels: a) by logical impossibility of its derivation (inference) from a given rationality model; b) by existing of accepted or acceptable inconsistency in derivation (inference) of a conclusion from given premises. Let’s examine in detail the two channels. (a) Logical impossibility to infer from a given (fixed) rationality model We already stated2 that the irrationality is not an a-contextual concept3 (the same can be said, also, about the concept of rationality), i.e., something (a decision, an action, etc.) is irrational if and only if it is not and cannot be a valid inference from a given rationality model. By valid inference we understand an inference that doesn’t violate the logic principles4. The crucial idea here is that the 1 And, maybe, about a rational irrationality. See, inter alia, our article Rationality and Irrationality, in Œconomica no.1/2015. 3 But the concept of a-rationality is an a-contextual concept. 4 We talk here about the bivalent logic, so about the four well-known logic principles. 2 2 rationality model is given. So, the irrationality can be established only related to that given rationality model. Now, if another rationality model is considered, and it is autonomous related to the first one, then it is possible the irrationality related to the first rationality model become rational related to the second one. This possibility arises just if the irrationality in case can be validly inferred from the second rationality model. Figure 1 exhibits this idea. Figure 1. Irrationality vs rationality contextualization There are, of course, many contemporary rationality models regarding the same cognitive (decision) or praxiological (action) entity. If the logical independence of all the rationality models among them (taken two by two) is verified, then the entity in case is rational only related to a single rationality model and can be5 irrational related to any of the other rationality models. So, given a cognitive or praxiological entity, it is generally irrational and only particularly it is rational. The world of irrationalities seems to be much more populated than the world of rationalities. We will denominate such kind of irrationality as irrationality of species 𝛼 (𝛼-irrationality). A special discussion can be built if we take into consideration some parallelisms: 1) between 𝛼irrationality and Kuhn’s concept of paradigm; 2) between 𝛼-irrationality and Gödel’s theorem of undecidability; 3) between 𝛼 -irrationality and Heisenberg’s concept of theoretical closing; 4) between 𝛼-irrationality and Nicolesco’s concept of levels of reality. (1) 𝛼-irrationality and Kuhn’s concept of paradigm Kuhn’s concept of paradigm says any result of a cognitive process will be constraint to a given and in force model of knowledge area (known as normal science, which describes a so-called paradigm). This compulsion addresses both the searched and the accepted kind of results6. So, the 𝛼-irrationality acts in a similar way: the 𝛼-irrationality is as such considered only if related to a given rationality model. Related to any other logically independent rationality model, it can be of rationality type. (2) 𝛼 -irrationality and Gödel’s theorem of un-decidability Gödel’s theorem of un-decidability says inside an axiomatic theory (that includes the arithmetic 7 ) necessarily there is at least a proposition correctly formed so it is undecidable, i.e., about it we cannot prove neither its truth nor its falsity. The crucial word here is inside, because if a new axiomatic theory (which includes the first theory) is built, 5 We think it is too much to say is irrational instead of can be irrational, because another rationality model can allow its inferential derivation even the new rationality model is logically independent from the first one. 6 The results which do not „verify” the current paradigm are considered anomalies and, regularly, are ignored (however, when the critical mass of accumulated anomalies is reached, a new paradigm, incommensurable with that in force, could occur). 7 The original proving of the theorem was delivered in an arithmetical way (any logical entities was denominated by a natural number). 3 the given un-decidable proposition could become decidable in the new theory8. Let’s observe the similar way in which the 𝛼-irrationality works: if a new model of rationality, including the old one, is built, it is possible the 𝛼-irrationality become a rationality because the new rationality model could allow its „legal” inference. (3) 𝛼 -irrationality and Heisenberg’s concept of theoretical closing Heisenberg’s concept of theoretical closing says any cognitive (at limit, any scientific) result must be considered valid (at limit, have the truth value true) only inside the accepted axioms of the theory that grounded the result obtaining9. Let’s observe that it is „illegal” to extrapolate an obtained result outside the ground theory, so there is here a similar condition like the 𝛼-irrationality case, where the irrational nature cannot be extrapolated to another rationality model different from the initial one and being logically independent from it. (4) 𝛼-irrationality and Nicolesco’s concept of levels of reality Nicolesco’s concept of levels of reality treats the issue of violating the logical principle of the third excluded. Nicolesco says: if the principle of the third excluded is violated, this means another level of reality must be considered (even by including the initial level of reality), so at the new level of reality the third truth logic value is accepted10 and the principle of the third excluded becomes the principle of the third included11. Once again, we can find similitudes with 𝛼-irrationality phenomenon: the 𝛼-irrationality related to a rationality model will „search” a new rationality model to become a rationality, in the same way in which the third excluded will „search” a new level of reality to become the third included. NB: In our opinion, Nicolesco’s concept of levels of reality is a gnoseological concept, although it is presented and explained as being an ontological one. By ontological concept we understand a concept that addresses the Popper’s worlds 1 and 2, while a gnoseological concept addresses the Popper’s third world. So, we think the ontological levels of reality might be named levels of order, while the concept of levels of reality must be reserved for the gnoseological field. Indeed, as Nicolesco argues, a new level of reality resolves the inconvenient of the old such level by a gnoseological way, i.e., by accepting the third included. Or, we have here a gnoseological new layer 8 Of course, we have here a regression to infinite, because the new axiomatic theory verifies the conditions of the first one (i.e., axiomatic character and arithmetic inclusion), so again at least a proposition correctly formed is necessarily undecidable, and so on. 9 For example, the absolute character of the time and space is valid (i.e., „true”) only inside the Newtonian mechanics, where the speed of objects are much under the speed of light in vacuum. So, these results (NB: in fact, Newton presumed initially, as axiom, this absolute character of the time and space) are valid only if we situate the analysis inside the Newtonian mechanics. 10 Essentially, Basarab Nicolesco initiated this theoretical construction in order to supplementary ground Stefan Lupasco’s works regarding a logic of the third included. Since, many logicians and philosophers did make confusion between the third excluded principle with the non-contradiction principle (Lupasco was even accused for rejecting the non-contradiction principle from logic), Nicolescu’s intention was to clarify this confusion and to prove Lupasco’s proposal regards the third excluded principle (so, a third truth logic value) and not the non-contradiction principle (i.e., the principle of principles, as Aristotle stated). 11 To be mentioned that Nicolesco doesn’t propose to elaborate a new logic at the initial level of reality (i.e., the level where the third is excluded), as many logicians made (see, for example Łukasiewicz’s logic with three truth logic values – true, false, and un-determined –, or the polyvalent logics, with a numerable infinite truth logic values). Nicolesco presumes, simply, that a new level of reality will resolve the anomaly identified at the old level of reality by granting the anomaly with the statute of citizenship at the new level of reality. One of the consequences of such an approach is that any new level of reality is naturally endowed with… the appropriate logic aimed to resolve the anomalies inside the initial level of reality. 4 not an ontological one (see in Annex some supplementary considerations on the concept of order and on the levels/layers of order). (b) Accepted (or acceptable) inconsistency of inference Another direction in which the bivalent logic was developed, by the side of accepting the third included, is that of accepting the principle of contradiction. This new logic12 remains bivalent, that is it maintains the two truth logic values (true and false) but concedes that something (either thing or property or relation) could be true and false in the same time and under the same relationship. Of course, a set of provisions must be stipulated to avoid the ex falso quodlibet sequitur13 but, in this case, it is possible a conclusion be derived (inferred) from a rationality model by violating the principle of non-contradiction. Such a conclusion must be considered as being irrational although it is associated and even derived (inferred) from a rationality model. I don’t know what will be the scientific (or, at least, cognitive) role of the paraconsistent logic 14 but for our discussion here it seems to ensure a way (channel) for irrationality occurring. We will denominate such kind of irrationality as irrationality of species 𝛽 (𝛽-irrationality). The issue of qualifying as irrational a valid logical consequence (inference) from a rationality model (as the case of paraconsistent logic) requires some supplementary considerations as follows: - firstly, we think is needed that the rationality model grounded on a paraconsistent logic be called para-rationality model. This way we avoid to weaken the previous assertion that a valid inference from a rationality model must be considered as rational. As a result, we have rationality if and only if we have a valid inference from a rationality model15. In other two cases we have irrationalities from the point of view of a given (fixed) rationality model: a) it is not a valid inference from the given (fixed) rationality model; b) it is a valid inference from a para-rationality model; figure 2 shows these general conclusions; Figure 2. Two ways to occur irrationalities - 12 secondly, a 𝛽-irrationality seems to be inferred simply through a… rational method, when we try to associate an inference either to a rationality model or to a pararationality model. This unavoidable rational behaviour seems to be an absolute limit for The best known name for such a logic is paraconsistent logic (the name was proposed by the Peruvian logician Miró Quesada, in 1976). One of the most productive logicians in the paraconsistent logic is the Brazilian Newton da Costa). In Romanian literature, see I. Lucica, D. Gheorghiu, R. Chirilă, Ex falso quodlibet. Studii de logică paraconsistentă, Editura Tehnică, București, 2004. 13 From false everything can be inferred (including the true). 14 For the moment, I think the paraconsistent logic could be useful for the theory of arguing, but less for the theory of demonstration (proving). So, the paraconsistent logic could contribute to the theory of convincing, but less to the theory of truth. Fortunately, it seems in the social field (including, of course, the economic field) not the truth is crucial, but the acceptable, the convenient, so the paraconsistent logic could be associated to such a soft „proving”. 15 A rationality model must be based only on the bivalent logic that verifies the four logic principles: a) of identity; b) of non-contradiction; c) of the third excluded; 4) of sufficient reason. 5 the human judgement. As consequence, the irrationality cannot be than a… rational outcome; - thirdly, following the second consideration, we would say that the irrationality can be identified, defined and described by only a rational approach. This assertion is very problematic, because it states there is no way to generally know something than the rational one. So, the irrational seems to be a residual of a rational searching. This conclusion brings a new question: really, we are unable to directly identify the irrationality, so we know it only as an unexpected result of our standard knowing process; - fourthly, to directly identify the irrational (or the irrationality) we probably need an… irrational method to examine the general phenomenology. What should mean irrational method is also problematic, because the irrational character of that method could be established, there’s no doubt about, by referring the… rationality; - fifthly, we have seen before that something must be considered as irrational if either it cannot be associated to a given (fixed) rationality model (as valid inference from it), or can be associated to a para-rationality model (also as valid inference from it). Let’s observe that in both cases we presume there is a given (fixed) rationality model, either orthodox or para-consistent. We will examine now the much more frequent case of irrationality as impossibility to be associated to a rationality model, either orthodox or para-consistent. Indeed, it is not always possible to associate an outcome (decision or action) to a somewhat rationality model simply because we don’t know such a rationality (or para-rationality) model. This case is outside the two already mentioned, so we still have irrationality when we are unable to associate an outcome to a rationality (or para-rationality) model. As consequence, we can establish a new kind of irrationality, based on this case, and that could be named 𝛾-irrationality. So, generally, there are three distinct categories of irrationality (figure 3). Figure 3. The three basic categories of irrationalities 3. What means q-rationality Most of recent works on the human behaviour put into evidence many cases and situations in which that behaviour cannot be qualified as being rational (either related to rationality or para-rationality models, or un-related to such models). So, either from theoretical perspectives or from experimental ones, both 𝛼-irrationality, and 𝛽-irrationality, and 𝛾-irrationality were identified or, at least, presumed to work in „explaining” the empirical human behaviour (especially at individual level). This might mean that such irrationalities are integrated by individuals in their current (praxiological and practical) behaviour. How this happens? We will propose below a theory in the matter. 6 As we stated in a recent article16, the intention (that is, the first objective, so observable, signal of the individual), as following the motivation, is „born” inside the under-awareness. The underawareness cannot be described in a rational way17, by definition. So, if any category of irrationality (either 𝛼, or 𝛽, or 𝛾) enters an examined outcome, so we should, probably, talk about an irrational rationality or about a quasi-rationality or, at least, about an impure rationality. In our opinion, the rationality is a concept of maximalist nature, so it doesn’t tolerate irrational ingredients (episodes, causes, conditionalities, etc. In this point we want to propose for this situation the term qrationality, (from quasi-rationality18) because, in fact, the rationality we have currently before eyes is not a kind of rationality that is truncated, bordered, or limited in any kind19, so it isn’t a form of imperfect or of incomplete rationality20, but something that qualitatively remains rationality. 4. Some lateral remarks 4.1. Q-rationality and bounded rationality More generally, we want to refer to the relationship between q-rationality and any quantitative adjustments of the complete/perfect rationality as ideal benchmark. The key-word here is „quantitative”. The economic case is the most exemplar: the initial rationality model of homo œconomicus was, almost permanently, adjusted by the analysts in order to bring it closer to the real (effective) economic behaviour. To be notified, however, that all these adjustments were of quantitative nature, that is, have been focused on restraining the sphere of the valid rationality model in case. So, the proposals have been made regarding the incompleteness of such a rationality (for example, the small capacity to get the information required), or the imperfectness of it (for example, the small capacity of calculus). The concept of bounded rationality is the most known concept regarding the adjustment of the initial rationality model of homo œconomicus (Smith’s genuine proposal). On the contrary, the q-rationality is not concerned about the quantitative sphere of the rationality (i.e., the extensive determination), but about the qualitative sphere of it (i.e., the intensive determination). For example, the 𝛼, 𝛽, or 𝛾-irrationalities (including the sub-category of 𝛾 ′ -irrationality) that enter the initial rationality modifies the structure of the rational decision or action21. 16 Selecting the intention: A Darwin-ist Approach (see Œconomica no.2/2015). However, such a trying is not theoretically impossible: indeed, probably the main only „criterion” working inside the under-awareness is the surviving criterion. So, based on this criterion, a „rationality” model of the „irrationality” could be built, in the same way in which the homo œconomicus rationality model was edified based on the egoism criterion of individual behaviour. 18 Although it seems we have here an oxymoron. 19 Let’s clarify here the well-known concept of bounded rationality (introduced by Herbert Simon). Simon didn’t intend to talk about an impure rationality but simply about a rationality that necessarily doesn’t control all of our decisions or actions, so about a quantitatively not qualitatively limited rationality. So, Simon’s concept addresses the referential sphere of the concept of rationality (diminishing it), not its semantic as such. By a contrary, what we want to express here is the semantic impurification of the concept of rationality, that is, the rationality is not only the orthodox (pure) rationality, but it contains some ingredients of irrationality in any of the three senses identified above. So, we could have still a bounded q-rationality by operating Simon’s suggestion not on the pure concept of rationality, but on the impure concept of rationality which we talk about here. More specific speaking, while Simon operates an extensive reduction on the concept of rationality we operate an intensive reduction on it. As already stated before, the two reductions are not inconsistent between them, on the contrary, they could logically interfere. 20 The current ways of adjusting the original rationality model named homo œconomicus have as purpose just the integration of imperfection, incompleteness, or other such vulnerabilities related to an ideal benchmark of the economic expected behaviour. 21 We will always consider the structure as a qualitative determination of an entity. The reason is that the structure ensures the identity of that entity. Or, the identity is the most qualitative issue of an entity. 17 7 4.2. Q-rationality and anticipations Let’s firstly clarify the logical statute of the anticipation: an anticipation is a result of calculus. Generally, any calculus is inferred from a rationality model. So, we have here some distinct situations related to an outcome from a given rationality model: a) the outcome is rational, so it is a valid inference from the given rationality model; if an anticipation is added to this outcome, it can be derived either: a.1) from the same given rationality model, so the initial outcome is not qualitatively perturbed; or a.2) from other rationality model, so it is irrational related to the given one ( 𝛼 -irrationality); or a.3) from a para-rationality model ( 𝛽 -irrationality); or a.4) from no rationality model identifiable (𝛾-irrationality). In the specialty literature is talking about two kind of anticipations: 1) rational anticipations, so here we have the case a.1) above; 2) adaptive anticipations. The adaptive anticipations are not conceptually different from the rational anticipations, the only distinctions being of procedural order only: in the case of adaptive anticipations, the… rational anticipations are permanently adjusted related to the difference between the initial anticipations and their effectiveness . So, the anticipations based on the same given rationality model don’t introduce modifications into the rationality. Instead, if we have the situations a.2, a.3, and a.4, the anticipations transform the initial rationality into q-rationality. 4.3. Q-rationality and expectations Unlike the anticipations case, the expectations are not the result of a calculus22, but simply they represent desires, hopes, dreams, etc. of the decision maker or of the action maker. So, the origin of the expectations is not the awareness (or the consciousness), but the under-awareness23. The most probable category of such expectations is that of 𝛾-irrationality, with the difference that it is not calculated in any kind. We could call this sub-category of the 𝛾-irrationality, that is not properly calculated, as being 𝛾 ′ -irrationality24. Selected bibliography 22 • Dinga, E. (2012), Rebuilding Economics. A Logical, Epistemological and Methodological Approach. Lambert Academic Publishing, Saarbrucken, Germany. • Hollis, M. (2001), Introducere în filosofia științelor sociale, Editura Trei, București, 2001. • Kincaid, H.; Ross, D. (2009), The Oxford Handbook of Philosophy of Economics, Oxford University Press. • Kincaid, H.; Ross, D. (2012), The Oxford Handbook of Philosophy of Social Sciences, Oxford University Press. • Mele, A.R.; Rawling, P. (2004), The Oxford Handbook of Rationality, Oxford University Press. • Nozick, R. (1995), The Nature of Rationality, Princeton University Press, Princeton, New Jersey. To be notified that no calculus is possible outside of a rationality model, whatever would be it. A sketched connection to the probability theory is un-avoidable here: indeed, the anticipations could be expressed through the objective probabilities (i.e., probabilities based on archived frequencies), while the expectations could be expressed through subjective probabilities (of course, expressing the expectations as subjective distributions of probability means to transform the 𝛾-irrationality into 𝛾 ′ -irrationality). To be mentioned that, in the case of subjective probabilities, expressing the expectations as distributions of probability (subjective random variables) doesn’t mean, in no case, something like calculation. 24 Logically, the expectations cannot be introduced in our rationality model, because this introduction means their awarenessing. But, the awarenessing means, in its turn, a quasi-calculus, so the transformation of the expectations into anticipations. Effectively, we can have within our rational decisions or actions anticipations only. In this consists, in fact, the difficulties of applying Popper’s criterion of falsifiability in the social field, where the world of expectations is much more populated than the world of anticipations. 23 8 • Pearl, J. (2009), Causality: Models, reasoning, and inference (second edition), New York, Cambridge University Press. Annex Levels/layers of order25 Thesis 1: The order has an ontological statute - the order exists independently from the subject (the Popper’s world 2 is also independent from the subject) - the subject perceives the order by two categories: a) discovery (accessible to any subject); b) invention (accessible only to cultural subjects26) - the order has two hypostases: a) the phenomenological hypostasis (perceived by any subject); b) gnoseological hypostasis (perceived only by the cultural subject) - NB: the gnoseological hypostasis is not independent from the phenomenological one, but implies it logically and chronologically (is imposed the Heidegger-ian requirement as, before scientific perceiving, must exist a phenomenological one as propaedeutic to the first) Thesis 2: The order is either potential or actual - the potential grounding of the order is delivered by the principle of causality (it has a necessary character and is independent from the subject) - the actual grounding of the order is delivered by the principle of intelligibility (it has a contingent character and is dependent from the subject) - the actualization of the potential order occurs through reflection - as perception for the a-cultural subject, having a primitive, non-mediated nature and addressing the signification, i.e., the denotation - as representation for the cultural subject, having a derived, mediated nature and addressing both the signification and sense, i.e. both the denotation and the connotation Thesis 3: There are three levels/layers of order - natural order (NO) - NO is an emergent order (i.e., a non-deliberative onticization) - emergence of NO is analytical, so it doesn’t generate novelty27 - the predictability of NO is complete, because of the lack of novelty - the predictability of NO is exclusively external (that is, it is possible only from superior levels/layers) - NO has finality, generated by the principle of causality - NO implies only objects (it doesn’t contain subjects) 25 More developments on the issue will be published in a future article. By cultural subject we understand the subject endowed with awareness (NB: the consciousness is grounded on the awareness). 27 By novelty we understand an un-predictable onticization. 26 9 - NO is not endowed with purposes (the purposes are prohibit because the lack of subjects) - (Example) a star system without life or a mineral on the Earth - quasi-social order or para-social order (C-SO) - C-SO is a down-top objectified order (down-top non-deliberative onticization) - C-SO objectifying is of synthetic nature (the novelty is possible) - C-OS predictability is incomplete (as follows of the novelty presence) - C-SO implies both objects and a-cultural subjects - C-SO predictability is both external and internal (the last as follows of the a-cultural subjects presence) - C-SO predictability is atomized (it occurs only at individual level of the a-cultural subject) - C-SO has finality - C-SO hasn’t purpose (because the a-cultural subjects are not capable of representations) - (Example) an ants colony or a natural reservation without cultural subjects - social order (SO) - SO is a top-down objectified order (top-down deliberative onticization) - SO objectifying is of synthetic nature (the novelty has a necessary character) - SO implies objects, a-cultural subjects, and cultural-subjects - SO predictability is impossible (as result of the necessary novelty generated by the cultural subjects28) - SO has purposes (as consequence of cultural subjects presence) - SO is preponderantly normative (as consequence of the top-down deliberativeness) - SO normativity can be either individual or aggregate - (Example): a human society in a country or on a planet Thesis 4: Levels/layers of reality vs. levels/layers of order - the level/layer of order is an ontological category, while the level/layer of reality is a gnoseological category - so, between the level of order and the level of reality no logical connection occurs - the gnoseological is transversal related to the ontological - the gnoseological can be applied to any ontological level - the „head” of gnoseological is exclusively the SO - 28 the criterion to require a new level/layer of reality is the explicative29 incompleteness The cultural subjects can modify both the initial conditions and the movement law of the dynamic systems (the Oedipus effect). 29 As we stated in many of articles published by Œconomica, an explanation is a description of causality. 10 - a new level/layer of reality is an „explicative world” that eliminates this incompleteness - so, there are as many levels/layers of reality as many explicative incompletenesses occur - there is a connection between the level/layer of reality and the meta-language - just they are logically equivalent - example 1: the Gӧdel incompleteness can be eliminated in a meta-language, so on other level/layer of reality (i.e., on a new gnoseological layer) - example 2: the inconsistence between the quantum mechanics and the relativistic mechanics can be eliminated in a meta-language, probably in a string theory (i.e., on a new gnoseological layer)