Evidence from formal logical reasoning reveals that the language of thought is not natural language — part 4/10

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MATERIALS AND METHODS
Study 1 (fMRI) Participants. Twenty-nine participants contributed data to the fMRI component
of the study (15 female; mean age = 27.3 years, SD = 12.9; all but three participants were right -
handed; the one ambidexterous and two left -handed participants had left -lateralized language
systems, as determined by the language localizer task described below. All participants completed
the language localizer task an d the Multiple Demand (MD) localizer task (used in control
analyses). Different subsets of the 29 participants completed the three logic tasks, with at least 17
participants performing each task ( 17 completed the induction task; 23 completed the verbal
deduction task; and 17 completed the deductive matrix reasoning task ). The participants were
recruited from MIT and the surrounding Cambridge/Boston, MA, community and paid for their
participation. All were native English speakers, had normal hearing and vision, and had no history
of language impairment. All participants provided written informed consent in line with the
requirements of MIT’s Committee on the Use of Humans as Experimental Subjects.
Study 2 (behavior) Participants. Two profoundly aphasic male participants took part in the study
(S.A. 78 years; G.S. 50 years). Both had large lesions that had significantly damaged the left
inferior frontal and left temporal brain areas. Both were native English speakers, did not present
with any visual impairm ents, and were pre -morbidly right -handed. Both individuals were
classified as severely agrammatic (SI Table 3), but their nonlinguistic cognitive skills were largely
spared, with the exception of below -average Digit Span scores, in line with an impaired
phonological loop (SI Table 3). We also tested 40 age -matched neurotypical control participants
(20 female; mean age 56 years, SD = 10.7, range: 40 to 86 years). The mean number of years of
education was 17.2 (SD = 2.3), perhaps driven up by the fact that our recruitment posters described
the study as consisting of logic puzzles. All participants were native English speakers, had normal,
or corrected -to-normal vision, and no history of speech or language disorders, neurological
diseases, or reading impairments, and performed within the normal range on the mini mental status
examination (MMSE; Folstein et al., 1975). All participants completed the experiments
individually, in a quiet room, with an experimenter present throughout the testing session. Ethics
approval was granted by the UCL Research Committee ( LC/2023/05). All participants provided
informed consent prior to taking part in the study.
Induction Task (fMRI, behavior). Participants were shown an input list of 1 -5 single -digit
numbers and an output list of 0-5 single-digit numbers and asked to guess the rule that transformed
the input list into the output list. They were then shown another input list and asked to provide the
output list. They were told whether or not their guess about the underlying rule is correct and are
shown another input list. In the fMRI version, the responses were entered via a scanner-safe fiber-
optic button response device (Nata Technologies LxPad system), which contains 12 buttons
allowing input of digits 0–9, backspace, and enter (Figure 1, left panel). Each trial (corresponding
to a rule) consisted of 8 problems. After the eighth problem, participants were told —via a
schematic (Figure 1, left panel)—the correct rule and were asked to apply this rule to two more
input lists. Because in most cases, participants guessed the correct rule part-way through the initial
list of 8 problems (as indicated by generating correct output lists for the last several problems), we
defined the induction period as the subset of the eight problems before the problem after which the
participant made no more errors, and the application period as the subsequent problems along with
the two problems after the correct rule was revealed. The induction > application contrast targets
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neural processes involved in hypothesis generation and rule discovery beyond those required for
rule implementation and response entry. Each participant completed 40 rules (all the materials are
available at OSF: https://osf.io/jm9rd). The rules were distributed across 20 scanning runs, with 2
rules per run and each run lasting between 200s and 420s (durations are variable given the self -
paced nature of the task; see SI Figure 3A for the timing details).

For the behavioral version of the task, the problems were presented on paper, and participants
provided written responses. The same 40 rules were used, except that a few problems were added
in order to have 14 problems (input-output pairs) per rule, and a few problems were replaced based
on feedback from the fMRI participants who found some input-output pairs confusing. The stimuli
were divided into four sets, with ten rules per set. GS completed all 40 rules across several sessions
(~6 rules per session); SA only completed sets 1-3 also across sessions (~4 rules per session); the
variability in the number of rules per session was due to age-related health conditions and because
the experiment had to be completed amongst other necessary activities at routine check-in sessions.
Prior to the experiment, participants with aphasia were s hown an example rule, which acted as a
training item. Control participants each completed one set of 10 rules within a single testing
session, and 10 participants completed each set. A break was offered half-way through the testing
session, during which th ey could rest and also complete the brief MMSE (performance on the
MMSE was used as an inclusion criterion). The order of the rules within a set was kept constant
across participants, but the order of the problems within a rule was randomized. For both the
patients and the controls, testing for a given rule was stopped after the participant answered four
problems in a row correctly, which was taken as evidence that they guessed the transformation
rule correctly. Time permitting, the participants with aphasi a were sometimes offered to
schematically illustrate the rule they guessed (see Figure 2 for an example).
Deduction Task 1 – Verbal deductive reasoning (fMRI). Participants were presented with classic
three-sentence syllogisms and asked to judge the validi ty of the third sentence (the conclusion)
given the first two sentences (the premises), by pressing one of two buttons on a button box. Each
trial corresponded to a syllogism, and trials varied in difficulty between harder deduction (Modus
Tollens) and eas ier deduction (Modus Ponens), and in whether the problems use d real words or
nonwords; the experiment also include d two conditions of no interest (challenging memory
conditions). The Modus Tollens > Modus Ponens contrast targets cognitive processes related to
the complexity of logical deductive reasoning. Each participant completed between 16 and 32 trials
of each condition (all the materials are available at OSF: https://osf.io/jm9rd). The trials were
distributed across two scanning runs, with 8 trials per condition per run and each run lasting
between 551 s and 1,034 s (durations are variable given the self -paced nature of the task; see SI
Figure 3B for the timing details).
Deduction Task 2 – Deductive matrix reasoning (fMRI). Participants were presented with sets of
four images of geometrical shapes and asked to decide which image does not fit with the others,
by pressing one of four buttons on a button box. The experiment use d a blocked design; trials in
the hard blocks use d stimuli from Cattell (1949), and trials in the easy blocks use d simpler
problems created by Woolgar et al. (2013), who adapted this task for fMRI (e.g., three images of
the same simple shape and an image of a different shape). The hard > easy contrast targets
cognitive processes related to relational reasoning, hypothesis generation, and deductive inference.
Each participant completed a single run of the task lasting 320 s and consisting of 8 easy blocks
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was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
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and 8 hard blocks. The blocks were of fixed length (16 s), which means that only a few hard trials
could be solved during this period (between one and six), and more easy trials could be solved
(between 4 and 15; see SI Figure 3C for the timing details); furthermore, because only 24 hard
items were available, some partic ipants did not have enough items for all 8 blocks, but every
participant completed at least 5 hard blocks (all the materials are available at OSF:
https://osf.io/jm9rd).
Deduction Task 3 – Deductive matrix reasoning (behavior). This task is the Matrix Reasoning
subtest of the Wechsler Abbreviated Scale of Intelligence, Second Edition (WASI -II), which is
conceptually parallel to the matrix reasoning fMRI task. Participants were presented with sets of
several images of geometrical shapes with one image missing and asked to choose the missing
image from five possible options to complete the pattern. The test was administered on paper and
participants indicated their choice by pointing. The items (total number = 30) were presented in
ascending order of difficulty, consistent with standard WASI -II administration procedures. Prior
to the main test, participants were shown a short set of practice items to familiarize them with the
task. These practice items illustrated the nature of the patterns, and participants were provided with
explanations (including gestural cues, where necessary) to aid comprehension. Testing was
stopped after the participant answered three problems incorrectly.
Critical Analyses - fMRI. (For the details of fMRI data acquisition, preprocessing, and modeling,
see Supplementary Methods.) To test whether the language areas respond during logical reasoning
tasks, we used an extensively validated language localizer (Fedorenko et al., 2010) to identify
regions of interest functionally in individual participants. Participants were asked to attentively
read sentences and sequences of nonwords; for details on this paradigm, see Supp. Methods. The
responses in the langua ge fROIs were statistically evaluated using linear mixed -effects models
implemented in R (lme4 package; Bates et al., 2015), with random intercepts for participants and
regions. P-values were approximated using the lmerTest package (Kuznetsova et al., 2017 ), and
effect sizes (Cohen’s d) were estimated using the EMAtools package (Kleiman, 2017). For each
contrast, we fit separate models at both the network level and for individual fROIs.
The network-level model: BOLD ∼ Condition + (1 | Participant) + (1 | fROI).
The individual fROI-level model: BOLD ∼ Condition + (1 | Participant).

To ensure that our logical reasoning tasks elicit a strong response somewhere in the brain, we
performed two analyses. First, we used a spatial working memory task (keeping track of 8 vs. 4
squares in a 3x4 grid) as a localizer for the Multiple Demand network (e.g., Assem et al., 2020b);
for details on this paradigm see Supp. Methods. And second, because the verbal deductive
reasoning task did not elicit a response in the MD networ k, we additionally performed a whole -
brain search for areas that respond to the Modus Tollens > Modus Ponens contrast. We used a
group-constrained subject -specific (GSS) analysis (Fedorenko et al., 2010; Julian et al., 2012),
which is similar to a random -effects group analysis but allows for inter -individual variability in
the precise locations of functional areas. This analysis identified a few areas in the frontal and
parietal cortex that responded strongly to the deduction contrast (in left -out data). The responses
in the MD and deductive -reasoning fROIs were statistically evaluated similarly to the language
fROIs’ responses.

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was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
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Critical Analyses – Behavior. For the induction task, we used the Crawford and Howell (1998)
test to compare each patient’s perfor mance to the controls. The Matrix Reasoning WASI -II data
were scored according to the standard guidelines provided in the official manual. Each item was
evaluated for accuracy, and raw scores (total correct out of 30) were converted into T-scores using
age-normed tables (μ = 50, σ = 10). These T-scores were the basis for statistical comparison with
the normative control sample from the testing manual, consistent with standard single -case
methods and group -level reference data. (For information on the behavi oral performance of
participants in the fMRI task, see Supp. Methods.)