Twenty-four right-handed young volunteers (12 men and 12 women), with a mean age of 24.67 years (SD = 3.3) and mean education level of 16 years (SD = 0.94) participated in this study. Four participants were excluded from the analysis (two due to noise in MRI images, two due to missing data). Participants spoke Greek as their native language. They all had normal or corrected-to-normal vision and were screened for the absence of neurological or psychiatric disorders. All participants gave signed informed consent, after being thoroughly informed about the procedure.

Verbal instructions, followed by two examples of valid, two of invalid, and two of paradoxical statements, were given to each participant as training in order to ensure that the participant had totally comprehended the task. The participant was instructed to ignore the actual truth value of the conclusion regarding each syllogism and emphasize on evaluating the validity of the arguments (whether the conclusion follows logically from the premises). It should be noted here that all participants had experience in similar tests of logical reasoning that are taught in the Greek high school education.

During the fMRI scanning procedure, participants laid in the MR-scanner with their head secured by foam rubber to minimize movement artefacts. The participants were shielded from noise by earplugs and headphones. Stimuli were presented using a projector outside the magnet room projecting onto a screen in the magnet room that was viewed by the participant via a mirror mounted on the head coil. The sentences were projected with black letters on a white background. E-prime software (Psychology Software Tools, Pittsburgh, PA, United States) running on a personal computer was used to generate visual stimuli and control experimental parameters.

The task was designed to compare two mental functions: processing of syllogisms characterized as paradoxical to processing of valid reasoning. Fifty deductive reasoning syllogisms (25 valid, 25 invalid), 25 paradoxes and 25 baseline trials (control condition) were generated. All valid deductive syllogisms resulted in true conclusions while 20 of the 25 invalid syllogisms resulted in non-true conclusions and five resulted in true conclusions. Stimuli from all conditions were presented pseudo-randomly, in an event-related design. The valid and paradoxical statements that we used are translated and available in a supplementary file submitted to the journal. The experiment was separated in three blocks of 12 min. The order of the trials at each block was counterbalanced. The onset of a deductive syllogism was signaled by a “+” sign, the onset of a paradoxical syllogism by an “*” sign, and the onset of a control trial by an “X” sign (Table 1). All triplets of sentences for each trial appeared on the screen simultaneously and remained visible for 16 s.

In the deduction reasoning trials, participants were required to determine whether the given conclusion followed logically from the premises, thus responding that it was right or wrong (i.e., valid or invalid syllogisms). In the paradoxical reasoning trials, participants were required to determine and respond whether the given conclusion was right or wrong. Finally, in control trials, participants were required to examine and respond whether the words’ spelling of the arguments was correct or wrong. Participants were verbally instructed to read carefully each statement, followed by the question “Right or Wrong?” and respond whether the statement was right or wrong, as quickly as possible. Correct and erroneous responses were recorded as key presses of two buttons on a MR compatible keypad.

Functional MRI was performed using a 3.0 T Achieva TX, Philips manufactured scanner equipped with an eight channel head coil. The brain imaging protocol consisted of axial T2-FLAIR, sagittal high resolution 3DT1-TFE and axial T2* EPI BOLD sequences. The used parameters in BOLD sequence were TR = 2,000 ms, TE = 3 0 ms, flip angle = 90^o, field of view = 256 × 256, acquisition and reconstructed voxel size 3 mm × 3 mm × 3 mm, and sensitivity encoding reduction factor of two. The BOLD sequence was repeated three times with scanning time 12 min for each scan. The scanner was synchronized with the presentation of all trials in each session. The acquisition protocol duration was approximately 45 min. All data underwent visual quality control before further post-processing.

Behavioral data analysis was conducted using IBM SPSS software (version 23). For each trial the type of response was recorded (correct/wrong) as well as the Reaction Time for the button press. Percentage of correct responses was calculated for each one of the valid, invalid, and control trials, for each participant. The percentage of correct responses was not measured for the paradoxes since by definition there is no correct response in this case. Indeed, the percentage of correct answers for paradoxes was close to 50% for each participant as expected. The percentage of correct responses for each trial type was entered in a one-way ANOVA with trial type as the within subject factor. The mean response time was also measured for each trial type (valid, invalid, paradox, and control) for each participant. Then, a one-way ANOVA was performed with trial type as the within-subject factor. Post hoc comparisons were used to test for differences among the four trial types using the Tuckey Honest significance test.

Analysis of fMRI data was conducted using Statistical Parametric Mapping, version 12 (SPM12; Wellcome Department of Cognitive Neurology, London). Functional image volumes were spatially realigned to the mean image to remove movement artifacts. Slice timing correction was also performed to correct for the slice acquisition during the fMRI scanning. Each participant’s T1 weighted structural images were then co-registered to the mean functional image of each scan, and the spatial normalization parameters from gray and white matter segmentation of anatomical images were used to normalize the realigned functional volumes to the Montreal Neurological Institute (MNI) space. The normalized volumes were then smoothed using an 8 mm full width half maximum Gaussian kernel. Canonical hemodynamic response function (HRF) of SPM12 standard was used to create the fMRI model. At the first level analysis, general linear model (GLM) was used to create t-statistical parametric maps for each subject and each session.

For each subject, t-test contrasts for the “valid arguments,” “invalid arguments,” and “paradoxes” vs. baseline (control condition) were calculated. These contrasts were calculated at the second level analysis to make inferences at the group level. Moreover, interaction analysis like the following: (valid reasoning—baseline) vs. (paradoxical reasoning—baseline), (invalid reasoning—baseline) vs. (paradoxical reasoning—baseline), (valid reasoning—baseline) vs. (invalid reasoning—baseline), and vice versa was performed. The results of the second-level analysis were corrected using Family Wise Error (FWE) to achieve corrected p values (p < 0.05). Age and gender were used as nuisance covariates.

The complete data set was transformed into Tailarach space (Talairach and Tournoux, 1988), after correction for differences between the MNI and Tailarach coordinate systems by means of a nonlinear transformation.

The group mean response accuracy was 84.50% (SD = 0.08) for the valid reasoning trials, 84.05% (SD = 0.10) for the invalid reasoning trials, and 85.1% (SD = 0.07) for the control condition. There was no significant difference in response accuracy among the three conditions [F (2, 57) = 0.07, p = 0.933]. The group mean response time (RΤ) was 8.7 s (SD: 1.21) for the valid reasoning trials, 8.63 s (SD: 1.17) for the invalid reasoning trials, 9.77 s (SD: 1.15) for the paradoxical reasoning trials, and 7.97 (SD: 1.34) for the control condition. There was a significant effect of trial type in RT [F (2, 57) = 7.825, p < 0.001]. Specifically, post hoc comparisons confirmed that the mean RT for valid (Tukey post hoc test p = 0.029) and invalid reasoning (Tukey post hoc test p = 0.017), as well as for the control condition (Tukey post hoc test p < 0.001), was significantly smaller than paradoxical reasoning, while all other comparisons did not reach significance.

Regions that demonstrated greater activation for paradoxical reasoning compared to control trials are shown in violet in Figure 1A. A number of frontal, temporal, and occipital cortex regions were activated, including bilateral middle temporal gyrus (BA 21, 19), left inferior frontal gyrus (BA 45), superior frontal gyrus (BA 9), and medial frontal gyrus (BA 8).

Regions that demonstrated greater activation for valid reasoning compared to control trials are shown in cyan in Figure 1B. A number of frontal, parietal, and occipital cortex regions were activated including bilateral parietal lobe (precuneus, BA 7), left inferior frontal gyrus (BA 44), lingual gyrus (BA 17), precentral gyrus (BA 6), right inferior frontal gyrus (BA 9), inferior occipital gyrus (BA 17), and cingulate gyrus (BA 32) were more active for valid reasoning vs. control.

Regions that demonstrated greater activation for the invalid reasoning compared to control trials are shown in blue in Figure 1C. Similar areas were more activated for invalid reasoning compared to control trials as were observed for the contrast of valid reasoning vs. control such as bilateral parietal lobe (precuneus, BA 7), left inferior frontal gyrus (BA 44), right inferior occipital gyrus (BA 17), cingulate gyrus (BA 32), inferior frontal gyrus (BA 9), and left middle temporal gyrus (BA 22).

The activation differences between valid reasoning and paradoxical reasoning trials are shown in Figure 2A. Valid reasoning preferentially activated bilateral inferior parietal lobe (BA 40), superior parietal lobe (precuneus, BA 7, 19) and right middle frontal gyrus (BA 46, 10). Paradoxical reasoning preferentially activated bilateral middle temporal gyrus (BA 21, 37), inferior frontal gyrus (BA 45, 47), and left medial frontal gyrus (BA 8).

The activation differences between invalid reasoning and paradoxical reasoning trials are shown in Figure 2B. The results reveal bilateral activation clusters associated with deductive (invalid) reasoning. Invalid reasoning preferentially activated bilateral inferior parietal lobe (BA 40), left parietal lobe (precuneus, BA 7), and bilateral middle frontal gyrus (BA 46, 10). Paradoxical reasoning preferentially activated left middle temporal gyrus (BA 21, 37) and inferior frontal gyrus (BA 45).

We also examined whether there were differences in activation for valid vs. invalid reasoning trials. We found no significant differences in activation patterns between these subtypes of reasoning. Finally, we examined whether there were activation differences between “yes/no” responses of the paradoxes. However, no significant differences in activation patterns were found.

There was no difference in accuracy (error rate) or response time between valid and invalid arguments in our study. Although, we have specifically instructed participants to concentrate on the logical validity of each argument and test whether the premises provide absolute grounds for accepting the conclusion there could still be a belief bias effect in deductive reasoning trials in which a conclusion might be reached by just checking the truth of the concluding statement. Since all 25 valid syllogisms resulted in true conclusions and 20% of the 25 invalid syllogisms also resulted in true conclusions, if the response was solely based on the truth of the conclusion, error rate should be systematically larger for invalid syllogisms compared to valid which was not the case. Thus, the behavioral results provide evidence against the hypothesis that participants used this strategy (heuristic model) in deductive reasoning trials.

Paradoxes require deep semantic comprehension and mapping procedures, like context and world knowledge integration, reanalyzing meanings, and semantic analysis beyond the surface meaning of the words within, even if they have traditionally simple syntactic structure. These facts could explain the increase in reaction time for paradoxical compared to deductive reasoning. Our results, also, showed that the group mean response accuracy for paradoxical trials was approximately 50%. That was the expected outcome since in paradoxes, there is no right or wrong response. The meaning of an erroneous response in paradoxes is relative and it depends on each subject’s critical point of view.

This is, to our knowledge, the first study to specifically investigate the neural substrate of paradoxical reasoning, using fMRI. Paradoxes activated a fronto-temporal brain network, including bilateral inferior frontal gyrus (BA 45/47), middle temporal gyrus (BA 21/19/37), left medial frontal gyrus (BA 8), and superior frontal gyrus (BA 9). A previous study that has used the same design as the current one was an ERP electrophysiological study (Papageorgiou et al., 2016). Their results suggested that deductive reasoning activated parieto-occipital areas associated with attention and subsequent memory processing, whereas paradoxical reasoning engaged frontal attention mechanisms. Both studies suggest the involvement of different neural networks for deductive and paradoxical reasoning, emphasizing the specific involvement of parietal cortical areas for the former and frontal cortical areas for the latter.

Since this is the first fMRI study attempting to investigate the specific neural network that is engaged in paradoxical reasoning, it is interesting to discuss the role of these areas in other cognitive tasks as suggested by the relevant literature. The left middle temporal gyrus is important for language comprehension and more specifically for lexical semantic processing at the sentence level and in semantic integration of word meaning in the sentence context (Vigneau et al., 2006; Chow et al., 2008; Bosco et al., 2017). Furthermore, this brain area has a key role within the language network, since it has multitudinous connections with different cortical association areas (Rapp et al., 2012). Moreover, right temporal lobe seems to be activated when there is increased need for lexical semantic integration and retrieval (Zempleni et al., 2007).

The inferior frontal gyrus (BA 45/47) plays a key role in semantic language comprehension at the sentence level (Petrides, 2005). The left inferior frontal gyrus is a key region of this fronto-temporal network (especially BA 45/47) and has been related with several higher order control processes, which regulate the selection among multiple competing responses (Petrides, 2005). This brain region, also, plays an important part in semantic retrieval on a sentence level (Petrides, 2005; Sakai, 2005). Moreover, recent studies propose that inferior frontal gyrus (BA 45/47) seems to have a crucial role in semantic and pragmatic processing, including pragmatic and semantic violations. The right inferior frontal gyrus is, also, involved when language processing demand increases (Zempleni et al., 2007).

We could thus hypothesize that this fronto-temporal network plays a dominant role in paradoxical syllogism, as this network is engaged in the comprehension of other non-literal expressions, such as metaphors (Rapp et al., 2004; Mashal et al., 2008; Bohrn et al., 2012), idioms (Zempleni et al., 2007; Bohrn et al., 2012), irony (Shibata et al., 2009; Bohrn et al., 2012), and metonymy resolution (Rapp et al., 2011). The activation of this network in our study might suggest the integration of semantic and world knowledge during comprehension of paradoxes.

Another possible interpretation of these results could be based on the hypothesis that paradoxical syllogisms engage a process of belief revision (retracting a proposition that makes a belief system incoherent by choosing to withdraw the proposition that implies a minimal cost). The Achilles paradox leads to a conflict between prior beliefs—the fleet-footed Achilles will manage to pass the slow-moving tortoise—and logic—Achilles will never surpass the tortoise, since there is an infinite number of points that Achilles must reach, before surpassing it, and by that time the tortoise will have already gone. Thus, the subject is obliged to choose the one proposition among these two that implies minimal cost. Goel et al. (2000) proposed the activation of right prefrontal cortex during belief-logic conflict arguments which is in line with the current study, activation results during paradoxical reasoning.

Finally paradoxical reasoning might be close to enthymematic reasoning, that is reasoning where a premise is missing (thus blocking inference) and an additional premise must be added to the initial stock of premises to carry out the inference process (see for example Brun and Rott, 2013). Prado et al. (2020) tried to investigate the neural substrates of argumentative reasoning. Namely, they designed a task, in which participants had to read and evaluate the same statement. This statement was presented either as an assertion or as the conclusion of an argument (enthymematic categorical syllogisms). They found that there was greater activation of the medial prefrontal cortex in conclusions of arguments than assertions, suggesting that argumentative reasoning might depend on mechanisms which support meta-representational processes.

In previous studies investigating the neural substrate of reasoning, many tasks were used that differed in the type of deductive arguments (relational, conditional, probabilistic, and inductive problems), while only rarely investigators have used a comparison with a non-logical task (Knauff et al., 2002). Our findings indicate that both valid and invalid deductive reasoning engages a neural network comprising bilateral precuneus (BA 7/19), inferior parietal lobule (BA 40) and right middle frontal gyrus (BA 46/10), left inferior frontal gyrus (BA 44), right inferior frontal gyrus (BA 9), left lingual gyrus (BA 17), cingulate gyrus (BA 32), precentral gyrus (BA 6), and right inferior occipital gyrus (BA 17).

Our results are consistent with previous neuroimaging studies, which favor the idea that deductive reasoning is supported by a distributed network of regions including frontal and parietal areas (Knauff et al., 2002; Goel and Dolan, 2004; Monti et al., 2007; Reverberi et al., 2012). Our results are, also, consistent with the idea that reasoning consists complex cognitive process that depends on the activation of several brain areas, including frontal and parietal cortices. This function is, also, linked to working memory, attention and language operations. Consequently, our neuroimaging results provide further support, based on the dual-processing hypothesis in reasoning, that our participants used the analytic slow, sequential process for making logical inferences activating parieto-occipital brain areas and working memory associated areas (De Neys, 2006; Stephens et al., 2020).