Evidence from formal logical reasoning reveals that the language of thought is not natural language — part 5/10

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Figure 1. Inductive and deductive logical reasoning paradigms. For inductive reasoning (left),
participants are 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 are then shown another
input list and asked to provide the output list. They are told whether or not their guess about the underlying
rule is correct and are shown another input list. In the fMRI version, after the eighth problem, participants
were told—via a schematic— the correct rule and were asked to apply this rule to two more input lists. For
deductive reasoning ( right), in the verbal version, participants are presented with classic three -sentence
syllogisms and asked to judge the validity of the third sentence (the conclusion) given the first two sentences
(the premises), by pressing one of tw o buttons on a button box. Trials vary in difficulty between harder
deduction (Modus Tollens) and easier deduction (Modus Ponens). In the matrix reasoning version, the fMRI
participants are 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 uses a blocked
design; trials in the hard blocks use stimuli from Cattell (1949), and trials in the easy blocks use 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). In the matrix reasoning version for the participants with
aphasia, the subtest of the Wechsler Abbreviated Scale of Intelligence, Second Edition (WASI-II) was used,
which is conceptually parallel to the matrix reasoning fMRI task. Participants are presented with sets of
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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) are presented in ascending order of difficulty,
consistent with standard WASI-II administration procedures.

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Figure 2. The language system does not support logical reasoning. A. Sample activation maps for the
language contrast (1st row, yellow) and three logical reasoning contrasts (2nd-4th rows, purple and green)
in two individual sample participants. B. Responses in the language network (individually defined in each
participant; see Methods), in percent BOLD signal change, to the language contrast (sentences >
nonwords; estimated in left-out data; grey), the induction contrast (induction > application; magenta), and
the two deduction contrasts (hard deduction > easy deduction; green shades). The bars show the across-
network averages; the means for each of the 5 language fROIs (IFGorb, IFG, MFG, AntTemp, and
PostTemp) are shown with horizontal dashed lines. The error bars correspond to the standard error of the
mean by participant; the light dots correspond to individual participants’ responses. C. The anatomical
scans of S.A. and G.S., brief info on the patients, and a projection of the probabilistic atlas for the
language network (from Lipkin et al., 2022) into the MRI image of G.S. D. Behavioral performance of the
patients with aphasia and—for the critical tasks—control participants. The first column shows
performance on the language evaluation tasks (spoken and written comprehension; Zimmerer et al., 2014)
for S.A. (light grey bars) and G.S. (dark grey bars). Both participants show at or below chance
performance. In the bottom row, we show sample items. (See Methods for additional details of the
linguistic evaluation of the patients.) The second and third columns show performance on the induction
and deduction tasks (S.A.: light grey dots; G.S.: dark grey dots). For the induction task, the control data
LANGUAGE
LOCALIZER...
WORDS
INDUCTION
TASK...
[ 1 2 3 ] --> [ 3 2 1]
[ 8 6 ] --> [ 6 8 ]
[ 5 9 2 ] -->
TASK 1...
If the block is blue,
then is is large.
The block is blue.
LANGUAGE
BEHAVIORAL
ASSESSMENTS
INDUCTION
BEHAVIORAL
TASK
DEDUCTION
BEHAVIORAL
TASK
fMRI participants
Patients with Aphasia
Sentences > Nonwords Rule Induction > Application Hard Deduction > Easy Deduction
Lorem ipsum
Sample Subject 1 Sample Subject 2
BOLD PSC
*He came my house
at six o’clock.
GS Raw Score = 26/30 (Age=50)
SA Raw Score = 25/30 (Age=78)
Rules
Solved
“Got It”
Trial
WASI Matrix Reasoning
PerformanceExample
Anatomical
MRI Image
?
The block is large.
DEDUCTION
TASK 2...
Induction
Activations
Language
Activations
Deduction 1
Activations
Sample Subject 1 Sample Subject 2
Deduction 2
Activations
Induction
Activations
Language
Activations
Deduction 1
Activations
Deduction 2
Activations
SA GS
Functional
Atlas Overlay
GS
Etiology: LH
45
78
LH stroke
48
50
epyema subdural
Age of
Testing:
Age of
Onset:
B.A.
D.C.
Post Temp
MFG
Ant Temp
IFG
IFGorb
Post Temp
MFG
Ant Temp
IFG
IFGorb
Post Temp
MFG
Ant Temp
IFGIFGorb
Post Temp
MFG
Ant Temp
IFG
IFGorb
Post Temp
MFG
Ant Temp
IFG
IFGorb Post Temp
MFG
Ant Temp
IFG
IFGorb
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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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are shown with a pink bar. In the bottom row, we show a sample rule representation generated by G.S.,
where he nicely illustrates the “reverse the numbers” rule. For the deduction task, the control data are
shown with the normal age-matched distribution, and in the bottom row, we show a sample item.

Predictors Estimates p-value
Language Task
Intercept (nonwords) 0.7407 0.0666
Critical Effect (sentences) 1.5518 <0.0001
Induction Task
Intercept (application/post-solution) 0.1408 0.7414
Critical Effect (induction/pre-solution) 0.2601 0.0224
Deduction Task 1
Intercept (easy/Modus Ponens) 1.9361 0.0065
Critical Effect (hard/Modus Tollens) -0.0444 0.7102
Deduction Task 2
Intercept (easy deduction) -0.2234 0.3527
Critical Effect (hard deduction) 0.1533 0.1185
Table 1. The responses of the language system to the language and logical reasoning contrasts. The
results from the linear mixed-effects models (see Methods) at the network level (see Supp. Table 1 for the
results broken down by fROI).

Supplementary Figure 1. The language system does not support logical reasoning: The results broken
down by fROI. A. Responses in the five language fROIs (individually defined and constituting 10% of the
broad parcel masks shown on the brain; see Methods), in percent BOLD signal change, to the language
(grey), induction (magenta), and deduction (green shades) contrasts. The style matches the style of main
Figure 2A. B. Responses in the five language fROIs to the individual conditions relative to the fixation
baseline (cf. the contrasts shown in panel A).

Supplementary Figure 2. The brain systems that support logical reasoning. A. Responses in the
Multiple Demand (MD) system, in percent BOLD signal change, to the MD localizer contrast (a spatial
working memory task; see Methods; blue), and the three logical reasoning contrasts (magenta and green
shades). The MD fROIs are defined within individuals and constitute 10% of the broad parcel masks shown
in blue on the brain. The MD system shows a reliable response to the induction contrast and the matrix
reasoning deduction contrast, but not to the verbal syllogism-based contrast, which more narrowly isolates
deductive reasoning complexity. B. Responses in the brain areas identified with the Hard > Easy contrast
in the verbal deductive reasoning paradigm (i.e., Modus Tollens > Modus Ponens). The fROIs are defined
within individuals (using a porti on of the data) and constitute 10% of the broad parcel masks shown in
green on the brain. The responses are shown in left-out data and reveal a robust and replicable effect.

Supplementary Figure 3. Timing details for the three reasoning tasks used in the fMRI study. Panel
A shows a sample trial structure for the Induction Task, in which participants iteratively generated outputs
from given input lists and received trial -by-trial feedback to discover an underlying transformation rule.
Each rule block consisted of 8 initial problems followed by 2 confirmation trials after the rule was revealed.
Blocks were self -paced, and each scanning run included 2 rule blocks. Panel B shows the trial timing
for Deduction Task 1, which involved syllogistic reasoning using three-statement arguments. Trials varied
in difficulty (e.g., Modus Ponens vs. Modus Tollens), and participants judged the logical validity of the
conclusion. Each run included multiple trials and was self -paced. Panel C shows a sample trial
from Deduction Task 2, which had a blocked design and which required participants to identify the odd
image out among abstract shape sets. Blocks were either “easy” (simple perceptual groupings) or “hard”
(Cattell-type fluid reasoning problems). Each block was 16 seconds long and fixed in length such that
participants could complete as many trials in a block as they were able; all participants completed at least
five hard blocks. See OSF (https://osf.io/jm9rd) for full task materials.

Task Type Beta p-value
Lang LH Inferior Frontal Gyrus (orbital) 1.218 <0.0001
Lang LH Inferior Frontal Gyrus 1.386 <0.0001
Lang LH Middle Frontal Gyrus 1.793 <0.0001
Lang LH Anterior Temporal 1.476 <0.0001
Lang LH Posterior Temporal 1.887 <0.0001
Induction LH Inferior Frontal Gyrus (orbital) 0.302 0.1360
Induction LH Inferior Frontal Gyrus 0.350 0.0092
Induction LH Middle Frontal Gyrus 0.396 0.0301
Induction LH Anterior Temporal -0.060 0.7500
Induction LH Posterior Temporal 0.312 0.0356
Deduction1 LH Inferior Frontal Gyrus (orbital) 0.0647 0.6466
Deduction1 LH Inferior Frontal Gyrus 0.0702 0.6059
Deduction1 LH Middle Frontal Gyrus 0.0645 0.7105
Deduction1 LH Anterior Temporal -0.225 0.0117
Deduction1 LH Posterior Temporal -0.197 0.1717
Deduction2 LH Inferior Frontal Gyrus (orbital) 0.272 0.0448
Deduction2 LH Inferior Frontal Gyrus 0.477 0.0077
Deduction2 LH Middle Frontal Gyrus 0.328 0.0655
Deduction2 LH Anterior Temporal -0.238 0.0265
Deduction2 LH Posterior Temporal -0.073 0.5734
Supplementary Table 1. The results from the linear mixed-effects models (see Methods) at the level of
individual language fROIs . We report uncorrected p -values, and we mark the values that survive the
Bonferroni correction for the number of fROIs (n=5) in bold.

Multiple Demand System Deduction-selective fROIs
Predictors Betas p-value Predictors Betas p-value
Spatial WM Task Deduction Task 1
Intercept (easy) 1.83 <0.0001 Intercept 0.76 0.0016
Critical (hard) 1.50 <0.0001 Critical 0.67 <0.0001
Induction Task
Intercept (application) 1.81 <0.0001
Critical (induction) 0.86 <0.0001
Deduction Task 1
Intercept (Modus Ponens) 2.26 <0.0001
Critical (Modus Tollens) 0.05 0.4822
Deduction Task 2
Intercept (easy deduction) 1.67 <0.0001
Critical (hard deduction) 0.84 <0.0001
Supplementary Table 2. The responses of the Multiple Demand system and the deduction-responsive
brain areas to the logical reasoning contrasts. The results from the linear mixed -effects model (see
Methods),