Cartographic systems and non-linguistic inference

Abstract

It is often assumed that the capability to make inferences requires language. Against this assumption, I claim that inferential abilities do not necessarily require a language. On the contrary, certain cartographic systems could be used to explain some forms of inferences, and they are capable of warranting rational relations between contents they represent. By arguing that certain maps, as well as sentences, are adequate for inferential processes, I do not mean to neglect that there are important differences between maps and sentences. Instead, the purpose of this paper is to highlight interesting distinctions that might affect the way that cartographic thinking works.

Keywords:

• Canonical structure
• content
• logical form
• predicates
• quantifiers

Acknowledgements

I am very grateful to Jake Beck, Daniel Burnston, Federico Castellano, Axel Barceló, Salma Saab, Elisabeth Camp, Inés Crespo, and Liza Skidelsky for their extremely helpful comments. Parts of this paper were presented at SPP-2012, in Boulder, and at the IIFs, in Mexico City. I want to thank the audiences for their feedback. I also want to thank the referees and the editor for this journal for all their extensive and insightful critiques and suggestions. This work was supported by CONICET and by PCC-UNC.

Notes

¹ See Bond, Kamil, and Balda (2003); Call (2006, 2006b); Cheney and Seyfarth (1990, 2007); and Seyfarth and Cheney (2001).

² When I say that the content of maps is cartographic, as opposed to propositional, I am using the notion of cartographic in an unusual sense to refer not to the system but to the way in which the content of such systems is structured. The issue about content addressed here is independent of the distinction between wide/narrow content. Particularly, the thesis that some contents are cartographic is compatible with both views since the distinction between propositional/cartographic content is related to the content’s structure, while the wide/narrow distinction is related to the determination of content—whether it is mind-dependent or not. Finally, this issue must be differentiated from another related debate about conceptual and non-conceptual content. Although this proposal can remain neutral to the conceptual and non-conceptual distinction, I have argued elsewhere that maps can have conceptual content in virtue of their predicative and inferential structure (Aguilera, 2014). However, I will not develop this argument here.

³ See Gould (2002); Hills, Jones, and Todd (2012); Moyer and Bayer (1976); O’Keefe and Nadel (1978); and Tolman (1948), among others.

⁴ This debate has been preceded by a long-standing dispute about the representational format of visual mental imagery—whether they are analogue or digital, pictorial or sentential. See Kosslyn (1975) and Pylyshyn (1973). These debates should be carefully distinguished from each other, since they differ not only in the kind of representation involved (pictorial versus cartographic), but also in the processes on which they are focused (mental imagery versus inferential processes).

⁵ Frege and others deny the idea of canonical structure (Gibson, 2004). All we need for the kind of inference of interest here are contents with a predicative structure. My thanks to Axel Barceló for this caveat. For the sake of argument, in this paper I will accept Fodor’s commitment to canonical structure. However, many arguments developed here still hold without it.

⁶ “See, for instance, London subway map at http://content.tfl.gov.uk/standard-tube-map.pdf”

⁶ But how does an element of a map get its meaning? This query is not more problematic than its analogue, “how is the meaning of an element of LOT determined?” An answer to both questions will depend on the theory of meaning selected. One can choose between a causal theory, a teleological one, or any other available in the field.

⁷ Westerhoff (2005) has defined an implication relation for pictures to represent conjunctions, disjunctions, negations, and conditionals. There is no barrier in principle to extend this characterization to cartographic systems. However, his proposal is restricted to the notion of external logical form.

⁸ Compare Dehaene, Dehaene-Lambertz, and Cohen (1998) and Beck (2012).

⁹ If this is so, then the map hypothesis can also explain both the relations and dissimilarities between different forms of human reasoning, such as spatial reasoning, and the justificatory relations between perceptual experience and beliefs.

¹⁰ In contrast to maps, Venn diagrams can represent quantification: an x or a dot in a circle is equal to an existential sentence. Universal information can also be represented, with relations between sets represented by circles. Nevertheless, these systems are inadequate for representing disjunction (Shin, 1994).

¹¹ From the fact that animals make deductive inferences, Burge (2010) concludes that they have propositional thought. However, propositional content requires also predicate-sensitive inferences. Other authors may claim that propositions are simply representations of facts (Casati & Varzi, 1999). Thus, if maps can represent facts, maps have propositional content. However, there are interesting differences in the way in which maps and sentences represent facts and even in the way different sentences do so. Some of those differences can be explained by exploring the structure of their representational content. Therefore, a fine-grained notion of propositional content is needed.

¹² Among other things, these properties provide the basis for many metaphors. A predicate like dark, commonly applied to colorful things, can be applied to mental states, as in ‘she had dark feelings’. See Camp (2004) and Evans (1982) for further discussion.

¹³ It is often claimed that animal cognition is domain-specific. There are different ways of understanding and explaining domain specificity. See, for example, Carruthers (2006) and Hurley (2003). From my point of view, domain specificity and what I call context-bounded predicates can be explained as properties which emerge from non-linguistic systems. But this is compatible with the existence of different origins of domain specificity.