Logical competence

The notion oflogical competence (LC)was first used by Macnamara (1986). It is used in cognitive psychology, analogously to the notion of linguistic competence

introduced by Noam Chomsky, to name a specific cognitive mechanism enabling to complete single logical tasks, for example performing reasoning in natural language according to some logical inference patterns. We assume that:

1. The human mind is equipped with such a mechanism.

2. This mechanism of logical competence consists of two basic functions: (a) Passive logical competence: an ability to evaluate, on the basis of given

premises, a given conclusion as a correct or incorrect inference.

(b) Active logical competence: nn ability to generate, on the basis of given premises, a correct conclusion.

Few things require explanation here – especially what we mean by a correct inference. It might seem that the notion of logical competence presupposes an absolute notion of logical correctness. The traditional approach to logical compe- tence follows this attitude and, putting the main stress on how logical competence is divergent from logical correctness, defines the later with respect to classical logic. Thus a reasoning instance is correct if it is a classically valid inference.

In the psychological literature, it is a widespread view that reasoning proceeds according to some pre-established logical laws and thus may be either correct of incorrect, depending on whether it stays in accordance with these laws or not. A list of logical mistakes most frequently made by people is usually given together with putative explanations as to why people tend to make these very

mistakes (and not some others). The famous atmosphere effect is an example. This is a notion used to explain people’s preference to infer conclusions of a specific form from premises of a specific form. For instance the lack of particular conclusions inferred in the case of syllogisms with both universal premises is explained by saying that universal premises create a “universal atmosphere” and in this way they suppress the particular conclusion. (Nęcka, 2006) Such a view ignores the fact that in the classical sense validity of an inference with a universal premise and a particular conclusion requires an additional assumption of non- empty domains. Thus it classifies correct – in the light of the classical logic – reasoning as incorrect. Moreover, it also tries to explain human behavior by a very vague, if not meaningless, notion of “atmosphere”. Such partial and unsuccessful theories are the result of a false conjecture that the correctness of a given piece of reasoning is somehow decided by the laws of the classical logic and disobeying these laws is a malfunction of our logical competence mechanism.

The root of such a view on reasoning is the assumption that logic is “domain- independent”, which means that what is a correct inference does not depend on a specific domain. In other words it is supposed that inferences are correct or incorrect independently of the domain in which one reasons. Logic indeed is domain-independent in a sense that each chosen logical system (classical logic, many-valued logic, etc.) is such. However the logic of reasoning, thus the set of schemata used by humans, is domain-dependent, which means that the valid schemata depend on the domain: different schemata from different logical models are applied to different domains. There is no absolute logical system that can be recognized as the “logic of mind”, no universal pattern applicable to all different forms of natural reasoning. Specific domains require specific interpretations.

It has been shown (most of psychology handbooks mention this as a fact: (Sternberg, 1996), (Nęcka, 2006)) that reasoning is indeed dependent on numer- ous factors, such as the linguistic context and content of a given reasoning, sub- ject’s knowledge or ontological status of alleged entities. Nevertheless, it is still frequently claimed that these phenomena are disturbances of logical competence and evidence that humans do not cope well with logic, and thus that our logical competence may or may not function in accordance with logical correctness.

However, if logical competence is a mechanism analogous to linguistic com- petence, the notion of logical correctness requires reformulation. A claim that some systematic discordance of human reasoning with classical inference schemes proves imperfection of our logical competence mechanism would be similar to telling that systematic ungrammaticality (in a sense of a language phenomenon not coherent with the prescriptive grammar) occurring in some ethnic language is a proof of dysfunction of human linguistic competence – a view contemporar- ily considered as false and obsolete. What is grammatical or ungrammatical is defined by our linguistic competence, so by some module we have in our heads determined partly by the Universal Grammar and partly by parameters of specific ethnic languages. Thus, this is grammar that should fit our linguistic competence

2.1. Introduction 29 and not the other way round. Similarly, it is ourlogical competence that de- fines what is a correct inference and hence there is no “divergence” between logical correctness and logical competence.1

Michiel van Lambalgen and Keith Stenning (2008) claim that human rea- soning consists of two stages: reasoning towards an interpretation (establishing the domain in which one reasons and its formal properties) and reasoning from an interpretation (following the formal laws that are implied by the fixed inter- pretation). We agree with this view and propose that the mechanism of logical competence applies to both stages. First of all, this is our competence that de- fines logical schemata for different domains of reasoning on the interpretation stage. Secondly, the competence enables to follow the rules as soon as the formal model is fixed (however unconscious may be this process). One should note, that even if we use in reasoning various domain-dependent schemata, we still have to be able to adhere to some logical laws – the ones that apply to a given domain. Otherwise one would have to agree that humans are totally irrational. Moreover, the schemata that are chosen at the stage of establishing an interpretation need to have some nice logical properties. What kind of properties is a vast question, which we will not answer now, however, intuitively, those schemata cannot be totally arbitrary. Last but not least, the logical competence mechanism must be in a sense universal, which means that similar domains involve similar schemata that are used by all humans. Whether or not this mechanism is universal in a sense that there exists a general theory (analogous to the X-bar theory in linguis- tics) that would universalize the “logic of mind” (so would imply all the schemata that are used in various domains) is another question and remains open.

The very last thing that needs explanation is the above-mentioned distinction between passive and active competence. One may doubt if these are really two separate functions of the mechanism, however it seems very plausible that there is indeed a difference between the two processes: passive evaluation of an inference and its active generation. Such a phenomenon has been observed also in linguistics – the skill of generating grammatical utterances differs from the skill of evaluation whether a given expression is grammatical or not.2

1_{On the other hand not every ungrammaticality is accepted, and also not every illogicality}

will be. In linguistics one differentiates betweencompetence andperformance – a competence defines grammar, but a specific use of competence may of course be incorrect because of various reasons, e.g. complicated multiply embedded constructions, processing difficulties, memory malfunctioning etc.; analogously in the case of logical competence – a big number of premises for example may be a hindering factor and a source of possible mistakes.

2_{Such a difference can be found also between language generation and language compre-}

hension mechanisms, which – since they can be separately impaired – are shown to be two distinct cognitive functions. There are kinds of aphasia consisting in dysfunction of production of grammatical language (both spoken and written) with a properly functioning language com- prehension. This is called “Broca’s aphasia”. In a related syndrome patients with Wernicke’s aphasia produce fluent, grammatical, but nonsensical (without semantical sense) speech and display problems with understanding language. In a sense, passive logical competence is more