Abstract

Deductive and probabilistic reasoning are central to cognition but the functional neuroanatomy underlying them is poorly understood. The present study contrasted these two kinds of reasoning via positron emission tomography. Relying on changes in instruction and psychological ‘set’, deductive versus probabilistic reasoning was induced using identical stimuli. The stimuli were arguments in propositional calculus not readily solved via mental diagrams. Probabilistic reasoning activated mostly left brain areas whereas deductive activated mostly right. Deduction activated areas near right brain homologues of left language areas in middle temporal lobe, inferior frontal cortex and basal ganglia, as well as right amygdala, but not spatial–visual areas. Right hemisphere activations in the deduction task cannot be explained by spill-over from overtaxed, left language areas. Probabilistic reasoning was mostly associated with left hemispheric areas in inferior frontal, posterior cingulate, parahippocampal, medial temporal, and superior and medial prefrontal cortices. The foregoing regions are implicated in recalling and evaluating a range of world knowledge, operations required during probabilistic thought. The findings confirm that deduction and induction are distinct processes, consistent with psychological theories enforcing their partial separation. The results also suggest that, except for statement decoding, deduction is largely independent of language, and that some forms of logical thinking are non-diagrammatic.

Introduction

Of the varied talents of the human brain, one of the most impressive is its ability to reason, that is, to reach new conclusions (however tentative) on the basis of facts and suppositions already in hand. As much as perception, language and motor behavior, it is reason that allows us to interact successfully with the physical and social environment. In spite of the centrality of reasoning, its functional neuroanatomy is at present poorly understood and has only recently begun to be examined via brain imaging.

The goal of the present study is to identify and contrast the brain areas underlying deductive versus probabilistic reasoning. Deduction underlies the intuition of necessity that accompanies inferences like: ‘No politician is both lazy and corrupt, therefore every politician is either not lazy or not corrupt’. Probabilistic reasoning yields intuitions of likelihood (in contrast to certainty). For example, many people judge it likely that the ice caps will melt before 2050 on the assumption of increased oil consumption in the next 50 years.

Alternative perspectives on the psychology of deductive and probabilistic thought suggest different hypotheses about the functional neuroanatomy of reasoning. According to one school of thought, deductive reasoning is grounded in the structure of language (Braine, 1978; Rips 1994). Such a view makes it plausible that logical thinking depends on left-hemisphere language areas. [The dependence is often claimed explicitly, as in Weston, p. 116 (Weston, 1999).] A rival perspective grounds logical implication in the non-linguistic interpretations that render sentences true or false (Johnson-Laird, 1994). Since the interpretations are conceived as schematic in character, right-hemisphere participation in logical thinking is foreseen [as in Johnson-Laird (Johnson-Laird, 1994)]. Theories that conceive probabilistic and logical reasoning as drawing on similar mental operations (Johnson-Laird et al., 2001) raise the possibility of similar neural substrates for the two kinds of thinking. This very hypothesis is advanced in Cosmides and Tooby (p. 61) (Cosmides and Tooby, 1996).

Some of the foregoing claims have been evaluated via neuro-imaging studies of syllogistic reasoning. Using positron emission tomography (PET) to record brain blood flow in men reasoning about syllogistic stimuli, two studies observed distinct neural activations for probabilistic versus deductive problems (Goel et al., 1997; Osherson et al., 1998). But in one study deduction was primarily in right posterior and right frontal brain areas (Osherson et al., 1998) whereas in the other it was mostly in left frontal and left temporal brain areas (Goel et al., 1997). The latter finding was replicated in a follow-up experiment in which men reasoned about categorical syllogistic, spatial relational and non-spatial relational deductive problems (Goel et al., 1998). Even for spatial relational syllogisms, Goel et al. observed activations only in the left hemisphere (Goel et al., 1998). This is unexpected in light of earlier reports of impaired reasoning on spatial relational problems by patients with insult to the right hemisphere (Caramazza et al., 1976; Hier and Kaplan, 1980, Read, 1981; Grossman, 1982; Grossman and Haberman, 1987).

The inconsistent findings may result from different methods of contrasting the activations associated with alternative forms of reasoning. In Osherson et al., identical stimuli were used to elicit both probabilistic and deductive reasoning; instructions and preceding problems were used to ‘set’ the thought processes applied to a given stimulus (Osherson et al., 1998). In Goel et al., distinct stimuli were employed to elicit the two forms of reasoning, thus leaving open the possibility that observed activations depended as much on the stimuli as the reasoning task (Goel et al., 1997). The discrepant findings might also be partly explained by the special character of syllogisms, which are known to encourage a variety of reasoning strategies, including mentally represented diagrams (Ford, 1995). It may be that subjects in the different studies relied on diagrammatic reasoning to different extents, leading to different activation levels in brain areas hypothesized to underlie visual imagery, i.e. bilateral or predominantly right posterior, frontal and prefrontal regions (Jonides et al., 1993; Kosslyn, 1994; Courtney et al., 1998; Parsons and Fox, 1998; Dehaene et al., 1999; Farah, 1999).

To reduce the role of strategies involving visual–spatial imagery, the present study employed tasks based on propositional logic, which lends itself less readily to diagrammatic reasoning. For example, from the premise If it is cold in Sacramento then it is cold and rainy in San Francisco, propositional logic allows deduction of the conclusion If it is not rainy in San Francisco then it is not cold in Sacramento. A sophisticated reasoner might discover a diagrammatic scheme for verifying the validity of such inferences, but this seems less likely than for syllogisms. We therefore constructed propositional logic stimuli each of which could support both probabilistic and deductive reasoning tasks, as well as a comprehension control task (involving detection of semantic anomaly). PET measures of regional cerebral blood flow were then obtained while subjects performed the three tasks with identical, visually presented stimuli. The different kinds of reasoning (probabilistic, deductive, anomaly detection) were psychologically ‘set’ by changing the instructions to subjects, and by embedding the scanned tasks within longer series of problems involving reasoning of the desired kind.

In sum, the present study was designed to determine the extent to which deductive and probabilistic reasoning rely on the same brain regions, as well as to shed light on the role of primary linguistic areas and of primary visual–spatial processing areas in each type of reasoning.

Materials and Methods

In overview, subjects faced three tasks. The deduction task required distinguishing valid from invalid arguments (a mix was given). The probability task required judging whether the conclusion of an argument was more likely to be true than false given the premises (based on pilot studies, we were able to construct arguments that elicit a range of intuitions). The comprehension control task required detecting anomalous content in premises or conclusion. We now provide details, starting with a description of the kind of arguments used across the three tasks.

Materials

On each trial, subjects viewed an argument composed of two premises followed by a conclusion. The first premise was shown for 3 s, then joined by the second premise for a further 3 s, and then joined by the conclusion for another 14 s. All arguments in the experiment were composed of sentences bearing on a man drawn randomly from a small Texas town known to the subjects. The chosen man was denoted ‘he’. Sample arguments are shown in Figure 1. In Figure 1a are examples of valid and invalid stimuli from the deduction task. Figure 1b contains examples of stimuli from the probabilistic reasoning task. In Figure 1c are examples of stimuli with and without anomalous content from the comprehension control task. As described below, six invalid arguments were evaluated on three separate occasions: once for validity (deduction task), once for high probability of the conclusion (probabilistic reasoning task), and once for anomaly (comprehension control). Figure 1d shows all six of these arguments. (The full set of stimuli is available at http://ric.uthscsa.edu/staff/parsonsprojects/stimuli.html.)

On each PET scan, or task, subjects evaluated a sequence of five distinct arguments. In the context of suitable instructions, the first two arguments in a task were designed to exercise a specific kind of reasoning (involving probability, deduction or comprehension). The subject was only scanned while reasoning about the third and fourth arguments. To summarize, a task was a sequence of five arguments of which just the third and fourth were involved in scanning; the others were used to establish ‘set’ and to exercise the desired form of reasoning.

Tasks were organized into ‘matched sets’. A matched set consisted of a probability task, a deduction task, and a comprehension task with the property that the scanned arguments (third and fourth) were identical across the three tasks. Three matched sets were constructed, with no overlap in the arguments composing them. The nine resulting tasks were presented to the subject in random order under the constraint that two tasks from the same matched set (hence, with identical scanned arguments) not occur successively. We now describe in more detail the three kinds of task figuring in each matched set.

In the probability task (Fig. 1b), subjects covertly judged whether a conclusion was more likely to be true than false, assuming the truth of the premises. All of the arguments in the probability task were (logically) invalid. The information in the premises was therefore insufficient to constrain the conclusion to have either high or low probability. The judgment was thus subjective in character, and required the reasoner to integrate background knowledge (e.g. about jobs and recreation) not explicitly presented in the argument. Of course, the reason for choosing only invalid arguments for the probability task is that valid arguments are probabilistically degenerate.

In the deduction task (Fig. 1a), subjects covertly judged whether the conclusion followed logically from the premises. This judgment involves the detection of logical necessity rather than probability. No background knowledge is required for the reasoning since the information provided by the premises suffices to determine whether the inference to the conclusion is logically valid. Approximately half the arguments in a given deduction task were valid, the rest invalid.

In the language comprehension task (which served as a control), subjects covertly judged whether there was anomalous content in any premise or conclusion, with no need to judge the relationship between statements (Fig. 1c). None of the arguments in the comprehension task were valid.

The two arguments common to all three tasks in a matched set were always invalid with no anomalous content (Fig. 1d). Only during performance with these common stimuli were subjects scanned. Identical stimuli were therefore processed with different psychological ‘set’, eliciting either deductive, probabilistic or semantic reasoning. Subjects were not informed about the presence of identical arguments across different tasks, and never remarked upon this fact spontaneously. Subjects were not informed about the onset or offset of PET scanning, for which there was no perceptible change in the immediate environment.

As noted, subjects were scanned during the deduction task only when they were reasoning about invalid arguments. The reasoning mechanisms engaged during scanning in the deduction task were likely to be the same or similar to those involved in evaluating valid arguments. This is because (i) subjects did not know when they would be scanned, (ii) scanned arguments were surrounded by both valid and invalid arguments, and (iii) subjects did not know prior to reasoning whether a given argument was valid or invalid.

It is also worth emphasizing that a yes/no response was required in the probability task, instead of a numerical judgment (see above). Identical response options were thus available for the probability and deduction tasks; all that differed was the kind of reasoning needed to choose between them. (We elected not to use numerical responses in the probability task because they would have introduced a confounding asymmetry vis-à-vis deduction.) Observe as well that there were no objectively correct answers to the probability questions. We decided not to frame probability questions with objectively correct answers (e.g. involving urns) because that would have converted them into disguised deduction problems (e.g. requiring the calculation of posterior odds from prior odds and likelihood). In contrast, the intuitions about chance at issue in the present paper are based on subjective assessments that cannot be determined by logic alone. Subjective assessments are often the focus of psychological research (Kahneman et al., 1982; Yates, 1990; Johnson-Laird et al., 2001).

Our stimuli underwent extensive pilot testing to ensure that subjects (i) could successfully perform the deduction tasks, (ii) felt intuitively that the deduction and probability tasks required distinct kinds of reasoning, (iii) could sustain reasoning to complete a judgment during the allotted response time interval, and (iv) agreed with the experimenters and each other about which arguments contained semantic anomaly. As a final check, 23 Rice University undergraduates were asked to carry out all nine tasks in front of a computer terminal, and then to answer follow-up questions about their thought processes. The average accuracy rate for the 15 deduction problems (which included eight valid arguments and seven invalid arguments) was 86.4% (SD = 9.1). This is reliably better than the 50% expected from mere guessing (P < 0.0001). There was significant concordance amongst the subject's responses on the probability trials (Kendall coefficient of concordance W = 0.11, χ2 = 36.2, P < 0.001). Virtually all of the students spotted the anomalies introduced into the arguments, with no false-positive responses.

The follow-up questionnaire included the query:

Did the logic and probability tasks differ only in how much time it took you to decide? Or do you think that you used different reasoning in the two tasks?

All 23 subjects said that ‘the two tasks required different reasoning’. On the other hand, there was some role for deduction in probabilistic reasoning. Thus, 12 students reported that ‘a considerable amount of my time on the probability questions was devoted to deduction’, and 11 reported that only ‘a small amount of my time on the probability questions was devoted to deduction’. Thirteen of the students reported that deductive reasoning was either ‘rather different’ or ‘very different’ from that for probability; 10 reported that the two tasks were ‘a little different’; no one denied any difference at all.

The use of deduction in the probabilistic reasoning task was expected: it is widely appreciated in the literature devoted to subjective probability that deductive relations among propositions condition their probabilities. [See presentations of the axioms for subjective probability in, for example, Skyrms, p. 168 (Skyrms, 1986), or Earman, p. 36 (Earman, 1992).] Moreover, various psychological theories envision a role for deduction in probabilistic contexts. This is true, for example, of Rips' account of the psychology of deduction (Rips, 1994) (pp. 278ff.). Indeed, Rips takes deduction to be the core of human cognitive architecture, hence involved in most aspects of problem solving, planning and categorization. It is therefore likely that the probability task recruited elements of deductive reasoning.

Regarding the comprehension task, 19 out of the 23 subjects reported thinking ‘about each statement by itself’, as requested in the instructions. Four students admitted that they ‘tended to think about connections between different statements’.

In summary, the design of our stimuli allows probabilistic and deductive reasoning to be carried out over identical stimuli by changing instructions. The resulting thought processes are intuitively distinct although partially overlapping. The comprehension task requires merely understanding the individual sentences of an argument, and elicits only a slight tendency to link premises to conclusion.

Subjects

Ten healthy right-handed adults participated in the PET study after giving written, informed consent. The five male and five female subjects ranged from 23 to 43 years of age (means, 32 for the male group and 32 for the female group). Subjects were screened to ensure no pre-experimental training in formal logic.

Procedure

During the PET session, each subject performed three matched sets of tasks (hence, nine tasks in all). In addition, they performed two replications of eyes-closed rest control. The three tasks in a given matched set involved judgments of probability, deductive validity and semantic well-formedness, as described above and illustrated in Figure 1. Before the PET session, subjects received supervised practice in each task (using stimuli not appearing in the experiment). During performance, subjects lay supine in the PET instrument, with the head immobilized by a closely fitted plastic facial mask. Stimuli were displayed on a 37.5 cm monitor suspended 42.5 cm from the patient's pupil. The first premise of each problem was presented for 3 s, then joined by the second premise for three more seconds, and then joined by the conclusion for 14 s (total display/trial time, 20 s). At the conclusion of the PET session subjects responded to a questionnaire eliciting introspections about the phenomenology of the three tasks.

For each task, the subject evaluated five arguments. During the third and fourth arguments, brain blood flow was imaged. For each argument, subjects were instructed to perform the task throughout its 20 s period; they were to continue to double-check their judgment to ensure accuracy if they finished before the stimuli were removed from view. The nine tasks (each consisting of five arguments, of which the third and fourth were scanned) plus the two rest conditions were administered in pseudo-random counterbalanced order such that (i) tasks from the same matched set not occur in succession, and (ii) tasks 1–3 include one deduction, one probability and one comprehension task, and similarly for tasks 5–7 and 9–11. Trials 4 and 8 were devoted to rest. Subjects reported their judgments at the end of each task (hence, after all five arguments were presented). As an aid to memory, the reports were made while the five arguments in a given task were presented a second time.

Imaging

PET scans were performed on a GE 4096 camera which has a pixel spacing of 2.0 mm, an inter-plane, center-to-center distance of 6.5 mm, 15 scan planes, and a z-axis field of view of 10 cm. Correction for radiation attenuation was made by means of a transmission scan collected before the first scan using a 68Ge/68Ga pin source. Cerebral blood flow was measured with H215O (half-life = 123 s), administered as an intravenous bolus of 8–10 ml of saline containing 60 mCi. At the start of a scanning session, an intravenous cannula was inserted into the subject's left forearm for injection of each tracer bolus. A 30 s scan was triggered as the radioactive tracer was detected in the field of view (the brain) by increases in the coincidence-counting rate. During this scan, the subject performed a task in one of the three conditions. Immediately following this, a 60 s scan was acquired as the subject lay with his/her eyes closed without performing a task. The latter rest PET images, in which task-related regional cerebral blood flow changes are still occurring in specific brain areas, are combined with the task PET images in order to enhance detection of relevant activations. Following the latter scan, subjects performed one final (fifth) trial (without being scanned). A 10 min inter-scan interval was sufficient for isotope decay (five half-lives) and return to resting state levels of regional blood flow within activated regions. Images were reconstructed using a Hann filter, resulting in images with a spatial resolution of ~7 mm [full-width at half-maximum (FWHM)].

Significant changes in cerebral blood flow indicating neural activity were detected using an ROI-free image subtraction strategy. High resolution magnetic resonance imaging (MRI) scans were acquired for each subject. Inter-scan, intra-subject movement was assessed and corrected using the Woods algorithm (Woods et al., 1993). Semi-automatic registration of PET to matched, spatially normalized MRI (in Talairach space) was performed using in-house spatial normalization software implementing an algorithm employing a nine-parameter, affine transformation (Lancaster et al., 1995; Talairach and Tournoux, 1988).

The data were smoothed with an isotropic 3 × 3 × 3 Gaussian kernal to yield a final image resolution of 8 mm. By use of moderate smoothing, resolution is not sacrificed; control for false positives is provided by the P value criteria used in later stages of the analysis stream employed here. The data were then analyzed using the Fox et al. (Fox et al., 1988) algorithm as implemented in the MIPS software package (Research Imaging Center, UTHSCSA, San Antonio, TX). Intra-subject image averaging was performed within conditions and the resulting image data were analyzed by an omnibus (whole-brain) test.

For this analysis, local extrema (positive and negative) were identified within each image using a 3-D search algorithm (Mintun et al., 1989). Each set of local extrema data was plotted as a frequency histogram (for visual inspection). Then, a beta-2 statistic measuring kurtosis and a beta-1 statistic measuring skewness of the histogram of the difference images [change distribution curve (Fox and Mintun, 1989)] were used as omnibus tests to assess overall significance (D'Agostino et al., 1990). Critical values for beta statistics were chosen at P < 0.01. The beta-1 and beta-2 tests, which are implemented in the MIPS software in a manner similar to the use of the gamma-1 and gamma-2 statistics (Fox and Mintun, 1989), improve on the gamma statistic by using a better estimate of the degrees of freedom (Worsley et al., 1992).

The null hypothesis of omnibus significance was rejected, so a post hoc (regional) test was done (Fox et al., 1988; Fox and Mintun, 1989). In this algorithm, the pooled variance of all brain voxels is used as the reference for computing significance. This method is distinct from methods which compute the variance at each voxel, but is more sensitive (Strother et al. 1997), particularly for small samples, than the voxel-wise variance methods of Friston et al. (Friston et al. 1991) and others. In this analysis, a maxima and minima search is conducted to identify local extrema within a search volume of 125 mm3 (Mintun et al., 1989). Cluster size was determined based on the number of significant, contiguous voxels within the search cube of 125 mm3. The statistical parameter images were converted to z-values by dividing each image voxel by the average standard deviation of the null distribution. P values were assigned from the Z distribution. Only Z values greater than 2.96 (P < 0.001) are reported. The critical value threshold for regional effects (Z > 2.96, P < 0.001) is not raised to correct for multiple comparisons (e.g. the number of image resolution elements). This is because omnibus statistics were established before post hoc analysis. The scanning methods used at the Research Imaging Center have been described previously (Raichle et al., 1983; Fox et al., 1985; Fox and Mintun, 1989; Lancaster et al., 1995).

Gross anatomical labels were applied to the detected local maxima using a volume-occupancy-based, anatomical labeling strategy as implemented in the Talairach DaemonTM (Lancaster et al., 2000), except for activations in cerebellum which were labeled manually with reference to an atlas of the cerebellum (Schmahmann et al., 1999).

Anatomical MRI scans were performed on an Elscint 1.9 T Prestige system. The scans employed 3D Gradient Recalled Acquisitions in the Steady State (3D GRASS), with a repetition time of 33 ms, an echo time of 12 ms, and a flip angle of 60° to obtain a 256 × 256 × 256 volume of data at a spatial resolution of 1 mm3.

Results

Our analysis of the brain blood flow data was designed to locate the active regions that were common to the two kinds of reasoning. In addition, it aimed to uncover the regions (if any) that were distinctive to reasoning compared to linguistic processing. A third goal was to determine whether the distinction between probabilistic and deductive reasoning interacted with left versus right hemispheric processing. Finally, we sought specific contrasts (if any existed) between the brain sites active for probabilistic versus deductive reasoning. Following a discussion of these four topics, we describe three additional analyses. Note that in the descriptions, figures and tables that follow we have excluded spurious activations that resulted from subtractions of deactivations. (In other words, all activations were verified by subtracting the rest condition from the relevant reasoning task.)

Activations Common to the Two Kinds of Reasoning

We found that many brain areas were significantly activated when the comprehension control task was subtracted from the probabilistic and deductive reasoning tasks (P < 0.001). However, only 8% of these areas were active in both contrasts despite the fact that the two reasoning tasks involved identical stimuli. The common, overlapping activation is in precuneus or posterior cingulate cortex [Brodmann area (BA) 31]. On an alternative analysis, in which the comprehension control task is subtracted from the average of the two reasoning tasks, again only the latter area is active. The lack of overlap in significant activity detected for the two tasks suggests that probabilistic and deductive reasoning were performed via different underlying neural mechanisms. This inference is consistent with subjects' introspective reports suggesting that different cognitive processes were used in the two tasks (see Materials and Methods).

Reasoning versus Language Processing

In the next analysis, we focus on the possible contribution of language processing areas to the activations elicited in the reasoning tasks. When the comprehension task is subtracted from the probability task, there is no activity in or near Broca's area (in BA 44/45), sub-Broca's area (in BA 47), or Wernicke's area (in BA 22/21). These three areas are known to contain primary left-hemispheric language sites (Petersen et al., 1989; Mazoyer et al., 1993; Stromswold et al., 1996; Price, 1998). Likewise, none of these areas show activity when comprehension is subtracted from the deduction task. Apparently, the purely linguistic load of the two reasoning tasks does not exceed what is necessary to spot semantic anomaly among the premises and conclusion of an argument. The foregoing contrasts with comprehension argue against interpreting the reasoning activations as ‘spillover’ from overloaded language areas, a phenomenon that appears to occur with the comprehension of sentences of increasing complexity (Just et al., 1996). We return to this issue in the Discussion.

Hemispheric Interaction with Type of Reasoning

We next sought to characterize the difference in the location of regions activated in the two reasoning tasks and found a relationship between task and cerebral lateralization. All activations discussed in this analysis were present in both (i) the direct contrast between probability and deduction (either probability subtracted from deduction or the reverse) and (ii) the subtraction of the comprehension task from the reasoning task in question.

When the probability task is subtracted from the deduction (or ‘logic’) task, 65% of all significantly activated voxels in the brain (excluding cerebellum) (P < 0.001) were in the right hemisphere. This contrast also showed lesser activations in left cerebral hemisphere but only in visual areas (BA 18, 31 and 39) and certain subcortical structures. To confirm the validity of this relationship, we conducted the following alternative analyses. We found the same pattern even when the threshold for statistical significance for the contrast is considerably relaxed (P < 0.05). The pattern also is present when a logical image analysis (in which every voxel is categorized as unique to one condition or the other, or common to both) is applied both to deduction minus rest and to comprehension minus rest, using a relaxed threshold of statistical significance (P < 0.05). The outcomes of these alternative analyses indicate that we are unlikely to have failed to detect activation in language areas that could be associated with deduction.

Continuing our examination of lateralization and reasoning, when deduction is subtracted from probability, 59% of all significantly activated voxels in the brain (excluding cerebellum) (P < 0.001) were in the left hemisphere. The activation in the right cerebral hemisphere was again only in areas likely to be involved in the control of attention and in some subcortical structures. The same pattern appears even when the threshold for statistical significance for this contrast is relaxed (P < 0.05). The pattern also holds in the logical image analysis of probabilistic reasoning minus rest, and comprehension control minus rest, with a relaxed statistical threshold (P < 0.05).

To further confirm the foregoing pattern of dissociated activation and hemispheric specialization for deductive versus probabilistic reasoning, we conducted an additional analysis. In a logical image analysis of both probabilistic reasoning minus rest and deduction minus rest, even when a relaxed threshold of statistical significance is employed (P < 0.05), we once again found the same interaction of task versus hemisphere.

Specific Sites for the Two Kinds of Reasoning

We now turn to direct contrasts between the two reasoning tasks. Once again, all activations in the present analysis were detected in both (i) the direct contrast between probability and deduction and (ii) the subtraction of the comprehension task from the reasoning task in question.

Deduction Minus Probability

In the contrast subtracting probabilistic from deductive reasoning (P < 0.001), the largest activation by far was in right middle temporal cortex (BA 21) (Fig. 2, Table 1). This activation (51, –27, –9) is just below a region homologous to one of the principal language areas of the left hemisphere (Wernicke's area). Although the exact boundaries of Wernicke's area are unknown, tasks thought to activate the region elicit peak intensity responses near a region homologous to that activated here. For example, Wernicke's area has been reported to be at (–48, –32, 6) in a recent report of a study of verb generation (Xiong et al., 2000), and to be at (–54, –41, 8) in a meta-analysis of four papers on word reading (Fiez and Petersen, 1998).

Another major focus was detected in right inferior frontal gyrus (BA 44) (Fig. 3). This activation (53, 16, 17) is adjacent to a region homologous to the other principal left language area (Broca's area). Again, although the precise boundaries of Broca's area are unknown, tasks which appear to activate it produce peak intensity responses near a region homologous to that activated here. Thus, in the average peak activation of 10 studies of language production tasks, Broca's area is at (–44, 10, 13) (Petrides et al., 1993, 1995; Becker et al., 1994; Price et al., 1994; Bookheimer et al., 1995; Buckner et al., 1995; Hirano et al., 1996, 1997; Braun et al., 1997; Petersen et al., 1988).

Two other activated foci of moderate cluster size and intensity in this contrast were in right caudate nucleus (Fig. 4) and right amygdala (Fig. 5). Other activations seen in the subtraction of probability from logic were generally smaller in size and intensity. They include foci in right dorsolateral and medial prefrontal cortex (BA 9, 10), right anterior cingulate cortex (BA 24), and right temporoparietal cortex (BA 39). Other right hemisphere activation were observed in thalamus, fusiform cortex (BA 37), midbrain and occipital cortex (BA 18). There were mostly small left hemisphere foci in midbrain, thalamus, posterior cingulate (BA 31), globus pallidus, temporoparietal (BA 39) and occipital cortex (BA 18). The majority of the other activations are associated with attentional or visual functions. Lastly, there were moderate bilateral posterior cerebellar foci.

Probability Minus Deduction

A different picture emerges of the areas specific to probabilistic reasoning. When deductive reasoning is subtracted from probabilistic reasoning, there are a number of large and intense activations in the left hemisphere areas of inferior frontal (BA 47) (Fig. 3 and 6, Table 1) and insular cortex, as well as posterior cingulate (BA 31) (Fig. 7), parahippocampal (BA 36) (Fig. 8), medial temporal (BA 35), and superior and medial prefrontal (BA 9) cortex.

Subtraction of logic from probability also revealed left hemispheric foci of moderate cluster size and intensity in subgyral lateral frontal (BA 6) and temporal (BA 35) cortex, midbrain and paracentral cortex (BA 5). The same contrast revealed right hemisphere foci, mainly in anterior cingulate (BA 24), globus pallidus and uncus (BA 28). Most of these areas are related to attentional or visual functions. Again, there were bilateral posterior cerebellar foci.

Comparison of Male and Female Reasoners

We also examined for the first time the possibility that there are differences in the neural systems supporting reasoning for male and females and found no significant differences in activation patterns between the groups. Both show the same degree of right hemispheric prevalence for deduction and left for probability. It must be borne in mind, however, that this comparison is based on a sample size that is relatively small for comparisons of PET data (n = 5 in each group).

Overall Activation and Task Difficulty

In order to further quantify the differences between deductive and probabilistic reasoning, we examined the amount of overall activity for each task. In total, there was a third more logic-specific activation foci than probability-specific ones in the direct contrasts between deduction and probability. The greater extent of deductive activations is unlikely to result from more vigorous use of the system underlying deduction compared to probability because eight of the 10 subjects judged probability to be the most difficult of the three tasks in a post-experimental questionnaire. (Likewise, 17 out of 23 subjects in our pilot study judged probability to the most difficult of the three tasks.)

Measures of Task Performance

Overall accuracy on the deduction problems, assessed against the criterion of standard logic, was 72% (69% for the scanned trials), which is comparable to logical performance without time stress (Rips, 1994), and is reliably better than chance (P < 0.001, binomial test). Regarding the probability task, across all trials the subjects judged 41% of the conclusions to be more likely than not (45% for the scanned trials). They also agreed with the experimenters' judgement 72% of the time. There is no objective standard of accuracy for the probability task since the laws of probability do not impose any particular value for the arguments we used. Thus, the best measure of the quality of the stimuli is the extent to which the subjects agreed with one another. The subjects' judgements were indeed concordant (Kendall coefficient of concordance W = 0.349, χ2 = 39.1, d.f. = 14, P < 0.001). Responses to the semantic comprehension test were virtually perfect.

Discussion

In the following discussion, we offer preliminary hypotheses about the neurobiology of deductive and probabilistic reasoning. To underline the provisional nature of our conclusions, let us affirm at the outset that the present results do not allow us to infer with certainty either the specific function of the activated areas, or even whether particular activations are essential to reasoning or just incidental. Compounding the ambiguity is the paucity of prior neurological or neuroimaging data about inferential reasoning (limited to the few, highly suggestive papers cited in the Introduction). Further studies will thus be required to assess the hypotheses we now present.

Dissociated Activations for the Two Types of Reasoning

A variety of brain areas were activated by the deduction and probability tasks. A few were active for both kinds of reasoning but many more were active uniquely for one or the other. Our results thus give evidence for a dissociation between the brain areas specifically activated for deductive versus probabilistic reasoning with propositional arguments. Although no single set of control conditions or contrasts is perfect in all respects, the same deduction-specific and probability-specific areas were indicated in all three possible contrasts, namely, each reasoning task minus rest, each task minus the language comprehension control, and in direct contrasts between the two reasoning tasks. Moreover, the activation common to deductive and probabilistic reasoning is largely restricted to precuneus and posterior cingulate cortex (BA 31). While the function of the latter areas is still under investigation, some studies suggest its involvement in aspects of attentional processing (Petrides et al., 1993; Shallice et al., 1994). If so, then the brain regions activated by both reasoning tasks may represent no more than similar attentional demands.

The dissociation we observed supports psychological theories that enforce a partial separation between the two reasoning processes (Braine, 1978). By the same token, the findings suggest that it is inaccurate from the point of view of functional neuroanatomy to claim that humans judge logical truth as a limiting case of probability assessment, i.e. that they use the same cognitive processes for deduction and probabilistic reasoning, as has been suggested (Johnson-Laird, 1994; Johnson-Laird et al., 2001). We now offer further remarks about each form of reasoning.

Probabilistic Reasoning

Recall that in probabilistic reasoning, assessing the likelihood of the conclusion requires integrating information that goes beyond what is available in the premises (otherwise, the reasoning would bear on deductive validity instead of probability). Consistent with this requirement, probabilistic reasoning activated a set of brain areas that appear to be involved in recalling and evaluating a range of world knowledge. For example, there was strong activation in left inferior frontal areas, which have been implicated in the retrieval of semantic information as well as the use of working memory (Demb et al., 1995; Petrides et al., 1995; Rushworth et al., 1997; D'Esposito et al., 1998). The posterior cingulate was also activated during the probability task. The function of the posterior cingulate is still debated but it has been associated with either attention or long-term episodic memory (Grasby et al., 1993; Petrides et al., 1993; Price et al., 1994; Shallice et al., 1994). In addition, probabilistic reasoning activated parahippocampal and medial temporal areas. These regions have been convincingly associated with declarative, semantic memory (Damasio et al., 1996; Brewer et al., 1998; Wagner et al., 1998). Finally, responses were observed in medial prefrontal cortex, which may be involved in executive attention (Petrides et al., 1993; Baker et al., 1996; Prabhakaran et al., 1997; Waltz et al., 1999).

Deduction

In contrast to probabilistic reasoning, deduction does not depend on general knowledge, but only on recognition and use of the logical structure spanning premises and conclusion. Our PET data indicated that, in distinction to probabilistic reasoning, deductive inference primarily activated a set of right brain areas, the major ones being proximal to homologues of the left hemisphere structures responsible for language processing (i.e. Wernicke's area and Broca's area). No such areas in right hemisphere were active for probabilistic reasoning.

To date, few functions have been attributed to the two principal regions we observed for deduction. All have involved higher-order linguistic tasks such as maintenance of thematic coherence (St George et al., 1999), discourse management (Beeman and Chiarello, 1998), and interpretation of context (Bottini et al., 1994; Just et al., 1996; Shammi and Stuss, 1999). We believe that the right brain areas specifically active for deduction are distinct from those supporting such higher-order language functions. This is because thematic coherence and discourse management are likely to be equally required for evaluating identical arguments under probabilistic versus deductive instructions. Yet the foci observed in those areas were present only for deduction. We therefore suggest that the activated areas support logical reasoning. This suggestion is consistent with reports that right frontal patients have specific difficulties making inferences and interpreting propositions joined or modified by logical connectives (Grossman and Haberman, 1987; Beeman and Chiarello, 1998).

Deduction also specifically produced an activation of moderate intensity and cluster size in the right caudate nucleus. Basal ganglia (e.g. caudate) connect through thalamus (also activated) to frontal cortex, and may mediate working memory, executive strategy and rule-based learning (Alexander et al., 1990; Middleton and Strick, 1991; Gabrieli, 1995; Rao et al., 1997; Poldrack et al., 1999). It has been suggested that left basal ganglia support left hemisphere grammatical rule processing (Damasio and Damasio, 1992; Ullman et al., 1997). If so, we may speculate that right basal ganglia support rule-based deduction in right frontal areas. This interpretation is consistent with the observation that Parkinson's disease patients (who have dys-functional basal ganglia) have specific difficulties making logical inferences (Natsopoulos et al., 1997).

Thus, the involvement of the right basal ganglia, in conjunction with right brain areas in or near those homologous to Wernicke's and Broca's areas, is consistent with the possibility that there is a logic-specific network that in some respects mirrors the language-specific network. In other words, deduction may be supported by a system of structures in the right hemisphere that is analogous to the structures supporting language in the left. Each system would allow for the successive transformation of mental representations according to encoded rules (linguistic rules on the left, deductive rules on the right).

Deduction also produced a major focus of activation in right amygdala. The amygdala has been implicated in the processing of emotion, most often fear, aggression, reward and risk (Hyman, 1998; LaBar et al., 1998; Kahn et al., 2000). In particular, it may play a role in learning to avoid neutral stimuli that are paired with aversive events (Sananes and David, 1992; Romanski et al., 1993; Cahill et al., 2001). The amygdala is suspected more generally of emotionally tagging learned associations (McGaugh et al., 1996), for example, recognizing the value of stimuli that predict positive reinforcers (Cador et al., 1989; Everitt et al., 1989).

The activation of the right amygdala (but not the left) in the deduction minus probability contrast suggests its connection to deductive reasoning, which activated predominantly right hemisphere structures. We speculate that an emotional basis for such activation is provided by the ‘Aha!’ phenomenology reported for the deduction task in post-experimental interviews. Indeed, 70% of our PET subjects noted sudden insight during the deduction task whereas 80% described probabilistic reasoning as involving the gradual stabilization of judgement. Consistent with the lack of an ‘Aha!’ during probabilistic reasoning, no activation was detected in either the left or right amygdala in the subtraction of deduction from probability. These observations reinforce the hypothesis that the two kinds of reasoning are fundamentally different. Deductive reasoning might thus involve a pleasurable release from tension as the subject suddenly perceives the logical status of an argument [as in other problem-solving settings (Davidson, 1995)]. Such an interpretation is consistent with studies that suggest a role of such structures as amygdala in interactions between emotion and higher cognitive processes like decision making (Damasio, 1994). Of course, the introspective ‘Aha’ is not guaranteed to signal a significant brain event. Its correlation with deductive (but not probabilistic) reasoning and with right (but not left) amygdala activation nonetheless makes it plausible that amygdala activation can be triggered by sudden insight achieved during deduction.

In addition, deduction activated medial and dorsolateral prefrontal cortex. These areas (which are still being vigorously explored with a variety of methods) have been associated with executive attention and strategy functions, including controlling or monitoring the contents of working memory (Petrides et al., 1993; Posner and Dehaene, 1995; Baker et al., 1996; Fiez et al., 1996). Moreover, there were deduction-specific responses in temporoparietal and anterior cingulate areas, which have been associated with selective and sustained attention and with response selection (Corbetta et al., 1995; McCarthy, 1996).

There was no significant activation for deductive reasoning in right hemispheric areas associated with visual–spatial processing, i.e. posterior parietal (BA 40) and lateral prefrontal (BA 46) cortex (Kosslyn, 1994; Parsons and Fox, 1998; Carpenter et al., 1999; Dehaene et al., 1999; Farah, 1999). This absence of activation is consistent with the fact that 80% of the PET subjects indicated on the post-experimental questionnaire that they did not generate visual diagrammatic representations of the stimulus information when performing the deductive problems. The use of stimuli from propositional logic seems therefore to have served its intended purpose of limiting recourse to diagrammatic strategies when reasoning deductively.

Finally, there were bilateral posterior cerebellar foci during deduction that were different from the bilateral posterior cerebellar foci seen during probabilistic reasoning. In the absence of overt motor behavior, apart from eye movements, these activations in neocerebellum are likely related to support processes for sensory or cognitive activity during the reasoning tasks (Akshoomooff et al., 1997; Hallett and Grafman, 1997; Parsons and Fox, 1997; Desmond and Fiez, 1998).

Deduction Across Individuals and Logical Forms

Our results held equally for men and women. Gender invariance is noteworthy in view of possible differences in cerebral organization and lateralization between the sexes (Gur et al., 1999; Kimura, 1999).

The findings reported here are consistent with our previous study of men using syllogisms (Osherson et al., 1998). Both studies showed right hemispheric dominance for deduction, left for probabilistic reasoning. The specific right hemispheric areas activated for deduction were more anterior in the present study, however, perhaps reflecting the predominantly non-spatial reasoning elicited by propositional stimuli. The syllogistic stimuli in Osherson et al. seemed to recruit more visuospatial reasoning, served by posterior parietal–occipital regions (Osherson et al., 1998). Unlike studies by Goel et al. (Goel et al., 1997, 1998), neither of our studies revealed deduction-specific activations in left frontal and left temporal brain areas, just as neither study by Goel et al. documented the deduction-specific right hemisphere activations that we have found. Further experiments are required to clarify the reason for these discrepancies, but one important factor might be the use of distinct stimuli for probabilistic and deductive reasoning in the Goel et al. studies, unlike the strictly identical stimuli employed here. Use of distinct stimuli for the two tasks leaves open the possibility that activation differences are partly driven by differences in stimuli rather than reasoning.

Deduction and Language Processing

We now examine the implications of our data for the relation between reasoning and language. To begin, it is worth considering an interpretation of the results that is alternative to the functional hypotheses discussed above. It assumes that comprehension and deduction are similar processes with common neural bases, and that the greater activation in the right hemisphere during deduction reflects the additional memory load of the latter. A straightforward version of this ‘spillover’ hypothesis is that deductive reasoning loads left hemisphere language areas beyond capacity, so other support areas (e.g. right hemispheric ones) are recruited to carry out aspects of the task [see Just et al. for evidence of such spillover in a different linguistic context (Just et al., 1996)].

The hypothesis of spillover is contradicted, however, by the fact that no activations are seen (even at a relaxed statistical threshold) in left language areas when the comprehension control task is subtracted from deduction. The latter contrast involves both location and intensity, and indicates that no excess intensity of activity is observed in left language areas beyond what is required to spot anomalous semantic content during the control task. In other words, the spillover hypothesis predicts at least as much activation in the primary language areas as in the right hemispheric regions that are recruited during overloading, yet, only the right hemisphere regions appear when the comprehension task is subtracted from deduction. It is also of interest that the comprehension task was consistently rated as easiest by our subjects. Hence, spillover during deduction would not be expected to allow left hemisphere activations to be erased by subtraction of the activations for the comprehension task.

On the basis of our data, we are led to conclude that deductive reasoning is localized in brain areas far from the principal language centers in left hemisphere. This raises the possibility that logical competence is largely independent of natural language processing, except for statement decoding. Although there is evidence that right hemisphere areas are involved in many higher-order language functions, as discussed earlier, the primary locus of linguistic analysis is left hemispheric (Petersen et al., 1989; Mazoyer et al., 1993; Stromswold et al., 1996; Price, 1998). Our findings thus contradict the belief often expressed in the cognitive sciences and philosophy that deductive reasoning is derivative to linguistic processing (Quine, 1970; Polk and Newell, 1995). This belief is sustained by the plausible thesis that logic licenses inferential relations among statements, and that statements must be embedded in a structured language if they are to have the kind of grammatical properties that permit deduction [such properties as being conditional in form, having quantifiers with determinate scope, etc.; see Fodor (Fodor, 1975)].

The language that supports deduction, however, need not be a natural language like English, burdened as it is by ambiguity and ellipsis. Deduction (as well as other forms of reasoning) might rather be performed in a format that is antecedent to natural language, the latter being acquired for the purpose of expressing meanings that exist prior to their linguistic expression. If logic and language are independent in this sense, then logic might be available to prelinguistic infants and other animal species – a prediction that is still without adequate test, in our opinion. [Consistent with our hypothesis, the presence of complex reasoning in a profoundly aphasic patient with extensive lesions in left hemisphere language areas is reported in Varley and Siegal (Varley and Siegal, 2000).]

Deduction Without Visualization

The brain activations seen here for deductive reasoning were largely outside regions known to serve spatial visualization. This finding suggests that at least some forms of logical thinking are non-diagrammatic, as well as being independent of natural language processing. Albeit non-linguistic, such forms of logical thinking may nonetheless be rule-based, and rely on a calculus of transformations carried out via right hemisphere mechanisms over formal structures retrieved by left hemisphere language areas. Such formal structures would be relatively coarse representations of the sentences from which they are abstracted since only the logical particles (and, if, etc.) need to be registered, along with facts about the identity and distinctness of phrases occurring across premises and conclusion.

Conclusion

We conclude by summarizing the working hypotheses that emerge from our data. We postulate the existence of a logic-specific network in the right hemisphere comparable to the language-specific network in the left. Both involve temporal, frontal and basal ganglia structures. Just as linguistic rules are encoded in the left hemisphere, deductive rules are encoded in the right. According to our hypothesis, each system allows for the successive transformation of mental representations specific to its function. The two circuits interact when the transformations for deduction are carried out via right hemisphere mechanisms over formal structures retrieved by left hemisphere language areas. The latter structures would be coarse representations of the sentences from which they are abstracted since only their logical structure would be retained.

We hypothesize that probabilistic judgement is achieved via non-linguistic left hemisphere areas that are involved in the recall and evaluation of world knowledge. Note that in contrast to the reliance of deductive reasoning on coarse linguistic representations, probabilistic judgement must rely on the fine detail of sentences, since every word contributes to overall plausibility. Our hypotheses are thus consistent with the conjecture that right hemisphere regions are specialized for processing relatively coarse aspects of stimuli whereas left hemisphere regions are favored for fine aspects. A variety of empirical findings support this broader conjecture [see Ivry and Robertson for a review of the evidence (Ivry and Robertson, 1998)].

Notes

Supported by grants from Rice University and the Research Imaging Center. We thank Mario Liotti and three anonymous reviewers for insightful and very helpful comments on earlier versions of the manuscript. We also thank Michael J. Martinez for assistance with the conduct and analysis of the study.

Table 1

Local maxima in regions demonstrating significant rCBF increases (P < 0.001) during deductive and probabilistic reasoning

Gyrus or regiona Brodmann areab Talairach coordinatesc Extent (mm3Z-score 
  x y z   
aIn parenthesis is the equivalent anatomical label of Schmahmann et al., based on that of Larsell and Jansen (Larsell and Jansen, 1972; Schmahmann et al., 1999).bDesignation of Brodmann areas is approximate and based on a brain atlas.cBrain atlas coordinates (Talairach and Tournoux, 1998) are in millimeters along left–right (x), anterior–posterior (y) and superior–inferior (z) axes. 
Deduction minus probabilistic reasoning 
Right hemisphere 
Middle temporal 21 51 –27 –9 312 4.89 
Anterior cingulate 24 18 –7 37 120 3.99 
Inferior frontal 44 53 16 17 96 3.44 
Caudate  10 72 3.64 
Amygdala  17 –9 –15 64 3.49 
Thalamus  16 –15 32 3.64 
Midbrain  –27 32  3.39 
Temporoparietal 39 34 –69 21 24 3.69 
Fusiform 37 49 –45 –11 16 3.49 
Anterior cingulate 24 18 –15 37 16 3.24 
Middle frontal 36 41 24 16 3.19 
Cuneus 18 –92 16 3.14 
Medial frontal 10 51 3.04 
Cerebellum       
Superior semilunar (crus I)  32 –64 –34 136 3.94 
Gracile (VIIB)  32 –47 –19 32 3.99 
Left hemisphere       
Midbrain  –4 –37 –18 216 5.04 
Thalamus  –10 –9 112 3.74 
Lingual 18 –7 –82 –2 32 3.69 
Lateral globus pallidus  –15 24 3.49 
Thalamus  –13 –17 24 3.24 
Sub-gyral 39 –32 –53 11 16 3.29 
Posterior cingulate 31 –1 –41 40 3.29 
Cerebellum       
Gracile (VIIB)  –23 –66 –33 104 3.59 
Posterior quadrangle (VI)  –20 –54 –14 40 3.39 
       
Probabilistic reasoning minus deduction 
Right hemisphere       
Anterior cingulate 24 –13 39 144 3.61 
Anterior cingulate 24 23 20 104 3.66 
Globus pallidus  13 –2 88 4.11 
Uncus 28 22 –20 72 3.86 
Cerebellum       
Superior semilunar (crus I)  23 –72 –21 56 3.46 
Inferior semilunar (crus II)  45 –50 –29 24 3.26 
Left hemisphere       
Inferior frontal 47 –26 29 –7 152 3.61 
Insula  –32 20 144 3.81 
Posterior cingulate 31 –5 –47 29 136 4.31 
Parahippocampal 36 –26 –43 –5  80 3.96 
Medial frontal –6 47 35 24 3.31 
Inferior frontal 47 –26 15 –18 16 3.26 
Sub-gyral 35 –35 –9 –24 16 3.21 
Paracentral lobule –10 –30 50 3.26 
Midbrain  –9 –25 –11 3.21 
Sub-gyral –34 –11 33 3.11 
Cerebellum       
Posterior quadrangle (VI)  –12 –56 –15 32 3.56 
Inferior semilunar (crus II)  –40 –44 –25 24 3.51 
Gracile (VIIB)  –36 –62 –34 3.11 
Gyrus or regiona Brodmann areab Talairach coordinatesc Extent (mm3Z-score 
  x y z   
aIn parenthesis is the equivalent anatomical label of Schmahmann et al., based on that of Larsell and Jansen (Larsell and Jansen, 1972; Schmahmann et al., 1999).bDesignation of Brodmann areas is approximate and based on a brain atlas.cBrain atlas coordinates (Talairach and Tournoux, 1998) are in millimeters along left–right (x), anterior–posterior (y) and superior–inferior (z) axes. 
Deduction minus probabilistic reasoning 
Right hemisphere 
Middle temporal 21 51 –27 –9 312 4.89 
Anterior cingulate 24 18 –7 37 120 3.99 
Inferior frontal 44 53 16 17 96 3.44 
Caudate  10 72 3.64 
Amygdala  17 –9 –15 64 3.49 
Thalamus  16 –15 32 3.64 
Midbrain  –27 32  3.39 
Temporoparietal 39 34 –69 21 24 3.69 
Fusiform 37 49 –45 –11 16 3.49 
Anterior cingulate 24 18 –15 37 16 3.24 
Middle frontal 36 41 24 16 3.19 
Cuneus 18 –92 16 3.14 
Medial frontal 10 51 3.04 
Cerebellum       
Superior semilunar (crus I)  32 –64 –34 136 3.94 
Gracile (VIIB)  32 –47 –19 32 3.99 
Left hemisphere       
Midbrain  –4 –37 –18 216 5.04 
Thalamus  –10 –9 112 3.74 
Lingual 18 –7 –82 –2 32 3.69 
Lateral globus pallidus  –15 24 3.49 
Thalamus  –13 –17 24 3.24 
Sub-gyral 39 –32 –53 11 16 3.29 
Posterior cingulate 31 –1 –41 40 3.29 
Cerebellum       
Gracile (VIIB)  –23 –66 –33 104 3.59 
Posterior quadrangle (VI)  –20 –54 –14 40 3.39 
       
Probabilistic reasoning minus deduction 
Right hemisphere       
Anterior cingulate 24 –13 39 144 3.61 
Anterior cingulate 24 23 20 104 3.66 
Globus pallidus  13 –2 88 4.11 
Uncus 28 22 –20 72 3.86 
Cerebellum       
Superior semilunar (crus I)  23 –72 –21 56 3.46 
Inferior semilunar (crus II)  45 –50 –29 24 3.26 
Left hemisphere       
Inferior frontal 47 –26 29 –7 152 3.61 
Insula  –32 20 144 3.81 
Posterior cingulate 31 –5 –47 29 136 4.31 
Parahippocampal 36 –26 –43 –5  80 3.96 
Medial frontal –6 47 35 24 3.31 
Inferior frontal 47 –26 15 –18 16 3.26 
Sub-gyral 35 –35 –9 –24 16 3.21 
Paracentral lobule –10 –30 50 3.26 
Midbrain  –9 –25 –11 3.21 
Sub-gyral –34 –11 33 3.11 
Cerebellum       
Posterior quadrangle (VI)  –12 –56 –15 32 3.56 
Inferior semilunar (crus II)  –40 –44 –25 24 3.51 
Gracile (VIIB)  –36 –62 –34 3.11 
Figure 1.

Sample argument stimuli. (a) Two examples of valid arguments followed by one example of an invalid argument, all used in the deduction task. (b) Three examples of arguments used in the probabilistic reasoning task. (The first was constructed to elicit a judgment of high likelihood for the conclusion; the second was constructed to elicit a judgment of low likelihood; the third was intermediate.) (c) Two examples of arguments with anomalous content followed by one without. (d) The six arguments that were evaluated on three separate occasions, once for validity, once for high probability of the conclusion, and once for anomaly.

Figure 1.

Sample argument stimuli. (a) Two examples of valid arguments followed by one example of an invalid argument, all used in the deduction task. (b) Three examples of arguments used in the probabilistic reasoning task. (The first was constructed to elicit a judgment of high likelihood for the conclusion; the second was constructed to elicit a judgment of low likelihood; the third was intermediate.) (c) Two examples of arguments with anomalous content followed by one without. (d) The six arguments that were evaluated on three separate occasions, once for validity, once for high probability of the conclusion, and once for anomaly.

Figure 2.

Deduction-specific rCBF increases in right middle temporal gyrus (BA 21, arrow).

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

Figure 2.

Deduction-specific rCBF increases in right middle temporal gyrus (BA 21, arrow).

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

Figure 3.

Deduction-specific rCBF increases in right inferior frontal cortex (BA 44) and probability-task-specific rCBF increases in left inferior frontal cortex (BA 47).

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

Figure 3.

Deduction-specific rCBF increases in right inferior frontal cortex (BA 44) and probability-task-specific rCBF increases in left inferior frontal cortex (BA 47).

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

Figure 4.

Deduction-specific rCBF increases in right basal ganglia (caudate nucleus, arrow).

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

Figure 4.

Deduction-specific rCBF increases in right basal ganglia (caudate nucleus, arrow).

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

Figure 5.

Deduction-specific rCBF increases in right amygdala; there were no probability-specific activations in amygdala.

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

Figure 5.

Deduction-specific rCBF increases in right amygdala; there were no probability-specific activations in amygdala.

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

Figure 6.

Probability-task specific rCBF increases in left inferior frontal cortex (BA 47).

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

Figure 6.

Probability-task specific rCBF increases in left inferior frontal cortex (BA 47).

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

Figure 7.

Probability-task specific rCBF increases in left posterior cingulate cortex (BA 31).

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

Figure 7.

Probability-task specific rCBF increases in left posterior cingulate cortex (BA 31).

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

Figure 8.

Probability-task specific rCBF increases in left parahippocampal cortex (BA 36).

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

Figure 8.

Probability-task specific rCBF increases in left parahippocampal cortex (BA 36).

Figures 2–8. Grand mean PET–rCBF increases (P < 0.001) for deduction minus probabilistic reasoning (in green–blue Z-score scale) and probabilistic reasoning minus deduction (in yellow–red Z-score scale) overlaid onto subjects' mean anatomical MR images (greyscale) in coronal planes.

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