Johan van Benthem (logic – University of Amsterdam): Opening
David Over (psychology – Durham): “New paradigm psychology of conditionals”
There is a new probabilistic, Bayesian paradigm in the psychology of reasoning, with new psychological accounts of the indicative conditional of natural language and conditional reasoning. This new paradigm is greatly supported by experimental results showing that people judge the probability of the indicative conditional, P(if A then B), to be the conditional probability, P(B|A). The experimental support for this conclusion will be described, and an explanation given of how the resulting psychological accounts of the conditional are related to normative theories in philosophical logic, going back to Ramsey and de Finetti. The question will be raised of what the psychological findings and accounts might in turn imply about normative theories.
Michiel van Lambalgen (logic and philosophy – University of Amsterdam): “Logical form in cognitive processes: causal inference in infants”
This talk is concerned with infants' (3 - 30 months) understanding of causality, continuity and inertia, and the role played by inference. While some authors, following Michotte (1962), have argued that causal judgements are based entirely on perceptual cues (e.g. contact), there is now a body of evidence (summarized in Saxe and Carey 2006) that shows that inference plays a role as well, for example inferences based on the dispositional character (inert or self-moving) of the objects involved. Gopnik et al (2004) have argued that these inferences are of a probabilistic nature, where the theory of causal Bayes networks plays the role of the inferential competence model. We will show that there exists a close connection between the theory of causal networks and logic programming with the closed world assumption, and that infants' probabilistic inferences as assumed by Gopnik et al (2004) can be represented as well as logical inferences. We will introduce the event calculus, a general framework for reasoning about causation, and will indicate how the inferences assumed by Saxe and Carey (2006) can be modelled. Lastly, we argue for the domain-generality of this inference mechanism by indicating how it also subserves language comprehension.
Helen de Cruz (philosophy – Leuven University): "Animal logic, an evolutionary perspective on deductive reasoning"
I will provide a comprehensive overview of the research on deductive reasoning in non-human animals, and discuss implications of this for the debate on animal rationality. Over the past decades, comparative psychologists have discovered remarkable capacities for deductive inference in animals, including reasoning by exclusion, transitive inference, and recognition of equivalence relations. Such abilities have sparked a debate about the possibility of logic in the absence of language. Some authors, like the primatologist Daniel Povinelli, have contended that the high context-sensitivity of deductive reasoning skills in animals, and their inability to readily transfer such skills from one domain to another (e.g., transitive inference in the social realm to the physical domain), implies a wide abyss between animal deductive reasoning and human logic. Such authors regard the human ability to use logical inference in a broad range of circumstances, subserved by language, as unique. Others, like the late philosopher Susan Hurley, have proposed that animal deductive reasoning consists of highly context-bound 'islands of practical rationality’. Their approach draws on folk psychology to stress continuities between animal and human rationality. In this paper, I outline an alternative approach, inspired by behavioral ecology and evolutionary theory, to examine animal deductive reasoning. According to this view, the ability for deductive reasoning in humans as well as in other animals can be explained by ecological, context-specific factors. I will relate this view to other recent approaches, including the anthropologist Dan Sperber's view of reasoning as a product of human argumentative skills, and the psychologist Richard Nisbett's observations of the culture-specificity of human reasoning. A behavioral ecological approach can not only explain differences in deductive reasoning between species; it can also clarify why human deductive reasoning is to a certain extent context- and culture-specific.
Keith Stenning (psychology and computer science – University of Edinburgh): "The emergence of classical logic in human reasoning as a case study of individual and societal origins of cognitive capacities"
Stenning and van Lambalgen (2008; 2005 and elsewhere) have argued at length that simple defeasible logics are good models of cooperative discourse in which the goal is to establish single mutual intended models using the surface discourse combined with general and specific contextual knowledge. This logical ability appears early in ontogeny and develops in all 'normal' children in all human cultures. It is foreshadowed in our non-human ancestors in their defeasible planning capacities. A natural question raised by this argument is that of the origin of classical logical (competence and performance) in ontogeny and phylogeny. On one kind of conventionalist view, classical logic was a societal discovery/invention, notably in classical Greece, but independently also in China, India and possibly other cultures. This discovery was incorporated into educational practices (of varying degrees of formality), and, on this story, people learn classical logic rather as they learn mathematics. On a contrasting naturalistic view, even quite young children have some grasp of adversarial reasoning which can appropriately be modelled by classical logic, but they need very considerable support from context to be able to perform simple classical reasoning, and to avoid distraction by, and confusion with, their defeasible reasoning capacities. On this view, what happened in ancient Greece was the emergence of societal institutions which allowed the externalisation of classical reasoning, and subsequently the formulation of the theories of that reasoning which we know as classical logic. Educational practices in different cultures, and even in the same culture, vary greatly in how they foster or suppress an explicit grasp of the principles of classical reasoning. This talk will attempt an exploration and synthesis of these two views, illustrated with evidence from empirical studies of students' logic learning.
Rafael Nuñez (cognitive science – UC San Diego): “Towards an embodied grounding of logic: a view from cognitive science”
What is the nature of logic, and where does it come from? For several centuries these foundational questions have been addressed primarily through the lens of formal tools, holding the belief that the study of how one ought to think can be a subject matter in itself. Such approaches have been unnecessarily reductionistic and have neglected important biological, cognitive, and cultural dimensions that make human thinking possible. Moreover, they have ignored the actual practice of how humans think in real-world settings with stable and precise conceptual systems. In this presentation I'll defend the view that essential ingredients of what we call logic today, such as validity, truth, consistency, and proof, are already present in everyday informal conceptual systems which have precise inferential organization, are ubiquitous and systematic, are largely shared by communities of individuals, and have psychological reality as they manifest unconsciously and effortlessly in empirically observable behaviors. These conceptual systems and their inferential organization are supra-individual in nature, and pre-exist argumentation, explanation, demonstration, proof, and notation (and therefore formalization); they are neither deductive nor are they determined evolutionarily via natural selection. Moreover, they can be internally consistent but mutually inconsistent. To support my arguments, I'll give examples from empirical work conducted in my lab on spatial conceptualizations of time involving psycholinguistic experiments, neuroimaging, and cross-cultural speech-gesture studies among the Aymara of the Andes and the Yupno from the remote highlands of Papua New Guinea.
Francis Jeffrey Pelletier (cognitive science, philosophy, linguistics – Simon Fraser University): "Reasoning with generic information"
The type of statement under consideration is what Krifka et al. (1995) called “characterizing genericity”. This type of genericity can be expressed in a number of different ways, they say. For instance (1) a. Predatory animals have sharp teeth. (Bare Plural) b. Most predatory animals have sharp teeth. (Quantificational) c. The typical predatory animal has sharp teeth. (Noun Modifier) d. Predatory animals usually have sharp teeth. (Adverb-1) e. Predatory animals normally have sharp teeth. (Adverb-2) There are other forms also, but the ones given in (1) are representative of the variety that are mentioned in the literature. Mostly, authors will mention all of these as merely alternative formulations of the same semantic item—that is, they are claimed to have the same generic force or meaning. Of course, just what is the generic force is a contested topic. According to a view commonly attributed to Greg Carlson (see, e.g., Carlson, 1995), there are two basic types of opinion on this matter: “the inductivist approach” and “the rules and regularities approach”. The former approach has a driving intuition that, underneath it all, generic sentences express inductive generalizations– where the basis of the generalization is some observed set of instances. The idea is that, after observing a number of instances of predatory animals with sharp teeth, a sentence like (1-a) is generated as a covering description. Carlson (1995, p. 225) says “the most natural bedfellows of this approach would be empiricists, verificationists, and nominalists of varying stripes.” The rules and regularities approach denies that generic statements are truly asserted on the basis of any array of instances, saying instead that their truth would mirror some causal organization within the world. The philosophical perspective of those who would adopt this view are those who “admire properties and propositions as real entities,. . . as would many realists”.
The present study aims to challenge the view that all genericity is viewed the same way by ordinary speakers of natural language. Intuitively, a sentence such as (1-b) ought to be a paradigm case of the inductivist approach since most seems clearly to call for some sort of explicit comparison of the number of predatory animals with versus without sharp teeth. The version worded as (1-a) seems most straightforwardly to embody the rules and regularities approach, since we seem to be appealing to the very kind itself, Predatory Animals, and its regulatory properties. The other versions in (1) can be seen as going either way, or perhaps even changing their interpretations depending on the context or example under discussion. We show, by means of an empirical study of the way ordinary speakers reason using these different expressions of generic information, that there are at least two different types of generic statements, and that they are differentiated by means of these modifiers. Although it is a further interpretation to put upon the present findings, a natural interpretation might be that the two types correspond to Carlson’s two viewpoints, and that each viewpoint finds itself most clearly represented by different ones of the sentences in (1). We can at least say that our findings are consistent with the view that the two different background interpretations for characterizing generics find expression in syntactically different sentence-types.
References
Carlson, G. (1995). Truth-conditions of generic sentences: Two contrasting views. In G. Carlson and F. J. Pelletier (Eds.), The Generic Book, pp. 224–237. Chicago: University of Chicago Press.
Krifka, M., F. J. Pelletier, G. Carlson, A. ter Meulen, G. Chierchia, and G. Link (1995). Genericity: An introduction. In G. Carlson and F. J. Pelletier (Eds.), The Generic Book, pp. 1–124. Chicago: University of Chicago Press.
Catarina Dutilh Novaes (philosophy – University of Amsterdam): “Formal languages and the extended, altered mind”
Clark and Chalmers (1998) have drawn our attention to the wide range of external devices that are inherently involved in some of our mental processes and reasoning. They claim that these devices can be considered as part and parcel of the agent’s mind in specific cases – hence, the extended mind hypothesis. Importantly, though, the subsequent debates on the notion of the extended mind have mostly focused on the increase in computational power afforded by such external devices. Indeed, to my knowledge, the possibility of actually ‘running a different software’, as it were, by means of external devices has not been seriously considered. In this talk, I will argue that formal languages, and more generally formal frameworks such as mathematical formalisms, may allow us to accomplish just that, i.e. to run a different software. I will argue that they make it possible to counter what Stanovich (2003, 292) has described as “one of the fundamental computational biases of human cognition – the tendency to automatically bring prior knowledge to bear when solving problems.” In virtue of a process of ‘de-semantification’ (Krämer 2003) that typically accompanies uses of formal languages, it becomes possible for the agent to reason following patterns other than the ones she typically follows when unaided by these devices. Hence, more than just extending the mind and increasing its computational power, formal languages may go as far as altering the mind (albeit momentarily) in that they offer a counterbalance to some deeply entrenched reasoning mechanisms.
References
A. Clark & D. Chalmers 1998, ‘The extended mind’. Analysis 58, 10-23.
S. Krämer 2003, ‘Writing, notational iconicity, calculus: on writing as a cultural technique’. Modern Languages Notes - German Issue, vol. 118, n. 3, John Hopkins University Press, 518-537.
K. E. Stanovich 2003, ‘The fundamental computational biases of human cognition: Heuristics that (sometimes) impair decision making and problem solving’. In J. E. Davidson & R. J. Sternberg (Eds.), The psychology of problem solving. New York, CUP, 291-342.
Abstracts -- Contributed talks
M.J. Frápolli & S. Assimakopoulos (University of Granada): “The inferential nature of logical constanthood: The case of conjunction”
There is currently no general definition of logical constanthood with which all logicians and philosophers of logic agree. In our talk, we want to address this issue by putting forward a proposal about what the distinctive feature of logical constants is. Our suggestion will be that by focusing too much on structural aspects we have forgotten Frege’s project. In this respect, the original intuitions that gave rise to the development of modern logic are closer to the insights of Relevance Theory and Truth Conditional Pragmatics than to the uninterpreted mathematical systems so commonly implemented by contemporary logicians. From our point of view, a logical constant has to be an aid to draw inferences. This means that the expressions that enjoy this status should have some kind of dynamic meaning, a meaning that conveys the idea that a truth preserving transition is taking place. In this setting, we will deal with the exemplar case of conjunction, the import of which cannot be realistically exhausted by its traditional truth-functional account. Contrary to the common assumption, we want to defend that when the meaning of conjunction is completely characterized by its classical truth-table, then it is not working as an inferential tool, and should not be understood as a logical constant. As we will argue, such a conclusion stems from the unification of arguments put forth in philosophy of logic, linguistics and cognitive psychology.
Shira Elqayam (De Montfort University, Leicester): “Normativism and descriptivism in psychology of reasoning: the role of formal systems”
The role of formal systems vis-à-vis psychological research can be conceptualised in two fundamentally different ways: descriptively, as competence- or computational-level analysis; and normatively, as normative, ‘ought’ systems (‘normativism’). While drawing on formal systems is inarguably beneficial for psychology as well as philosophy, I will propose that the normativist view of this relationship has outlived its usefulness and is now more hindrance than help. First, normativism leads psychologists to arbitrate between alternative normative systems by drawing on empirical data, thus running afoul of the notorious is-ought problem. Second, normativism has engendered a host of research biases in psychology of reasoning; for example, psychologists tend to avoid research questions with no obvious norms, even when they reflect pertinent philosophical issues. Lastly, I will argue that normativism is not only harmful but unnecessary as well, as computational-level descriptivism can preserve the benefits that formal systems and psychology can offer each other.
Ole Hjortland (Arché-St. Andrews): “Is logic empirical?”
Logical inferentialism says that the meaning of a logical connective is determined by the inference rules that govern its use. For the inferentialist, acquisition and possession of a logical concept require competence with the corresponding set of basic inference rules. Frequently, such inference rules are characterised proof-theoretically, say, in natural deduction or sequent calculus. Ultimately, the inferentialist claims that competence with such rules entitles the reasoner to a priori basic beliefs about logic. Williamson (2007) has raised a number of objections to inferentialist views formulated by Boghossian (2003) and Wright (2001). Here we will pursue one of these objections, an argument from the psychology of reasoning. Williamson suggests that the inferentialist's proof-theoretic characterisation of logical reasoning is misguided. This, he contends, is evidenced by experimental data which supports a 'mental models' account of reasoning rather than a 'mental rules' account. We argue against Williamson that he overestimates the connection between formal model- and proof-theory and their psychological counterparts. However, the inferentialist hypothesis does have empirical content, and we will outline where such theories are vulnerable to experimental data.
Ben Sheredos & Tyler Marghetis (University of California, San Diego): “Towards a new psychologistic logic; some anti-Fregean (and Fregean!) hypotheses”
Frege provided a model for understanding natural language, as well as some of the most influential developments in the history of logic. In doing so, he famously criticized the psychologistic logicians of his day. Frege viewed psychology as a descriptive science of mind-dependent, private, subjective states. This rendered psychology irrelevant to a theory of natural language (since nothing psychological was readily communicable) and irrelevant to a universal, prescriptive, mind-independent logic. We have three main goals in this talk. First, using the case of natural language, we show how modern sciences of the mind are not the introspective psychology which Frege found wanting: contra Frege, cognitive sciences can and do locate shared cognitive and semantic structures which underwrite natural language communication. More generally, cognitive science is not confined to the study of private, subjective mental states: the in-principle complaint that psychologism cannot speak to issues of objectivity or universality is thus avoided. Our second aim is to assess the remaining claim against psychologism: the gulf between logic as prescriptive, and psychology as descriptive. Drawing from similar debates elsewhere, we sketch three mutually-supporting hypotheses which are empirically testable, and which would undermine the presumed prescriptive character of logic. Third and finally, we hope to bring attention to some of Frege’s less-celebrated remarks regarding the use of sensible symbol-systems as crucial aids for abstract reasoning, suggesting some positive, Fregean hypotheses that a new psychologism could pursue on its own terms.
Fred Sommers (Brandeis University): “A Cognitive Logic””
The fact that we reason with ‘the speed of thought’ has always fascinated me. Even an 8 year old can instantly transform ‘Not all dogs are friendly’ into its logical equivalent ‘Some dogs aren’t friendly.’ I discovered that a fully realized algebraic calculus for logic could explain how we are able to reckon algebraically with the natural formative elements that drive everyday reasoning: We reckon with words and particles like ’is,’ ‘some,’ ‘and’ as plus-signs and with words like ‘not’ ‘all,’ and ‘if,’ as minus-signs. That’s why we can reason as efficiently and rapidly as we reckon with the pluses and minuses of expressions in elementary algebra. Sensitive to the +/- character of the natural formatives, a child will instantly transform ‘Not{-} all{-} dogs are{+} friendly’ into its “logibraic” equivalent ‘Some {+} dogs aren’t{-} friendly’ by reckoning ‘ -(-D+F)’ equal to ‘+D-F’. Coming across an assertion like ‘every dog is a canine but someone who petted a dog didn’t pet a canine’ an adult will instantly reject it because it (syllogistically) entails ‘someone who petted a canine didn’t pet a canine:
-D+C
+(P+D) – (P+C)
+(P+C) – (P+C)
I hope to interest cognitive psychologists to empirically investigate the hypothesis that we actually-- intuitively, unconsciously-- reason in this “logibraic” manner .
Adam Streed (University of California, San Diego): “Expressivism as a Reasonable Psychologism”
Fregean objections to psychologism seemed to have doomed empirical approaches to the philosophy of logic, but in his flight from psychologism Frege arrived at an unpalatable Platonism. For anyone wishing to steer a middle course between Platonism and psychologism, expressivism---the view that logic's distinctive role is to express reasoners' attitudes---looks attractive. I will first examine the most fully-worked-out expressive account of logic, presented by Robert Brandom (1994, 2008), showing how it is a kind of psychologism that is not vulnerable to the classic Fregean objections. I then offer some reason to think that Brandom's account is not especially amenable to input from empirical work on cognition. Finally, I attempt to generalize expressivism in such a way as to make empirical work relevant, by decoupling the expressive conception from Brandom's account of reasoning.
Alexandra Varga (Central European University - Budapest) & Michiel van Lambalgen (University of Amsterdam): “Infants’ closed-world reasoning about what to do, when, what for”
Infants’ observational learning of means actions involving artifact manipulation, as it manifests itself in selective reenactment, is a form of rational behavior (Gergely et al. 2002). It is supported by non-monotonic goal-centered reasoning processes such as goal attribution, plan recognition, offline and online planning of own actions, constrained by closed-world assumptions. We spell out these processes in the logical framework of the event calculus, which embodies default closed-world reasoning, and has a non-monotonic consequence relation. The methodological implication stresses the insightful role of using logical formalisms for fine-grained explanations of psychological findings.
Mark Zelcer & Leib Litman (Touro College) : “A cognitive neuroscience approach to the sorites paradox”
Typical approaches to resolving the sorites paradox attempt to show, in one way or another, that the sorites argument is not paradoxical after all. However, if one can show that the sorites is not really paradoxical then the task remains of explaining why it appears to be a paradox. Our approach to the paradox begins by addressing the appearance of paradox then explores what this means for the paradox itself. We examine the paradox from the perspective of the various brain systems that are intuitively comfortable with the key features of the premises of the sorites argument. We suggest that the explicit and implicit, or symbolic and sub-symbolic, cognitive systems are separately responsible for the initial plausibility of the categorical and inductive premises. The appearance of paradox is a function of our brain's architecture and arises from the conflicting interactions of neurologically distinct systems.
