A theoretical pillars of vision science in the information-processing tradition is that perception involves unconscious inference. The classic support for this claim is that, since retinal inputs underdetermine their distal causes, visual perception must be the conclusion of a process that starts with premises representing both the sensory input and previous knowledge about the visible world. Focus on this “argument from underdetermination” gives the impression that, if it fails, there is little reason to think that visual processing involves unconscious (...) inference. Here an alternative means of support for this pillar is proposed, based on another foundational challenge for the visual system: recognizing invariant properties of objects in the environment even though anything we encounter is never seen exactly the same way twice. Explaining how the visual system solves this invariance problem requires positing visual processes that exhibit many commonalities with inductive inference. Thus, this novel “argument from invariance” reveals one way in which visual processing clearly involves unconscious inference. (shrink)

I show that a version of Ockham’s razor (a preference for simple answers) is advantageous in both domains when infallible inference is infeasible. A familiar response to the empirical problem..

We show that the consistency of the first order arithmetic $PA$ follows from the pointwise induction up to the Howard ordinal. Our proof differs from U. Schmerl [Sc]: We do not need Girard's Hierarchy Comparison Theorem. A modification on the ordinal assignment to proofs by Gentzen and Takeuti [T] is made so that one step reduction on proofs exactly corresponds to the stepping down $\alpha\mapsto\alpha [1]$ in ordinals. Also a generalization to theories $ID_q$ of finitely iterated inductive definitions is (...) proved. (shrink)

Putnam and Laudan separately argue that the falsity of past scientific theories gives us reason to doubt the truth of current theories. Their arguments have been highly influential, and have generated a significant literature over the past couple of decades. Most of this literature attempts to defend scientific realism by attacking the historical evidence on which the premises of the relevant argument are based. However, I argue that both Putnam's and Laudan's arguments are fallacious, and hence attacking their premises is (...) unnecessary. The paper concludes with a discussion of the further historical evidence that would be required if the pessimistic induction is to present a serious threat to scientific realism. (shrink)

In _Reliable Reasoning_, Gilbert Harman and Sanjeev Kulkarni -- a philosopher and an engineer -- argue that philosophy and cognitive science can benefit from statistical learning theory, the theory that lies behind recent advances in machine learning. The philosophical problem of induction, for example, is in part about the reliability of inductive reasoning, where the reliability of a method is measured by its statistically expected percentage of errors -- a central topic in SLT. After discussing philosophical attempts to evade (...) the problem of induction, Harman and Kulkarni provide an admirably clear account of the basic framework of SLT and its implications for inductive reasoning. They explain the Vapnik-Chervonenkis dimension of a set of hypotheses and distinguish two kinds of inductive reasoning. The authors discuss various topics in machine learning, including nearest-neighbor methods, neural networks, and support vector machines. Finally, they describe transductive reasoning and suggest possible new models of human reasoning suggested by developments in SLT. (shrink)

Through a study of argument, science, art, and human intelligence, Louis Groarke explores and builds on a line of Aristotelian thought that traces the origins of logic and knowledge to a mental creativity that is able to leap to insightful and truthful conclusions on the basis of restricted evidence. In an Aristotelian Account of Induction Groarke discusses the intellectual process through which we access the "first principles" of human thought - the most basic concepts, The laws of logic, The (...) universal claims of science and metaphysics, And The deepest moral truths. Following Aristotle and others, Groarke situates the first stirrings of human understanding in a creative capacity for discernment that precedes knowledge, even logic. Relying on a new historical study of philosophical theories of inductive reasoning from Aristotle To The twenty-first century, Groarke explains how Aristotle offers a viable solution To The so-called problem of induction, while offering new contributions to contemporary accounts of reasoning and argument and challenging the conventional wisdom about induction. In recovering and developing philosophical ideas that have been largely overlooked or misrepresented by more recent sources, An Aristotelian Account of Induction makes a major contribution To The historical study of philosophy and to critical debate. (shrink)

I consider and reject William Whewell's attack on the inductivism of Isaac Newton and John Stuart Mill, as well as John Norton's attack on any universal system of inductive rules. I also explain how a system of inductive rules of the sort proposed by Newton and Mill should be understood.

My purpose in this chapter is to survey some of the principal approaches to inductive inference in the philosophy of science literature. My first concern will be the general principles that underlie the many accounts of induction in this literature. When these accounts are considered in isolation, as is more commonly the case, it is easy to overlook that virtually all accounts depend on one of very few basic principles and that the proliferation of accounts can be understood as (...) efforts to ameliorate the weaknesses of those few principles. In the earlier sections, I will lay out three inductive principles and the families of accounts of induction they engender. In later sections I will review standard problems in the philosophical literature that have supported some pessimism about induction and suggest that their import has been greatly overrated. In the final sections I will return to the proliferation of accounts of induction that frustrates efforts at a final codification. I will suggest that this proliferation appears troublesome only as long as we expect inductive inference to be subsumed under a single formal theory. If we adopt a material theory of induction in which individual inductions are licensed by particular facts that prevail only in local domains, then the proliferation is expected and not problematic. (shrink)

1. I shall attempt in this paper to give a rounded, if schematic, account of the concept of probability. My central concern will be to clarify the sense in which law-like statements (including 'statistical' law-like statements) are made probable by observational data which, in a sense equally demanding analysis, 'accord' with them.

By a well-known result of Kotlarski et al., first-order Peano arithmetic \ can be conservatively extended to the theory \ of a truth predicate satisfying compositional axioms, i.e., axioms stating that the truth predicate is correct on atomic formulae and commutes with all the propositional connectives and quantifiers. This result motivates the general question of determining natural axioms concerning the truth predicate that can be added to \ while maintaining conservativity over \. Our main result shows that conservativity fails even (...) for the extension of \ obtained by the seemingly weak axiom of disjunctive correctness \ that asserts that the truth predicate commutes with disjunctions of arbitrary finite size. In particular, \ implies \\). Our main result states that the theory \ coincides with the theory \ obtained by adding \-induction in the language with the truth predicate. This result strengthens earlier work by Kotlarski and Cieśliński. For our proof we develop a new general form of Visser’s theorem on non-existence of infinite descending chains of truth definitions and prove it by reduction to Gödel’s second incompleteness theorem, rather than by using the Visser–Yablo paradox, as in Visser’s original proof. (shrink)

The basic assumptions in the physical theory of Brownian motion are analized and the arbitrary character of certain aspects of the current theories is emphasized. The most serious limitations of the theory arise from the fact that in the theory, the elementary processes of the individual collisions are nowhere discussed. However, it is shown that the encounters between stars under their Newtonian inverse square attractions considered in Stellar Dynamics provides, in virtue of the peculiar character of inverse square forces, a (...) case in Brownian motion in which all phases of the problem can be explicitly analyzed. Thus, the separation, of the effects of encounters into a dynamical friction and a random fluctuation is explicitly demonstrated from a direct analysis based on the dynamics of the encounters themselves; similary, the ratio of the frictional to the diffusion coefficients can also be shown to have the value which is required for the restoration and maintenance of a Max‐wellian distribution of velocities from any arbitrary initial distribution. ‐ S. C. (shrink)

We present an explanatory objection to Norton's material theory of induction, as applied to predictive inferences. According to the objection we present, there is an explanatory disconnect between our beliefs about the future and the relevant future facts. We argue that if we recognize such a disconnect, we are no longer rationally entitled to our future beliefs.

In a formal theory of induction, inductive inferences are licensed by universal schemas. In a material theory of induction, inductive inferences are licensed by facts. With this change in the conception of the nature of induction, I argue that the celebrated “problem of induction” can no longer be set up and is thereby dissolved. Attempts to recreate the problem in the material theory of induction fail. They require relations of inductive support to conform to an (...) unsustainable, hierarchical empiricism. (shrink)

I wish more books of philosophy were like this one. It is elegantly written. It is filled with provocative claims and ingenious arguments. It is a really good read, even while it forces us to rethink many of our assumptions about practical reason and practical reasoning, morality and agency.

Many philosophers agree that Hume was not simply objecting to inductive inferences on the grounds of their logical invalidity and that his description of our inductive behaviour was inadequate, but none the less regard his argument against induction as irrefutable. I argue that this constellation of opinions contains a serious tension. In the light of the tension, I re-examine Hume’s actual sceptical argument and show that the argument as it stands is valid but unsound. I argue that it can (...) only be converted into a sound one if our inductive behaviour can be characterized as a process of rule-governed ampliation. Drawing on some Bayesian ideas, I argue that our inductive behaviour probably cannot be characterized in that way, so our immunity from Hume is secure. Finally, I compare my response to Hume’s argument with some other well known responses. (shrink)

Does the past rationally bear on the future? David Hume argued that we lack good reason to think that it does. He insisted in particular that we lack — and forever will lack — anything like a demonstrative proof of such a rational bearing. A surprising mathematical result can be read as an invitation to reconsider Hume's confidence.

In a recent essay, John Norton proposes a material theory of induction, according to which all justification for inductive inference ultimately stems from the particular facts of the case at hand. Despite being sympathetic to the pluralistic spirit of this proposal, I argue that central controversies among leading theories of inductive inference turn not on material facts but upon normative judgments regarding the proper standards and aims of induction. Thus, a pluralistic approach to induction can be successfully (...) developed only given an explanation of how the choice of such aims and standards depends on features of particular cases. (shrink)

The necessitarian solution to the problem of induction involves two claims: first, that necessary connections are justified by an inference to the best explanation; second, that the best theory of necessary connections entails the timeless uniformity of nature. In this paper, I defend the second claim. My arguments are based on considerations from the metaphysics of laws, properties, and fundamentality.

Graphical displays of simple moving geometrical figures have been repeatedly used to study the attribution of animacy in human observers. Yet little is known about the relevant movement characteristics responsible for this experience. The present study introduces a novel parametric research paradigm, which allows for the experimental control of specific motion parameters and a predictable influence on the attribution of animacy. Two experiments were conducted using 3D computer animations of one or two objects systematically introducing variations in the following aspects (...) of motion: directionality, discontinuity and responsiveness. Both experiments further varied temporal kinematics. Results showed that animacy experience increased with the time a moving object paused in the vicinity of a second object and with increasing complexity of interaction between the objects . The experience of animacy could be successfully modulated in a parametric fashion by the systematic variation of comparably simple differential movement characteristics. (shrink)

This article poses a challenge to Schurz’s proposed metainductive justification of induction. It is argued that Schurz’s argument requires a notion of optimality that can deal with an expanding pool of prediction strategies.

One type of soft-line reply to manipulation arguments, which I call ‘the another-agent reply’, focuses on the existence of some controlling agent and how this can undermine the actor's moral responsibility. A well-known challenge to this type of reply is the so-called ‘machine induction’ case. This paper provides an argument for why ‘machine induction’ presents no real challenge to the another-agent reply. It further argues that any soft-liner who does not leave room for the existence of some controlling (...) agent in their explanation of why manipulation undermines responsibility will face a dilemma. Thus, instead of presenting a challenge to the another-agent reply, ‘machine induction’ actually presents a reason in support of it. (shrink)

Over the last few decades Michael Dummett developed a rich program for assessing logic and the meaning of the terms of a language. He is also a major exponent of Frege's version of logicism in the philosophy of mathematics. Over the last decade, Neil Tennant developed an extensive version of logicism in Dummettian terms, and Dummett influenced other contemporary logicists such as Crispin Wright and Bob Hale. The purpose of this paper is to explore the prospects for Fregean logicism within (...) a broadly Dummettian framework. The conclusions are mostly negative: Dummett's views on analyticity and the logical/non-logical boundary leave little room for logicism. Dummett's considerations concerning manifestation and separability lead to a conservative extension requirement: if a sentence S is logically true, then there is a proof of S which uses only the introduction and elimination rules of the logical terms that occur in S. If basic arithmetic propositions are logically true-as the logicist contends-then there is tension between this conservation requirement and the ontological commitments of arithmetic. It follows from Dummett's manifestation requirements that if a sentence S is composed entirely of logical terminology, then there is a formal deductive system D such that S is analytic, or logically true, if and only if S is a theorem of D. There is a deep conflict between this result and the essential incompleteness, or as Dummett puts it, the indefinite extensibility, of arithmetic truth. (shrink)

In this paper Beebee argues that the problem of induction, which she describes as a genuine sceptical problem, is the same for Humeans than for Necessitarians. Neither scientific essentialists nor Armstrong can solve the problem of induction by appealing to IBE, for both arguments take an illicit inductive step.

We show there is only one consistent way to update a probability assignment, that given by Bayes's rule. The price of inconsistent updating is a loss of efficiency. The implications of this for the problem of induction are discussed.