Recently, a cottage industry has formed with the goal of analyzing reasoning. The relevant notion of reasoning in which philosophers are expressly interested is fixed through an epistemic functional description: reasoning—whatever it is—is our personal-level, rationally evaluable means of meeting our rational requirements through managing and updating our attitudes. Roughly, the dominant view in the extant literature as developed by Paul Boghossian, John Broome, and others is that reasoning (in the relevant sense) is a rule-governed operation over propositional attitudes (or their contents) that results in a change in attitude (e.g., the adoption of a new belief). In this paper, I argue that our personal-level operations over mental models and visuospatial imagery, which are representations in a non-propositional/analogue format, can be rationally evaluable processes of managing our attitudes and, thus, should be considered reasoning in the relevant sense. Furthermore, I show that if reasoning can occur through operations over mental models and imagery, then the dominant rule-following account mischaracterizes (a) the cognitive operations and representational states assumed to be constitutive of reasoning and (b) what grounds the rational status of a line of reasoning.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
In this paper, I focus on theoretical (as opposed to practical) reasoning, that is, reasoning that culminates in a change in attitude with mind-to-world direction of fit. Although my arguments can be extended to practical reasoning as well, I focus on theoretical reasoning for sake of space.
Outside of Koziolek (2017), Quilty-Dunn and Mandelbaum (2018) contemporary theorists rarely distinguish between inference and reasoning. I follow suit and speak of inference and reasoning interchangeably. In older philosophical discussions of inference and reasoning it appears more popular to distinguish between the two (e.g., Brown 1955; Ryle 1949; Welsh 1957).
My characterization of Canonical Form borrows from Broome (2013, Ch. 14) who argues that the diachronic rules that govern reasoning are instances of the following schema:
From S to derive Q
where proper substitutions for ‘S’ and ‘Q’ are expressions of marked contents, which are pairs of propositions and attitude types (e.g., beliefs or suppositions).
Broome (2013, chapter 14), for example, argues that a bit of reasoning is correct if the rules one follows in reasoning correspond to basing permissions. A basing permission for a proposition or proposition type, P, indicates a further proposition or proposition type on which a belief in P can be based.
I characterize the algorithmic model as involving the following position,
The fact that we can operate over our propositional attitudes by following rules that are a function of the syntactic structure of their contents requires that we have access to this structure; in order for us to have this access, the structure of the representational states through which we reason must reflect the structure of the propositional contents of those representations.
On an alternate way of reading Broome, he is also arguing that the rules we follow in reasoning are always functions of the form of (as opposed to the conceptual content of) our premise and conclusion attitudes. Under this reading, Broome’s account of reasoning couldn’t cover the possibility of material inference (cf. Brandom 1994). However, seeing that there is a substantive debate regarding, for example, whether inductive inference as practiced in the sciences is licensed by universal formal schemas or by a series of domain-specific empirical facts, we oughtn’t analyze reasoning in a manner that doesn’t allow for material inference (Norton 2003). Regardless, I am reading Broome as making a claim about the structure of the representational states involved in reasoning as opposed to the rules we follow in reasoning. Thank you to an anonymous referee for a discussion of this point.
Alternatively, one could argue that reasoning requires representing both (a) the contents of our occurrent attitudes and (b) the syntax of those propositional contents. Representations of a and b would give us the syntactic awareness needed to apply rules that are functions of syntax without requiring that the mental states through which we reason be of any particular representational format. For example, Machery (2005) argues that conscious thought can involve representing natural language sentences in inner speech without thereby requiring the thought itself to occur in language. Machery argues that inner speech involves auditory or articulatory images, which are not themselves syntactically structured. In inner speech, the content of one’s auditory images is a sentence (or sentences), and, thereby, one has access to the syntax of the content of one’s representation without the auditory images themselves (the representational vehicle) having a discursive structure. This idea doesn’t avoid the objections I raise for the algorithmic model. Even if we can make sense of the syntax of the contents of models or images, I will discuss reasoning that involves entertaining mental models or images that don’t involve a representation of the syntax of the contents of those models or images.
The fact that Quilty-Dunn and Mandelbaum distinguish inference from reasoning should be kept in mind. But the mental models account of deductive reasoning, for example, is an alternative account of how we perform deductive inference that doesn’t require that the representational states through which we reason have a discursive structure.
Broome (ibid., p. 224) asserts, “I am inclined to believe that…to reason consciously, you must express your attitudes to yourself in language.” It appears that Broome is attracted to the position that conscious reasoning has to occur through something like inner or explicit speech. Boghossian explicitly distances himself from Broome’s remarks that reasoning requires expressing our thoughts in language. In order for Broome to argue that all conscious reasoning occurs through something akin to inner or explicit speech he would need to argue that (a) all reasoning is propositional reasoning (the position I argue against in this paper), and (b) all propositional thought must occur through inner or explicit speech. In support of b theorists like Carruthers (2002), for example, have argued that conscious propositional thinking occurs in something like inner speech (although Carruthers allows that non-propositional conscious thought can occur through, e.g., visuospatial imagery). But evidence for unsymbolized thinking (Heavey and Hurlburt 2008; Hurlburt and Akhter 2008) challenges the plausibility of b. Roughly, an unsymbolized thought is a conscious thought with a particular (potentially propositional) content that isn’t accompanied phenomenologically by words expressed in inner or explicit speech, symbols, or images. One may be able to recreate the content of the unsymbolized thought in speech, but there was no inner or explicit speech or mental image experienced at the time one was entertaining the content. Hurlburt and Heavey provide compelling reason to believe that unsymbolized thinking occurs quite commonly. I will not take the algorithmic model to be committed to b and, therefore, I focus my critique on a. However, Broome’s apparent commitment to b open’s his theory to further empirical critique.
A large body of empirical literature provides support for the claim that reasoning can involve the transformation and manipulation of representations in non-propositional formats. For example, classic work on mental rotation (Shepard and Metzler 1971) and scanning tasks (Kosslyn et al. 1978) is frequently cited by advocates of pictorial reasoning. Performance on mechanical reasoning tasks, like determining from a diagram how certain gears and pulleys will interact, is highly correlated with spatial but not verbal ability (Hegarty 2004; Hegarty and Sims 1994). If the algorithmic model were correct, we would expect to see a high correlation between mechanical reasoning and verbal ability—but this is not the case. In addition, reasoning processes used in spatial transformation tasks, like Move and MA, involve brain regions that subserve visuospatial and visuomotor processing as opposed to regions involving linguistic processing (Hanakawa et al. 2003; Kosslyn 2005). Insofar as we allow that perceptual processing involves non-propositional formats of representation, we have reason to accept that imaginative simulations are not propositional.
It should be noted that the propositional/non-propositional distinction, as I am understanding it, is a distinction between formats or vehicles of representation. As Heck (2000) notes, there is an ambiguity in how the conceptual/non-conceptual or propositional/non-propositional content distinction is traditionally drawn in terms of whether the distinction is one between types of content (e.g., Fregean senses or sets of possible worlds) or the structure of the states that bear the content. Although there are detractors (cf. Crane 2009), its generally accepted that perception has propositional content and, thereby, qualifies as a propositional attitude (Kalpokas forthcoming). Similarly, I accept—at least for the sake of this paper—that mental models and imagery have propositional content; I am arguing that the representational states that bare this content and figure in reasoning are not of a discursive, language-like format of representation. However, Heck (2007) argues that mental imagery, specifically, cognitive maps representing a spatial layout, have non-propositional content. Heck argues further that we use cognitive maps in reasoning, e.g., to form attitudes about how to navigate an environment, and that we update our maps in light of relevant evidence as we would propositional attitudes. One could argue against the dominant rule-following account by arguing that reasoning needn’t involve operations over propositional attitudes. However, arguing that we can reason through operations over attitudes with non-propositional content would require an account of (a) the nature of non-propositional content and (b) how representational states with non-propositional content can bare epistemic support relations to other attitudes with propositional content, like beliefs. Providing an account of a and b is beyond the scope of this paper.
I defend the claim that imaginative simulations are rationally evaluable in Sect. 3.3.
Although there are various simulation theories of disparate aspects of cognition in the cognitive psychological literature (Hesslow 2012), not all of these theories use the term ‘simulation’ univocally and not every type of simulation will count as reasoning. For example, take Goldman (2006) simulation theory of mind reading—our ability to determine the mental states of others based on various cues and background knowledge. Goldman distinguishes between various types of simulation and claims that mind reading involves what he terms ‘replication simulation’. To understand replication simulation, imagine that you are trying to determine how some individual, T, is feeling in light of being in certain other mental states, M1, M2, …Mn. On Goldman’s simulation theory, you determine how T feels by ‘replicating’ M1, M2, …Mn in yourself and processing these states in the (purportedly) same fashion as T through ‘enactment imagination’. This enactment imagination is not suppositional; in imagining that you feel or desire as T you don’t merely adopt the supposition that you feel or desire as T. According to Goldman, you put yourself in states of quasi-feeling, quasi-desiring, etc., (I will label these quasi states as ‘QM1’, ‘QM2’,…‘QMn’) and then allow your cognitive architecture to naturally take its course in generating some output, QMn+1, which you subsequently interpret to be how T feels (minus the pretensive aspect of the state). Your pretensive mental states are not representations of the corresponding M1, M2, …Mn in T, and you do not employ any type of background theory or information about T’s mental life, e.g., folk psychology, to operate over these representations to determine how T feels in light of M1, M2,…Mn. Instead, you merely exploit (though not necessarily self-consciously) the fact that you cognitively operate like T. Your transition from QM1, QM2, …QMn to QMn+1 is not part of your reasoning about T; you merely use your cognitive functioning as a source of evidence about T’s cognitive functioning.
Unlike replication simulation, the simulations involved in MA and Move are properly part of your calculation and your determination of how to maneuver the chair through the door, respectively. In Move and MA, you are not exploiting similarities between your cognitive functioning and the physical systems of the chair and door or the abacus that you model in imagination; you are generating representations of the chair and door and the abacus and operating over those representations in light of background information about how these systems function. A full discussion of various notions of simulation is beyond the scope of this paper, but it should be clear what features of the imaginative simulations in Move and MA qualify these simulations as reasoning in the relevant sense. Again, Move and MA consist in rationally evaluable, reason responsive operations over representational states with mind-to-world direction of fit with the end of determining the attitudes that are rationally appropriate given our background attitudes and evidence—not all simulations discussed in simulation theories of cognition involve these features.
By “mere mental search for justifying evidence” I mean a search process that doesn’t itself constitute reasoning. In order to successfully raise a challenge for my position on the grounds that the cognitive operations in Move are a search for evidence, one has to demonstrate that Move is a mere search where the successive generation of dynamic visuospatial representations of moving the chair through the door is not itself reasoning but is instead, say, the result of some non-reasoned capacity we have for generating visuospatial representations. Of course, a search for justifying evidence can constitute reasoning. For example, say you are attempting to determine whether some proposition, p, is the case. You rightly determine that (a) if some further proposition, q, is the case, you would have very good evidence for p, and (b) you can conclude p on the basis of q. You also have reason to believe that attempting to determine whether q is the case would be easier than attempting to determine p directly. You may then try and abandon several lines of reasoning after determining they are dead ends before finally realizing that you can conclude q by reasoning thusly (deixis to the line of reasoning you perform in successfully concluding q). Your various attempts to reason to q can be described as a targeted search for evidence, but this search is itself reasoning, unlike the mere mental search involved in the word jumble. Analogously, we can describe the reasoning involved in Move as a targeted search for evidence, i.e., a search for a dynamic visuospatial representation of a means of moving the chair through the door that is consistent with your background (tacit) attitudes regarding, e.g., the structural properties of solid objects, the interaction of physical bodies, etc. Describing Move as a targeted search for evidence doesn’t preclude Move from being reasoning. Thank you to an anonymous referee for urging me to clarify this point.
Gauker argues that non-conceptual content cannot provide justification for propositional attitudes, but Gauker allows that non-conceptual content can play an important epistemic role through guiding belief formation. Gauker’s claims are not incompatible with my argument.
Various cultures have developed different abaci types, which represent integers through different bead arrangements. Different abacus systems will require moving beads in different ways to perform one and the same mathematical operations.
MA is not merely a convenient mnemonic device for storing antecedently calculated values. One determines sums through ‘moving’ bead representations. One of the cognitive benefits of using MA is that one can perform calculations through the concrete task of ‘moving’ bead representations.
Otherwise, we run into familiar Carroll (1895) regress worries.
Aguilera, M. (2016). Cartographic systems and non-linguistic inference. Philosophical Psychology,29(3), 349–364.
Audi, R. (1986). Belief, reason, and inference. Philosophical Topics,14(1), 27–65.
Blachowicz, J. (1997). Analog representation beyond mental imagery. Journal of Philosophy,94(2), 55–84.
Boghossian, P. (2008). Epistemic rules. Journal of Philosophy,105(9), 472–500.
Boghossian, P. (2014). What is inference? Philosophical Studies,169(1), 1–18.
Boghossian, P. (2018). Delimiting the boundaries of inference. Philosophical Issues,28(1), 55–69.
Braine, M., & O’Brien, D. (Eds.). (1998). Mental logic. Mahaw, NJ: Lawrence Erlbaum Associates, Publishers.
Brandom, R. (1994). Making it explicit: Reasoning, representing, and discursive commitment. Cambridge, MA: Harvard University Press.
Broome, J. (2013). Rationality through reasoning. Malden, MA: Wiley-Blackwell.
Broome, J. (2014). Normativity in reasoning. Pacific Philosophical Quarterly,95(4), 622–633.
Brown, D. (1955). The nature of inference. The Philosophical Review,64(3), 351–369.
Camp, E. (2007). Thinking with maps. Philosophical Perspectives,21(1), 145–182.
Carroll, L. (1895). What the tortoise said to achilles. Mind,4(14), 278–280.
Carruthers, P. (2002). The cognitive functions of language. Behavioral Brain Sciences,25(6), 657–674.
Crane, T. (2009). Is perception a propositional attitude? Philosophical Quarterly,59(236), 452–469.
Dominowski, R. L., & Ekstrand, B. R. (1967). Direct and associative priming in anagram solving. Journal of Experimental Psychology,74(1), 84–86.
Drayson, Z. (2012). The uses and abuses of the personal/subpersonal distinction. Philosophical Perspectives,26(1), 1–18.
Frank, M. C., & Barner, D. (2012). Representing exact number visually using mental abacus. Journal of Experimental Psychology: General,141(1), 134–139.
Gauker, C. (2011). Words and images: An essay on the origin of ideas. Oxford: Oxford University Press.
Glüer, K., & Wikforss, Å. (2009). Against content normativity. Mind,118(469), 31–70.
Glüer, K., & Wikforss, Å. (2013). Against Belief Normativity. In T. Chan (Ed.), The aim of belief (pp. 80-99). Oxford Oxford University Press.
Goldman, A. I. (2006). Simulating minds: The philosophy, psychology, and neuroscience of mindreading. Oxford: Oxford University Press.
Gottschling, V. (2006). Visual imagery, mental models, and reasoning. In C. Held, M. Knauff, & G. Vosgerau (Eds.), Advances in psychology (Vol. 138, pp. 211–235). Amsterdam: Elsevier.
Hanakawa, T., Honda, M., Okada, T., Fukuyama, H., & Shibasaki, H. (2003). Neural correlates underlying mental calculation in abacus experts: A functional magnetic resonance imaging study. Neuroimage,19(2), 296–307.
Hatfield, G. (2002). Perception as unconscious inference. In D. Heyer & R. Mausfeld (Eds.), Perception and the physical world: Psychological and philosophical issues in perception (pp. 113–143). West Sussex, UK: Wiley.
Heavey, C. L., & Hurlburt, R. T. (2008). The phenomena of inner experience. Consciousness and Cognition,17(3), 798–810.
Heck, R. (2000). Nonconceptual content and the “space of reasons”. Philosophical Review,109(4), 483–523.
Heck, R. (2007). Are there different kinds of content? In B. P. McLaughlin & J. D. Cohen (Eds.), Contemporary debates in philosophy of mind (pp. 117–138). Oxford: Blackwell.
Hegarty, M. (2004). Mechanical reasoning by mental simulation. Trends in Cognitive Sciences,8(6), 280–285.
Hegarty, M., & Sims, V. K. (1994). Individual differences in mental animation during mechanical reasoning. Memory & Cognition,22(4), 411–430.
Hesslow, G. (2012). The current status of the simulation theory of cognition. Brain Research,1428, 71–79.
Hlobil, U. (2016). What is inference? Or the force of reasoning (PhD—Doctor of Philosophy Unpublished Doctoral dissertation). University of Pittsburgh. Retrieved from http://d-scholarship.pitt.edu/28130/.
Hurlburt, R. T., & Akhter, S. A. (2008). Unsymbolized thinking. Consciousness Cognition,17(4), 1364–1374.
Jackson, M. B., & Jackson, B. B. (2013). Reasoning as a source of justification. Philosophical Studies,164(1), 113–126.
Johnson-Laird, P. N. (1980). Mental models in cognitive science. Cognitive science,4(1), 71–115.
Johnson-Laird, P. N. (1998). Imagery, visualization, and thinking. In J. Hochberg (Ed.), Perception and cognition at century’s end (pp. 441–467). London: Academic Press.
Johnson-Laird, P. N. (2006). How we reason. Oxford: Oxford University Press.
Kalpokas, D. (forthcoming). Perception as a propositional attitude. Theoria. An International Journal for Theory, History and Foundations of Science. https://www.ehu.eus/ojs/index.php/THEORIA/article/view/20574/18873.
Kosslyn, S. M. (1981). The medium and the message in mental imagery: A theory. Psychological Review,88(1), 46–66.
Kosslyn, S. M. (1996). Image and brain: The resolution of the imagery debate. Boston, MA: MIT press.
Kosslyn, S. M. (2005). Mental images and the brain. Cognitive Neuropsychology,22(3–4), 333–347.
Kosslyn, S. M., Ball, T. M., & Reiser, B. J. (1978). Visual images preserve metric spatial information: Evidence from studies of image scanning. Journal of Experimental Psychology: Human Perception and Performance,4(1), 47–60.
Kosslyn, S. M., Thompson, W. L., & Ganis, G. (2006). The case for mental imagery. Oxford: Oxford University Press.
Koziolek, N. (2017). Inferring as a way of knowing. Synthese. https://doi.org/10.1007/s11229-017-1632-4.
Leibowitz, H., Brislin, R., Perlmutrer, L., & Hennessy, R. (1969). Ponzo perspective illusion as a manifestation of space perception. Science,166(3909), 1174–1176.
Machery, E. (2005). You don’t know how you think: Introspection and language of thought. British Journal for the Philosophy of Science,56(3), 469–485.
Maley, C. J. (2011). Analog and digital, continuous and discrete. Philosophical Studies,155(1), 117–131.
Malmgren, A. S. (2018). Varieties of inference? Philosophical Issues,28, 221–254.
McCloskey, M., Caramazza, A., & Green, B. (1980). Curvilinear motion in the absence of external forces: Naive beliefs about the motion of objects. Science,210(4474), 1139–1141.
Munroe, W. (2019). Rationality, reasoning well, and extramental props. Res Philosophica,96(2), 175–198.
Nersessian, N. J. (2002). The Cognitive Basis of Model-Based Reasoning in Science. In P. Carruthers, S. Stich, & M. Siegal (Eds.), The cognitive basis of science (pp. 133–153). Cambridge: Cambridge University Press.
Nersessian, N. J. (2007). Thought experimenting as mental modeling: Empiricism without logic. Croatian Journal of Philosophy,7(20), 125–161.
Nes, A. (2016). The sense of natural meaning in conscious inference. In T. Breyer & C. Gutland (Eds.), Phenomenology of thinking (pp. 97–115). New York: Routledge.
Neta, R. (2013). What is an inference? Philosophical Issues,23(1), 388–407.
Nisbett, R. E., & Wilson, T. D. (1977). Telling more than we can know: Verbal reports on mental processes. Psychological Review,84(3), 231–259.
Nolfi, K. (2015). Which mental states are rationally evaluable, and why? Philosophical Issues,25(1), 41–63.
Norton, J. D. (2003). A material theory of induction. Philosophy of Science,70(4), 647–670.
Pollock, J. L., & Cruz, J. (1999). Contemporary theories of knowledge (2nd ed., Vol. 35). Lanham, MD: Rowman & Littlefield.
Pylyshyn, Z. W. (1981). The imagery debate: Analogue media versus tacit knowledge. Psychological Review,88(1), 16–45.
Pylyshyn, Z. W. (2002). Mental imagery: In search of a theory. Behavioral and Brain Sciences,25(2), 157–182.
Pylyshyn, Z. W. (2003). Return of the mental image: Are there really pictures in the brain? Trends in Cognitive Sciences,7(3), 113–118.
Quilty-Dunn, J., & Mandelbaum, E. (2018). Inferential transitions. Australasian Journal of Philosophy,96(3), 532–547.
Ramsey, W. M. (2007). Representation reconsidered. Cambridge: Cambridge University Press.
Rescorla, M. (2009). Cognitive maps and the language of thought. British Journal for the Philosophy of Science,60(2), 377–407.
Rips, L. J. (1990). Reasoning. Annual Review of Psychology,41(1), 321–353.
Rips, L. J. (1994). The psychology of proof: Deductive reasoning in human thinking. Boston, MA: MIT Press.
Rumfitt, I. (2015). The boundary stones of thought: An essay in the philosophy of logic. Oxford: Oxford University Press, USA.
Ryle, G. (1949). The concept of mind. London: Hutchinson’s University Library.
Schonbein, W. (2014). Varieties of analog and digital representation. Minds and Machines,24(4), 415–438.
Schwartz, D. L., & Black, T. (1999). Inferences through imagined actions: knowing by simulated doing. Journal of Experimental Psychology. Learning, Memory, and Cognition,25(1), 116.
Schwitzgebel, E. (2008). The unreliability of naive introspection. Philosophical Review,117(2), 245–273.
Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science,171(3972), 701–703.
Smith, E. E., Langston, C., & Nisbett, R. E. (1992). The case for rules in reasoning. Cognitive science,16(1), 1–40.
Stich, S. P. (1978). Beliefs and subdoxastic states. Philosophy of Science,45, 499–518.
Titelbaum, M. (2015). Rationality’s fixed point (or: In defense of right reason). In T. S. Gendler & J. Hawthorne (Eds.), Oxford studies in epistemology (Vol. 5, pp. 253–294). Oxford: Oxford University Press.
Toppinen, T. (2015). How norms (might) guide belief. International Journal of Philosophical Studies,23(3), 396–409.
Valaris, M. (2014). Reasoning and regress. Mind,123(489), 101–127.
Valaris, M. (2017). What reasoning might be. Synthese,194(6), 2007–2024.
Valaris, M. (2019). Reasoning and deducing. Mind,128(511), 861–885.
Vosgerau, G. (2006). The perceptual nature of mental models. In C. Held, M. Knauff, & G. Vosgerau (Eds.), Advances in psychology (Vol. 138, pp. 255–275). Amsterdam: Elsevier.
Wedgwood, R. (2006). The normative force of reasoning. Noûs,40(4), 660–686.
Welsh, P. (1957). On the nature of inference. Philosophical Review,66(4), 509–524.
Westerhoff, J. (2005). Logical relations between pictures. Journal of Philosophy,102(12), 603–623.
White, A. R. (1971). Inference. Philosophical Quarterly,21(85), 289–302.
Williamson, T. (2007). The philosophy of philosophy. Malden, MA: Blackwell Publishing.
Worsnip, A. (2019). Isolating correct reasoning. In M. B. Jackson & B. B. Jackson (Eds.), Reasoning: New essays on theoretical and practical thinking. Oxford: Oxford University Press.
I would like to thank Kirk Ludwig, Emmalon Davis, Timothy Perrine, Cameron Buckner, and Wendy Rosenthal for comments on earlier drafts. I am also indebted to two anonymous referees for their insightful remarks on the manuscript.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Munroe, W. Reasoning, rationality, and representation. Synthese (2020). https://doi.org/10.1007/s11229-020-02575-6