The inaugural title in the new, Open Access series BSPS Open, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single (...) formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. Which that is, and its extent, is determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. (shrink)

Je vais traiter ici des inférences dont la validité tient au rôle qu'y jouent les cinq connecteurs « ⊃ », « ∼ », « & », « V » et « ≡ », les deux quantificateurs « ∀ » et « ∃ », et le signe d'identité « = ». Qu'on me permette de rappeler que les deux conjectures présentéd dans ma première étude se sont avéré'es justes. En premier lieu, toute règle de structure et toute règie d'élimination ou d'introduction (...) pour « & » ou « V » qui vaut pour la logique classique des connecteurs vaut également pour la logique intuitionniste des connecteurs. En second lieu, tout énoncé du genre A1, A2, …, An ⊢ B qui vaut pour la logique classique des connecteurs peut s'obtenir exclusivement à l'aide des règles de structure R, P, E, S, et des règles d'elimination et d'introduction pour ceux des connecteurs « ⊃ », « ∼ », « & », « V » et « ≡ » qui figurent dans A1, A2, …, An, et B. (shrink)

RésuméLa croyance que l'on est (ou pas) dans un état de douleur est singulière en ceci qu'elle semble pouvoir être qualifiée d'infaillibilité ou d'incorrigibilité logique, de même que le cogito. Mais comment se peut-il que l'existence d'une croyance (vraie) et l'existence du fait qui est l'objet de cette croyance puisssent constituer la même existence? Je propose ici une réponse à cette question. Parfois, une croyance peut être un désir.

In her engaging book, The referential mechanism of proper names, Li presents empirical studies involving American and Chinese laypeople. Li interprets her results as supporting an epistemic‐perspective reading of the variability in referential intuitions on proper names. Building upon this thesis, Li defends the ambiguity view, claiming that names are ambiguous between a descriptivist and a causal‐historical meaning. I argue that either Li's data do not enable a comparison of the two theories of reference, or support for the ambiguity view (...) is limited to the Chinese sample at most and does not rely upon the inference that Li employs. (shrink)

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...) computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed. (shrink)

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector,” a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine's activation that (...) required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4-year-olds were found. We suggest that children's causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base rate of certain events occurring. Four-year-olds, but not 3-year-olds were able to make this inference. (shrink)

Dag Prawitz’s theory of grounds proposes a fresh approach to valid inferences. Its main aim is to clarify nature and reasons of their epistemic power. The notion of ground is taken to denote what one is in possession of when in a state of evidence, and valid inferences are described in terms of operations that make us pass from grounds we already have to new grounds. Thanks to a rigorously developed proof-as-chains conception, the ground-theoretic framework permits Prawitz to overcome some (...) conceptual difficulties of his earlier proof-theoretic explanation. Though from different points of view, anyway, the two accounts share an issue of recognizability of relevant operational properties. (shrink)

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian (...) conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality. (shrink)

Prawitz has recently developed a theory of epistemic grounding that differs in many respects from his earlier semantics of arguments and proofs. An innovative approach to inferences yields a new conception of the intertwinement of the notions of valid inference and proof. We aim at singling out three reasons that may have led Prawitz to the ground-theoretic turn, i.e.: a better order in the explanation of the relation between valid inferences and proofs; a notion of valid inference based on which (...) valid inferences and proofs are recognisable as such; a reconstruction of the deductive activity that makes inferences capable of yielding justification per se. These topics are discussed by Prawitz with reference to a very general and ancient question: why and how correct deduction has the epistemic power to compel us to accept its conclusions, provided its premises are justified? We conclude by remarking that, in spite of some improvements, the ground-theoretic approach shares with the previous one a problem of vacuous validity which, as Prawitz himself points out, blocks in both cases a satisfactory explanation of epistemic compulsion. (shrink)

The many-property problem has traditionally been taken to show that the adverbial theory of perception is untenable. This paper first shows that several widely accepted views concerning the nature of perception---including both representational and non-representational views---likewise face the many-property problem. It then presents a solution to the many-property problem for these views, but goes on to show how this solution can be adapted to provide a novel, fully compositional solution to the many-property problem for adverbialism. Thus, with respect to the (...) many-property problem, adverbialism and several widely accepted views in the philosophy of perception are on a par, and the problem is solved. (shrink)

We define a class of formal systems inspired by Prawitz’s theory of grounds. The latter is a semantics that aims at accounting for epistemic grounding, namely, at explaining why and how deductively valid inferences have the power to epistemically compel to accept the conclusion. Validity is defined in terms of typed objects, called grounds, that reify evidence for given judgments. An inference is valid when a function exists from grounds for the premises to grounds for the conclusion. Grounds are described (...) by formal terms, either directly when the terms are in canonical form, or indirectly when they are in non-canonical form. Non-canonical terms must reduce to canonical form, and two terms may be said to be equal when they converge towards equivalent grounds. In our systems these properties can be proved through rules distinguished according to whether they concern types or logic. Type rules involve type introduction and elimination, equality for application of operational symbols, and re-writing equations for non-canonical terms. The logic amounts to a sort of intuitionistic system in a Gentzen format. To conclude, we show that each system of our class enjoys a normalization property. (shrink)

Formal models of argumentation have been investigated in several areas, from multi-agent systems and artificial intelligence (AI) to decision making, philosophy and law. In artificial intelligence, logic-based models have been the standard for the representation of argumentative reasoning. More recently, the standard logic-based models have been shown equivalent to standard connectionist models. This has created a new line of research where (i) neural networks can be used as a parallel computational model for argumentation and (ii) neural networks can be used (...) to combine argumentation, quantitative reasoning and statistical learning. At the same time, non-standard logic models of argumentation started to emerge. In this paper, we propose a connectionist cognitive model of argumentation that accounts for both standard and non-standard forms of argumentation. The model is shown to be an adequate framework for dealing with standard and non-standard argumentation, including joint-attacks, argument support, ordered attacks, disjunctive attacks, meta-level attacks, self-defeating attacks, argument accrual and uncertainty. We show that the neural cognitive approach offers an adequate way of modelling all of these different aspects of argumentation. We have applied the framework to the modelling of a public prosecution charging decision as part of a real legal decision making case study containing many of the above aspects of argumentation. The results show that the model can be a useful tool in the analysis of legal decision making, including the analysis of what-if questions and the analysis of alternative conclusions. The approach opens up two new perspectives in the short-term: the use of neural networks for computing prevailing arguments efficiently through the propagation in parallel of neuronal activations, and the use of the same networks to evolve the structure of the argumentation network through learning (e.g. to learn the strength of arguments from data). (shrink)

_Probability: A Philosophical Introduction_ introduces and explains the principal concepts and applications of probability. It is intended for philosophers and others who want to understand probability as we all apply it in our working and everyday lives. The book is not a course in mathematical probability, of which it uses only the simplest results, and avoids all needless technicality. The role of probability in modern theories of knowledge, inference, induction, causation, laws of nature, action and decision-making makes an understanding of (...) it especially important to philosophers and students of philosophy, to whom this book will be invaluable both as a textbook and a work of reference. In this book D. H. Mellor discusses the three basic kinds of probability – physical, epistemic, and subjective – and introduces and assesses the main theories and interpretations of them. The topics and concepts covered include: * chance * frequency * possibility * propensity * credence * confirmation * Bayesianism. _Probability: A Philosophical Introduction_ is essential reading for all philosophy students and others who encounter or need to apply ideas of probability. (shrink)

Upshot: In our target article we claimed that, at least since Weber and Varela, enactivism has incorporated a theoretical commitment to one important aspect of Jonas’s philosophical biology, namely its anthropomorphism, which is at odds with the methodological commitments of modern science. In this general reply we want to clarify what we mean by anthropomorphism, and explain why we think it is incompatible with science. We do this by spelling out what we call the “Jonasian inference,” i.e., the idea that (...) we are entitled, based on our first-person experience of teleology, to take the appearance of teleology in other living beings at face value. (shrink)

This paper advances a version of the theory whereby logic had deep origins in democracy, by re-reading Gorgias’ Encomium of Helen. Democracy, ‘the government by debate’, called political (and scientific) attention to the inferential abilities of citizens and to politicians’ ability of taking advantage of them. Sophists, in particular, discovered that people’s inferences follow constant repeatable forms, that these forms have impact on choices and decisions concerning public good, and then by dominating them you dominate politics in democracy. With the (...) Encomium Gorgias launched these ideas, so laying the ground for Aristotle’s science of deduction. (shrink)

Monte Carlo simulations arrive at their results by introducing randomness, sometimes derived from a physical randomizing device. Nonetheless, we argue, they open no new epistemic channels beyond that already employed by traditional simulations: the inference by ordinary argumentation of conclusions from assumptions built into the simulations. We show that Monte Carlo simulations cannot produce knowledge other than by inference, and that they resemble other computer simulations in the manner in which they derive their conclusions. Simple examples of Monte Carlo simulations (...) are analysed to identify the underlying inferences. (shrink)

In Prawitz’s semantics, the validity of an argument may be defined, either relatively to an atomic base which determines the meaning of the non-logical terminology, or relatively to the whole class of atomic bases, namely as logical validity. In the first case, which may be qualified as local, one has to choose whether validity of arguments is or not monotonic over expansions of bases, while in the second case, which may be qualified as global, one has to choose whether the (...) reduction functions which justify non-primitive inferences are or not base-depending. I claim that these oppositions enjoy some conceptual symmetries, and that these symmetries may be understood as putting restrictions on one’s choice both at the local and at the global level. This produces two different proof-theoretic semantics in line with Prawitz’s tenets. However, I also argue that the symmetries stem from a deeper interaction within Prawitz’s semantics, i.e. non-logical meanings vs interpretation of rules. This interaction is in turn based on some primitive ingredients which, when suitably combined, produce other two Prawitz-compatible readings. The four readings form a diagram where some order relations hold. I finally claim that this diagram is complete, namely that, if we combine the ingredients in ways other than those giving rise to the four readings above, we obtain nothing new, or nothing compatible with general semantic requirements. Thus, symmetries between the local and the global level, and interaction between non-logical meaning and interpretation of rules, produce a complete classification of potential Prawitzian semantics. (shrink)

I provide a general introduction to the notion at issue in this volume, i.e. deduction, and to some akin notions like inference and reasoning. I also argue that logic is, or should be concerned with three attitudes: an archaeological attitude, a nomological attitude, and an aetiological attitude. Then, I sum up the content of the contributions in this volume.

In lieu of an abstract, here is a brief excerpt of the content:69. A PROPOS D'UNE DIFFICULTE LOGIQUE DANS L'ARGUMENT DE CLEANTHE L'argument de Cléanthe ("the Argument from Design", c'est-à-dire la preuve de Dieu par le dessein du monde) se fonde sur le principe que "des effets semblables prouvent des causes semblables" pour montrer que la ressemblance entre le dessein du monde et le dessein des machines amène la conclusion que la cause du dessein du monde ressemble à l'intelligence (...) humaine. Dans l'attaque de Philon contre cet argument, nous trouvons deux passages dans les Parties IV et V consacrés aux difficultés qui proviennent de l'anthropomorphisme de Cléanthe. Et le raisonnement par l'absurde de Philon prend pour point de départ cette conception anthropomorphique de Dieu: Et que dites-vous des découvertes d'anatomie, de chimie, de botanique?... - Ce ne sont certes pas là des objections, répondit Cléanthe; elles découvrent seulment de nouveaux exemples d'art et d'industrie. C'est encore l'image de l'esprit que réfléchissent sur nous d'innombrables objets. - Ajoutez: un esprit pareil à l'esprit humain, dit Philon. - Je n'en connais point d'autre, répondit Cléanthe. - Et plus it est pareil, mieux cela vaut? insista Philon. - Bien sûr, dit Cléanthe. (p. 53) La première étape de son argument s'ensuit: Eh bien, Cléanthe, dit Philon, avec un air d'allégresse et de triomphe, remarquez les conséquences. Premièrement, par cette méthode de raisonnement, vous renoncez à toute prétention à l'infinité en aucun des attributs de la Divinité. Car, puisque la cause doit seulement être proportionnée à l'effet, et que l'effet, pour autant qu'il tombe sous notre connaissance, n'est pas infini, quel droit avons-nous, selon vos suppositions, de prêter cet attribut à l'Etre divin? Vous soutiendrez encore 70. qu'en l'éloignant à ce point de toute similitude avec les créatures humaines, nous donnons dans l'hypothèse la plus arbitraire, et, en même temps, affaiblissons toutes les preuves de son existence. (p. 53) On pourrait croire que l'argument de Philon est inadmissible, soit à cause de son pyrrhonisme, soit à cause de sa doctrine sur la causalité (celle de Hume lui-même) qui n'admet pas la connaissance a priori des causes. Mais en fait l'argument déployé par Philon ne représente pas sa propre position (et n'entre donc pas en conflit avec son pyrrhonisme), et en tant qu'il fait appel à la causalité, n'est point valable. Pour voir qu'il en est ainsi, on n'a qu'à regarder sa phrase préliminaire "par cette méthode du raisonnement" ainsi que la phrase "selon vos suppositions" qui montrent que cette première étape s'ensuit de la position de Cléanthe. Pourquoi Philon met-il en avant cet argument? Ou plutôt, qu'a dit Cléanthe pour amener Philon à mettre cet argument à son compte? La response se trouve dans la version de Cléanthe de la preuve de Dieu par le dessein, dans la Partie II: "Puis donc que les effets se ressemblent entre eux, nous sommes conduits à inférer, d'après toutes les règles de l'analogie, que les causes se ressemblent également, et que l'auteur de la nature est quelque peu semblable à l'esprit de l'homme, quoique doué de facultés bien plus vastes, proportionnées à la grandeur de l'oeuvre qu'il a exécutée. Par cet argument a posteriori, et par cet argument seul, nous prouvons à la fois l'existence d'une Divinité et sa similitude avec l'esprit et l'intelligence de l'homme." (p. 26 les italiques sont de moi) C'est donc Cléanthe qui peu après le début voudrait que, dans ces cas où seul l'effet se fait observer, nous devions proportionner la cause à l'effet. 71. On pourrait m'objecter que je n'ai pas encore montré que l'argument de Philon ne l'engage pas à poser un Dieu fini qui conviendrait à l'effet fini (le dessein du monde), que son propos que "la cause devrait être proportionnée à l... (shrink)

Transcranial magnetic stimulation (TMS) is a method capable of transiently modulating neural excitability. Depending on the stimulation parameters information processing in the brain can be either enhanced or disrupted. This way the contribution of different brain areas involved in mental processes can be studied, allowing a functional decomposition of cognitive behavior both in the temporal and spatial domain, hence providing a functional resolution of brain/mind processes. The aim of the present paper is to argue that TMS with its ability to (...) draw causal inferences on function and its neural representations is a valuable neurophysiological tool for investigating the causal basis of neuronal functions and can provide substantive insight into the modern interdisciplinary and (anti)reductionist neurophilosophical debates concerning the relationships between brain functions and mental abilities. Thus, TMS can serve as a heuristic method for resolving causal issues in an arena where only correlative tools have traditionally been available. (shrink)

The received theories of epistemology identify abductive inferences with the cognitive patterns of speculation (hypothesis formation) and insist that they cannot verify or confirm hypotheses. I criticize various descriptions of abduction, offer a structural analysis of abductive inference,, characterize abduction without alluding to its putative role in inquiry, and then demonstrate that some abductions do provide evidence and that not all scientific hypotheses derive from abductive inferences. This result challenges those notions of scientific k knowledge that dismiss some central scientific (...) ideas (for example, evolution) as ‘meta-physical research programs’ or ‘just theories’ when they are instead well substantiated by abductive evidence. (shrink)