Deductive inference seems to reveal semantic connections between their premise(s) and conclusion that were there all along. This looks inconsistent with Wittgenstein's later views on meaning. The paper argues that W's treatment of aspects suggests a Wittgensteinian treatment of deduction that accommodates the troublesome phenomenon without conceding its force.

What is an inference and when is an inference deductive rather than inductive, abductive, etc. The goal of this paper is precisely to determine what is that we, humans, do when we engage in deduction, i.e., whether there is something that satisfies both our pre-theoretical intuitions and theoretical presuppositions about deduction, as a cognitive process. The paper is structured in two parts: the first one deals with the issue of what is an inference. There, I will (...) defend the hypothesis that an inference is a causal process where an initial cognitive state causes another in such a way that the causal translation depends essentially on the content of the involved states. In other words, in an inference, a mental state A causes another B, partially because they have the content they have. Based on the conclusion from the first part, I will develop an account of deductive inference in the second part of the article. In order to achieve this, I will start by setting the stage and developing four constraints that an adequate account of deductive inference ought to satisfy. Then, I will present six different hypotheses that one might propose to characterize inferences of this kind. I have divided the proposals in two groups, the first one – which I will call the “logical proposals” – assume that whether an inference is a deduction or not depends exclusively on the content of the mental states involved in the inference, while the second – which I will call the “cognitive proposals” – reject the aforementioned assumption and instead recognize that extra cognitive information is required to determine whether an inference is a deduction or not. I will evaluate each proposal in turn, according to whether they satisfy the constraints introduced at the beginning of this second part. As a result of such evaluation, I will conclude that only one of the cognitive proposals actually satisfies the four constraints and therefore should be considered to give an adequate characterization of deductive inference. (shrink)

From the standpoint of the theory of medicine, a formulation is given of three types of reasoning used by physicians. The first is deduction from probability models (as in prognosis or genetic counseling for Mendelian disorders). It is a branch of mathematics that leads to predictive statements about outcomes of individual events in terms of known formal assumptions and parameters. The second type is inference (as in interpreting clinical trials). In it the arguments from replications of the same process (...) (data) lead to conclusions about the parameters of a system, without calling into question either the probabilistic model or the criteria of evidence. The third is illation (as in the elucidation of symptoms in a patient). It is a process whereby, in the light of the total evidence and the conclusions from the other types of reasoning, one may modify, expand, simplify or demolish a conceptual framework proposed for deductions, and modify the nature of the evidence sought, the criteriology, the axioms, and the surmised complexity of the scientific theory. (The process of diagnosis as applied to a patient may in extreme cases lead to the discovery of an entirely new disease with its own, quite new, set of diagnostic criteria. This course cannot be accommodated inside either of the other two types of reasoning.) Illation has something of the character of Kuhn's scientific revolution in physics; but it differs in that it is the nature, not the degree or frequency of change that distinguishes it from Kuhn's normal science. (shrink)

In his Logic, Pierre Gassendi proposes that our inductive inferences lack the information we would need to be certain of the claims that they suggest. Not even deductivist inference can insure certainty about empirical claims because the experientially attained premises with which we adduce support for such claims are no greater than probable. While something is surely amiss in calling deductivist inference "probabilistic," it seems Gassendi has hit upon a now-familiar, sensible point—namely, the use of deductive reasoning (...) in empirical contexts, while providing certain formal guarantees, does not insulate empirical arguments from judgment by the measure of belief which we invest in their premises. The more general point, which distinguishes Gassendi among his contemporaries, is that the strength shared by all empirical claims consists in the warrant from experience for those claims we introduce in their support. (shrink)

Logic, in one of the many sense of that term, is a theory about what follows from what and why. Arguably, the correct theory has to be determined by abduction. Over recent years, so called logical anti-exceptionalists have investigated this matter. Current discussions have been restricted to deductive logic. However, there are also, of course, various forms of non-deductive reasoning. Indeed, abduction itself is one of these. What is to be said about the way of choosing the best (...) theory of non-deductive inferences? It would seem clear that an anti-exceptionalist should hold that essentially the same method of choice should apply to non-deductive logic. A number of issues need to be faced in the process, not the least of which is the circularity involved in an abductive justification for a theory of abduction. This paper discusses matters. (shrink)

The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic uncertainty (...) in known premises. The first strategy, while effective, retains little of the original idea—conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson’s safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson’s theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge. (shrink)

This paper deals with Popper's little-known work on deductive logic, published between 1947 and 1949. According to his theory of deductive inference, the meaning of logical signs is determined by certain rules derived from ?inferential definitions? of those signs. Although strong arguments have been presented against Popper's claims (e.g. by Curry, Kleene, Lejewski and McKinsey), his theory can be reconstructed when it is viewed primarily as an attempt to demarcate logical from non-logical constants rather than as a (...) semantic foundation for logic. A criterion of logicality is obtained which is based on conjunction, implication and universal quantification as fundamental logical operations. (shrink)

Knowledge can be transmitted by a valid deductive inference. If I know that p, and I know that if p then q, then I can infer that q, and I can thereby come to know that q. What feature of a valid deductive inference enables it to transmit knowledge? In some cases, it is a proof of validity that grounds the transmission of knowledge. If the subject can prove that her inference follows a valid rule, (...) then her inference transmits knowledge. However, this only pushes the question back to the inference that was made in this proof. What feature of that inference enables it to transmit knowledge? A vicious regress looms here. Every proof requires a valid inference, and every valid inference must follow at least one rule of inference. So every proof must follow at least one rule of inference. Therefore not every valid inference that transmits knowledge can acquire this power through a proof, on pain of vicious infinite regress. So it must be possible to transmit knowledge by making an inference that follows an underived rule. A deductive inference that follows an underived rule is what I will call a basic deductive inference. It must be possible to transmit knowledge by making a basic deductive inference. But how is this possible? What feature of a basic deductive inference gives it this power to transmit knowledge? (shrink)

This article provides the first comprehensive reconstruction and analysis of Hintikka’s attempt to obtain a measure of the information yield of deductive inferences. The reconstruction is detailed by necessity due to the originality of Hintikka’s contribution. The analysis will turn out to be destructive. It dismisses Hintikka’s distinction between surface information and depth information as being of any utility towards obtaining a measure of the information yield of deductive inferences. Hintikka is right to identify the failure of canonical (...) information theory to give an account of the information yield of deductions as a scandal, however this article demonstrates that his attempt to provide such an account fails. It fails primarily because it applies to only a restricted set of deductions in the polyadic predicate calculus, and fails to apply at all to the deductions in the monadic predicate calculus and the propositional calculus. Some corollaries of these facts are a number of undesirable and counterintuitive results concerning the proposed relation of linguistic meaning (and hence synonymy) with surface information. Some of these results will be seen to contradict Hintikka’s stated aims, whilst others are seen to be false. The consequence is that the problem of obtaining a measure of the information yield of deductive inferences remains an open one. The failure of Hintikka’s proposal will suggest that a purely syntactic approach to the problem be abandoned in favour of an intrinsically semantic one. (shrink)

The present PhD thesis is concerned with the question whether good reasoning requires that the subject has some cognitive grip on the relation between premises and conclusion. One consideration in favor of such a requirement goes as follows: In order for my belief-formation to be an instance of reasoning, and not merely a causally related sequence of beliefs, the process must be guided by my endorsement of a rule of reasoning. Therefore I must have justified beliefs about the relation between (...) my premises and my conclusion. -/- The rationality of a belief often depends on whether it is rightly connected to other beliefs, or more generally to other mental states —the states capable of providing a reason to holding the belief in question. For instance, some rational beliefs are connected to other beliefs by being inferred from them. It is often accepted that the connection implies that the subject in some sense ‘takes the mental states in question to be reason-providing’. But views on how exactly this is to be understood differ widely. They range from interpretations according to which ‘taking a mental state to be reason-providing’ imposes a mere causal sustaining relation between belief and reason-providing state to interpretations according to which one ‘takes a mental state to be reason-providing’ only if one believes that the state is reason-providing. The most common worry about the latter view is that it faces a vicious regress. In this thesis a different but in some respects similar interpretation of ‘taking something as reason-providing’ is given. It is argued to consist of a disposition to react in certain ways to information that challenges the reason-providing capacity of the allegedly reason-providing state. For instance, that one has inferred A from B partly consists in being disposed to suspend judgment about A if one obtains a reason to believe that B does not render A probable. The account is defended against regress-objections and the suspicion of explanatory circularity. (shrink)

We provide a new link between deductive and probabilistic reasoning fallacies. Illusory inferences from disjunction are a broad class of deductive fallacies traditionally explained by recourse to a matching procedure that looks for content overlap between premises. In two behavioral experiments, we show that this phenomenon is instead sensitive to real-world causal dependencies and not to exact content overlap. A group of participants rated the strength of the causal dependence between pairs of sentences. This measure is a near (...) perfect predictor of fallacious reasoning by an independent group of participants in illusory inference tasks with the same materials. In light of these results, we argue that all extant accounts of these deductive fallacies require non-trivial adjustments. Crucially, these novel _indirect_ illusory inferences from disjunction bear a structural similarity to seemingly unrelated _probabilistic reasoning_ problems, in particular the conjunction fallacy from the heuristics and biases literature. This structural connection was entirely obscure in previous work on these deductive problems, due to the theoretical and empirical focus on content overlap. We argue that this structural parallelism provides arguments against the need for rich descriptions and individuating information in the conjunction fallacy, and we outline a unified theory of deductive illusory inferences from disjunction and the conjunction fallacy, in terms of Bayesian confirmation theory. (shrink)

This article examines the current justifications of deductive inferences, and finds them wanting. It argues that this depends on the fact that all such justification take no account of the role deductive inferences play in knowledge. Alternatively, the article argues that a justification of deductive inferences may be given in terms of the fact that they are non-ampliative, in the sense that the content of the conclusion is merely a reformulation of the content of the premises. Some (...) possible objections to this view are discussed and found inadequate. (shrink)

Is it possible to give a justification of our own practice of deductive inference? The purpose of this paper is to explain what such a justification might consist in and what its purpose could be. On the conception that we are going to pursue, to give a justification for a deductive practice means to explain in terms of an intuitively satisfactory notion of validity why the inferences that conform to the practice coincide with the valid ones. That (...) is, a justification should provide an analysis of the notion of validity and show that the inferences that conform to the practice are just the ones that are valid. Moreover, a complete justification should also explain the purpose, or point, of our inferential practice. We are first going to discuss the objection that any justification of our deductive practice must use deduction and therefore be circular. Then we will consider a particular model of justificatory explanation, building on Georg Kreisel’s concept of informal rigour. Finally, in the main part of the paper, we will discuss three ideas for defining the notion of validity: (i) the classical conception according to which the notion of (bivalent) truth is taken as basic and validity is defined in terms of the preservation of truth; (ii) the constructivist idea of starting instead with the notion of (a canonical) proof (or verification) and define validity in terms of this notion; (iii) the idea of taking the notions of rational acceptance and rejection as given and define an argument to be valid just in case it is irrational to simultaneously accept its premises and reject its conclusion (or conclusions, if we allow for multiple conclusions). Building on work by Dana Scott, we show that the last conception may be viewed as being, in a certain sense, equivalent to the first one. Finally, we discuss the so-called paradox of inference and the informativeness of deductive arguments. (shrink)

A number of single- and dual-process theories provide competing explanations as to how reasoners evaluate conditional arguments. Some of these theories are typically linked to different instructions—namely deductive and inductive instructions. To assess whether responses under both instructions can be explained by a single process, or if they reflect two modes of conditional reasoning, we re-analysed four experiments that used both deductive and inductive instructions for conditional inference tasks. Our re-analysis provided evidence consistent with a single process. (...) In two new experiments we established a double dissociation of deductive and inductive instructions when validity and plausibility of conditional problems were pitted against each other. This indicates that at least two processes contribute to conditional reasoning. We conclude that single-process theories of conditional reasoning cannot explain the observed results. Theories that postulate at least two processes are needed to account for our findings. (shrink)

This is a textbook in symbolic logic comprising sentential and quantificational theory only. The logic of the propositional calculus is developed in a natural-deduction form reminiscent of Fitch's technique; therefore, most of the theorems take the form of metamathematical assertions and possess corresponding meta-proofs. The classical propositional calculus SCc is then formulated in the Hilbert-style axiomatic way which naturally leads to consistency, completeness, and decidability theorems for the system. The theory of quantifiers is also first set up in natural deduction (...) form, and then reformulated classically. Leblanc spends considerable time in a careful treatment of satisfiability and validity in first-order logic, this leading naturally to the Löweheim-Skolem [[sic]] theorem and related completeness results. There is an appendix containing some relevant results from set theory. In general this is a most thorough and neat job which succeeds admirably in giving in semantical form a rigorous introduction to logic.—P. J. M. (shrink)

In this article, we address fallacious analogical reasoning and the Metaphoric Fallacy to a Deductive Inference (MFDI), recently discussed by B. Lightbody and M. Berman (2010). We claim that the authors’ proposal to introduce a new fallacy is only partly justified. We also argue that, in some relevant cases, fallacious analogical reasoning involving metaphors is only affected by the use of quaternio terminorum.

Our article identifies and describes the metaphoric fallacy to a deductive inference (MFDI) that is an example of incorrect reasoning along the lines of the false analogy fallacy. The MFDI proceeds from informal semantical (metaphorical) claims to a supposedly formally deductive and necessary inference. We charge that such an inference is invalid. We provide three examples of the MFDI to demonstrate the structure of this invalid form of reasoning. Our goal is to contribute to the (...) set of known informal fallacies. (shrink)

Many philosophers have claimed that Bayesianism can provide a simple justification for hypothetico-deductive inference, long regarded as a cornerstone of the scientific method. Following up a remark of van Fraassen, we analyze a problem for the putative Bayesian justification of H-D inference in the case where what we learn from observation is logically stronger than what our theory implies. Firstly, we demonstrate that in such cases the simple Bayesian justification does not necessarily apply. Secondly, we identify a (...) set of sufficient conditions for the mismatch in logical strength to be justifiably ignored as a "harmless idealization''. Thirdly, we argue, based upon scientific examples, that the pattern of H-D inference of which there is a ready Bayesian justification is only rarely the pattern that one actually finds at work in science. Whatever the other virtues of Bayesianism, the idea that it yields a simple justification of a pervasive pattern of scientific inference appears to have been oversold. (shrink)

Our article identifies and describes the metaphoric fallacy to a deductive inference (MFDI) that is an example of incorrect reasoning along the lines of the false analogy fallacy. The MFDI proceeds from informal semantical (metaphorical) claims to a supposedly formally deductive and necessary inference. We charge that such an inference is invalid. We provide three examples of the MFDI to demonstrate the structure of this invalid form of reasoning. Our goal is to contribute to the (...) set of known informal fallacies. (shrink)

This monograph provides a new account of justified inference as a cognitive process. In contrast to the prevailing tradition in epistemology, the focus is on low-level inferences, i.e., those inferences that we are usually not consciously aware of and that we share with the cat nearby which infers that the bird which she sees picking grains from the dirt, is able to fly. Presumably, such inferences are not generated by explicit logical reasoning, but logical methods can be used to (...) describe and analyze such inferences. Part 1 gives a purely system-theoretic explication of belief and inference. Part 2 adds a reliabilist theory of justification for inference, with a qualitative notion of reliability being employed. Part 3 recalls and extends various systems of deductive and nonmonotonic logic and thereby explains the semantics of absolute and high reliability. In Part 4 it is proven that qualitative neural networks are able to draw justified deductive and nonmonotonic inferences on the basis of distributed representations. This is derived from a soundness/completeness theorem with regard to cognitive semantics of nonmonotonic reasoning. The appendix extends the theory both logically and ontologically, and relates it to A. Goldman's reliability account of justified belief. This text will be of interest to epistemologists and logicians, to all computer scientists who work on nonmonotonic reasoning and neural networks, and to cognitive scientists. (shrink)

This chapter contains sections titled: Validity and Necessity The Validity Paradox Gödel Arithmetizing the Validity Paradox The Validity Paradox in S5 Validity, Necessity, and Deductive Inference.