How our brains reason logically Markus

The intention of this article is to create a link between cognitive brain research and formal logic. As the paper is aimed at a highly interdisciplinary readership, I have cut down the physiological/anatomical and logical/technical treatments to a minimum. The work covers three fundamental sorts of logical inferences: reasoning in the propositional calculus, i.e. inferences with the conditional “if...then”, reasoning in the predicate calculus, i.e. inferences based on quantifiers such as “all” some”, “none”, and reasoning with n-place relations. Studies with brain-damaged patients and neuroimaging experiments indicate that such logical inferences are implemented in overlapping but different bilateral cortical networks, including parts of the fronto-temporal cortex, the posterior parietal cortex, and the visual cortices. I argue that these findings show that we do not use a single deterministic strategy for solving logical reasoning problems. Sometimes the way we reason is logically analogous to the proofs of formal logic, sometimes we think logically by using models in the strict logical sense, and sometimes we use visual mental images. This account resolves many useless disputes about how humans reason logically and why we sometimes deviate from the norms of formal logic. Knauff: How our brains reason logically 3 It was the second half of the winter term 1888-1889. I was a medical student at the psychiatric clinic of Professor Otto Binswanger in Jena. One day a patient was brought in to the lecture hall, who had been recently committed to the institution. Binswanger introduced him to us Professor Friedrich Nietzsche! [...] At first sight, he did not appear like a sick man. He was of middle size, and his expressive face was angular, but not derelict. [...]. Sometime later I saw him again and then he appeared completely different. He was in a highly excitable state and his consciousness was obviously clouded. He was sitting there with wild-painful, fiery eyes and was watched by a guardsman. Friedrich Nietzsche was one of the greatest philosophers of the nineteenth century. The report of his mental illness was published by a medical student later Dr. S. Simchowitz – in the Frankfurter Zeitung from Sep./07/1900 (Simchowitz, 1900, the above passage is my translation from the original German newspaper article). Figure 1 shows the admission files from the psychiatric clinic in Jena and Figure 2 a photograph of Nietzsche sitting in the sanatorium. Some scholars have spread the rumor that Nietzsche’s dementia was caused by a cerebral syphilis that he had contracted some 20 years ago (Möbius, 1902). The diagnosis now seems problematic, because no Wasserman test (an antibody test for syphilis) was yet available, no autopsy was performed, and clinical grounds alone argue against the diagnosis (Fishman, 2002; Sax, 2003; Schain, 2001). However, for a cognitive neuroscientist it is of more interest that some of Nietzsche’s mental abilities were strongly affected by his brain illness while others seemed to be completely intact. Many witnesses reported that Nietzsche was unable to formulate coherent thoughts or to think rationally. His friends and relatives were unable to distinguish the ideas of the genial thinker from those of a madman. On the other hand, many biographers report that his memory was almost intact and he could speak without slurring his words (Schain, 2001). Knauff: How our brains reason logically 4 Figure 1: Left: Coversheet of the admission files from the psychiatric clinic in Jena. Right: filled-in patient admission form. © Picture: Dwars; Source: Klassik Stiftung Weimer, Goethe Schiller Archiv. Figure 2: Nietzsche sitting in the “IrrenHeilund Pflege-Anstalt zu Jena”. © Picture: Schellbach; Source: Klassik Stiftung Weimar, Goethe Schiller Archiv. Knauff: How our brains reason logically 5 Today, about one century later, it is well known that brain infections, or damages from tumors, strokes, or brain traumata, can have severe effects on some cognitive functions while others remain entirely untouched. Historically viewed, the famous psychologist Karl Lashley (1929) was obviously wrong when he claimed that cognitive functions are distributed throughout the entire cortex rather than localized to one part of the brain. We now know that there is a degree of modularity in the brain’s overall organization (Goel, 2005). For instance, we have identified some brain regions specifically involved in the processing of visual information, others in the processing of spatial information, and yet more in the processing of heard language and the generation of speech. A few years ago a small number of psychological laboratories started to systematically investigate the connection between logical reasoning and the brain (overviews in: Goel, 2005; Grafman & Goel, 2002; Knauff, 2006; Wharton & Grafman, 1998). Before that most reasoning researchers were committed to the assumption that human reasoning should be studied in terms of computational processes. How these computations are biologically implemented in the human brain has been considered insufficient, because each computational function can be computed on each hardware (and thus also the brain) that is equivalent to a Turing machine (e.g. Fodor, 1975; Newell, 1980; Pylyshyn, 1984). The progressing neuro-cognitive movement in reasoning research is based on the fact that this “independence of computational level” hypothesis seems questionable to several researchers. First, the assumption that each function computable by a Turing Machine can be computed on all Turingequivalent machines is not entirely true (Giunti 1997, Goel 1995). It is true that computational processes can be realized in many different systems, but it is not true that they can be realized in all Turingequivalent machines. The assumption of universal realizability thus appears to be unjustifiable (Goel 2005). A second reason for the new interest of reasoning researchers is that localization in the brain can help us to understand the format of mental representations. As already mentioned there are highly specific brain regions dedicated to particular representational formats. If a reasoning process is Knauff: How our brains reason logically 6 associated with brain areas which are known to respond to verbal information, then this might support one class of reasoning theories. If it is associated with brain areas that are typically involved in the computation of information in a visual or spatial format then this speaks in favor of other theories of reasoning. It is this commitment to the testing of cognitive hypotheses that distinguishes the cognitive neuroscience of reasoning from pure brain research. The cognitive neuroscience of reasoning is not interested in what Uttal (2001) called the “new phrenology”, namely the pure localization of cognitive processes including all the reductionistic implications. Another way in which the field differs from pure brain research is that cognitive neuroscientists combine their exploration of the brain with behavioral methods in which we typically measure error rates, solution times, and response preferences. This is done because there is a many to many mapping between cortical regions and cognitive functions, and thus neuroanatomical data alone are too weak to formulate cognitive theories of human reasoning. The aim of the paper is to create a link between the cognitive neuroscience of reasoning and formal logic. This paper covers three fundamental sorts of logical inferences: Cognitive psychologists refer to the first as conditional reasoning. In such inferences the statements of the problem consists of an “if A then B” construct that posits B to be true if A is true. The two logically valid inferences are the Modus Ponens (if p then q; p; q, MP) and the Modus Tollens (if p then q; not-q; not-p, MT). For a logician the normative model of such inferences is the propositional calculus. The second type of inference, cognitive scientists call syllogistic reasoning. Here the problem consist of quantified statements such as “All A are B”, “Some A are B”, “No A are B”, and “Some A are not B”. Logically speaking, the normative model for such inferences is the Aristotelian syllogisms which are a subset of the (first order) predicate calculus. The third group of inferences treated in this paper is probably the most frequently used in daily life (and in the psychological lab). It is based on n-place relations. At least two relational terms A r1 B and B r2 C are given as premises and the goal is to find a conclusion A r3 C that is consistent with the premises. These relations can represent spatial (e.g., left of), temporal (e.g., Knauff: How our brains reason logically 7 earlier than), or more abstract information (e.g., is akin to). Logicians have studied such inferences since classical times, but the most ingenious work was done by the American logician C. S. Peirce (see the collected writings of Peirce in Hartshorne, Weiss, & Burks, 1931-1958). Pierce formally explored the way in which relations can be combined to form a single new relation and his approach still serves as the normative model to evaluate the formal correctness of relational inferences. In the first part of the paper, I report empirical findings on all three sorts of inferences. The findings show how we deal with such problems, which logical abilities break down after local brain injuries, and which areas of the cortex are involved if neuropsychologically healthy human beings think logically. The second part of the paper is concerned with one of the oldest questions related to logical reasoning. What is the role of imagination in (logical) thinking? Aristotle regarded imagination as a sort of mental faculty that plays indispensable roles in perception and thought (Aristotle, De Anima, III: 3, quoted after Wedin, 1988). In the Critique of Pure Reason, Kant distinguished between “reproductive” and “productive” imagination (Einbildungskraft; see Kant, 1787/1998, e.g. A 100-102, A 118-120). Reproductive imagination is essential in the apprehension of empirical phenomena as it supplements the incomplete input of the sensory systems; its materials are past perceptions and experiences. Productive imagination, in contrast, transcends the perceivable or what is empirically given and is the source of abstract and universal categories and thoughts. This “productive” imagination is, psychologically speaking, probably what humans introspectively experience as “thinking in the inner eye”. People with no education in the cognitive sciences but also many cognitive researchers often believe that our ability to reason logically relies on such “productive imaginations”. So do we think logically by visualizing “mental pictures” in the “mind’s eye” and “look” at these pictures to find new, not explicitly given information? I will use the subset of relational inferences to describe the research in our lab on this question. I start from Peirce’s work on the composition of relations. Peirce did not distinguish between formal and mental reasoning with relations and simply referred to all representations and thoughts Knauff: How our brains reason logically 8 collectively as signs. He distinguished three properties of signs. A sign can be iconic, such as a visual image, if it is structurally similar to what it represents, it can be indexical, if it uses direct physical connections such as in an act of pointing, and it can be symbolic, such as in a verbal description (Peirce, 1931-1958). I will show that iconic representations do indeed play a role in human logical reasoning. Yet, they have other functions than those one might expect. In the third part of the paper I formulate some general ideas on the link between formal and mental logical reasoning and the role of cognitive neuroscience in reasoning research. I will formulate some thoughts on the question of whether brain-events tell us something about mental logical reasoning and will argue that the huge explanatory gap between the behaviors we can observe and the brain activity we can measure can be closed by computational theories of human mental reasoning. The article ends with the conclusion that sometimes the way we reason is logically analogous to the proofs of formal logic, sometimes we think logically by using models in the strict logical sense, and yet sometimes we use visual mental images. Logical thinking from a neuro-cognitive perspective When we use the term “logical thinking” in daily life, we mean almost all kinds of thoughts, ranging from very elemental inferences up to the complex development of scientific theories and the creation of pieces of art. From the writings of Nietzsche’s biographers it is not really clear what they meant when they said that he was unable to think logically. Most likely, the witnesses used the term in a very broad sense too and in fact the biographers do not report any psychological tests that are today routinely used to test brain damaged patients logical skills. Probably, Nietzsche had no deficits in logical reasoning in the literal sense. To avoid such a terminological confusion in contemporary psychology we prefer the term “deductive reasoning” instead of “logical reasoning”, although formally speaking both expressions mean exactly the same: an inference in which one or more propositions are true given that other Knauff: How our brains reason logically 9 propositions are true. The propositions that are taken for granted are called premises. The propositions that are deducted from the premises are referred to as conclusions. The participants of an experiment can draw the conclusions in many different ways. I will refer to them as “inference verification” and two sorts of “active inference” (Knauff, Rauh, & Schlieder, 1995). To make the difference explicit we can introduce the notation {φ1 , φ1} > φ3, to denote the fact that the conclusion is compatible with the premises. Then the three paradigms may be written as follows: (1) inference verification: does {φ1 , φ1} > φ3 hold? (2a) active general inference: find all φ3 such that {φ1 , φ1} > φ3 (2b) active particular inference: find some φ3 such that {φ1 , φ1} > φ3 It is essential to see that the term “conclusion” is only used as the last statement of a deductive problem. The conclusion must be generated by a human reasoner or a statement referred to as “conclusion” is presented and the individual has to decide if it logically follows on from the premises. Thus, in the psychology of reasoning a “conclusion” can be logically invalid and the response of a human reasoner is correct if he or she recognizes that it is. The words “true” and “false” and “valid” and “invalid” are strictly reserved for the logical evaluation of the statement, while the terms “correct” and “incorrect”, “right” or “wrong” refer to the reasoners’ decisions. Reasoning researchers typically distinguish between two types of correct and two types of incorrect decisions. The distinction is borrowed from the signal detection theory, which is an important statistical theory of psychophysics that is used when psychologists explore how individuals make judgments under uncertainty (Wickens, 2001). The model is comparable to the signal to noise ratio used in the engineering sciences, for instance when important signals of a machine must be separated from background noise. In this metaphor it becomes apparent that formal logic plays an essential role for the psychology of reasoning. The latter serves as the normative model for the former, or, in other words, for a reasoning researcher the logical validity has the same facticity as a physical signal. The researcher explores how well individuals can separate a logically Knauff: How our brains reason logically 10 valid conclusion from other (invalid) alternatives and why they (sometimes) deviate from the norms of logic. The psychology of reasoning is descriptive and concerned with mental logical reasoning, whereas formal logic is normative and defines the criteria that must be satisfied to call such mental inferences logically valid. In this vein, an individuals’ decision is counted as a correct response if a presented conclusion is logically valid and she or he says it is valid. This match between logic and decision is labeled a “hit”. If the presented conclusion is logically invalid and the participants identifies it as invalid this is also a correct response – a “correct rejection”. If the presented conclusion is logically valid and the participant says it is invalid then the response is considered as incorrect – “false alarm”. If, finally, the presented conclusion is logically valid but the participants of the experiment says it is in invalid this is also an incorrect response – a “miss”. This important connection between logical validity and psychological correctness is summarized in Table 1. Table 1. The connection between logical validity and psychological correctness.