About this topic

Deductive reasoning is (very roughly) the kind of reasoning in which the premises logically entail the conclusion, at least assuming that no mistake has been made in the reasoning. The premises of a deductive argument may be propositions that the thinker believes or propositions that the thinker temporarily assumes to be true in order to explore their consequences. Deductive reasoning contrasts with inductive (or ampliative ) reasoning, the kind of reasoning in which the truth of the premises does not guarantee the truth of the conclusion.

One important question concerning deductive reasoning is whether we do, in fact, engage in anything that could reasonably be called “deductive reasoning”. Some philosophers and psychologists have denied that there is any such thing, though the consensus in both psychology and philosophy seems to be that there is a distinctive kind of deductive reasoning. Within cognitive science, an important question concerns the nature of deductive reasoning – does it depend on applying rules to mental representations that resemble the sentences of natural language or does it involve reasoning with diagrammic models? Within philosophy, there are important questions concerning the epistemology of deductive reasoning. Which deductive rules are thinkers justified in employing? What makes it the case that certain rules of inference preserve justification (or knowledge) rather than others?

Key works See Harman 1986 for the claim that logic does not provide a theory of good reasoning (and that there is no such thing as deductive inference). See Field 2009 for a reply. A classic paper on deduction is Carroll 1895, which raises the question of how deductive inferences rationally compel belief in their conclusion.  Dummett 1974 discusses the issue of what it is to justify deduction raised in the context of deciding between classical and intuitionist logic). Also see Haack 1976 on the difficulty of justifying deduction in a non-circular way. There are many different account of the justification of deductive rules of inference. They are often presented as part of a more general theory of a priori knowledge and justification. For instance, Bealer 2000 presents a theory based on intuition. BonJour 1998 presents a theory based on rational insight. Boghossian 2003 and Peacocke 1993 present theories based on the nature of concepts. Horwich 2008 argues that it is a primitive fact which rules of inference are justified.
Introductions For a brief introductory article, see Schechter 2013
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  1. A Note on the Fruitfulness of Deduction.Leo Abraham - 1936 - Philosophy of Science 3 (2):152-155.
  2. Reasoning: Studies of Human Inference and its Foundations.Jonathan E. Adler & Lance J. Rips (eds.) - 2008 - Cambridge University Press.
    This interdisciplinary work is a collection of major essays on reasoning: deductive, inductive, abductive, belief revision, defeasible, cross cultural, conversational, and argumentative. They are each oriented toward contemporary empirical studies. The book focuses on foundational issues, including paradoxes, fallacies, and debates about the nature of rationality, the traditional modes of reasoning, as well as counterfactual and causal reasoning. It also includes chapters on the interface between reasoning and other forms of thought. In general, this last set of essays represents growth (...)
  3. Deductive Inference and Aspect Perception.Arif Ahmed - 2010 - In Wittgenstein's Philosophical Investigations: A Critical Guide. Cambridge University Press.
    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.
  4. Deductive Reasoning in the Structuralist Approach.Holger Andreas - 2013 - Studia Logica 101 (5):1093-1113.
    The distinction between the syntactic and the semantic approach to scientific theories emerged in formal philosophy of science. The semantic approach is commonly considered more advanced and more successful than the syntactic one, but the transition from the one approach to the other was not brought about without any loss. In essence, it is the formal analysis of atomic propositions and the analysis of deductive reasoning that dropped out of consideration in at least some of the elaborated versions of the (...)
  5. Mental Models in Prepositional Reasoning.B. C. Bara, P. N. Johnson-Laird & V. Lombarde - 1994 - In Ashwin Ram & Kurt Eiselt (eds.), Proceedings of the Sixteenth Annual Conference of the Cognitive Science Society. Erlbaum. pp. 16--15.
  6. Deduction and Induction: Reasoning Through Mental Models. [REVIEW]Bruno G. Bara & Monica Bucciarelli - 2000 - Mind and Society 1 (1):95-107.
    In this paper we deal with two types of reasoning: induction, and deduction First, we present a unified computational model of deductive reasoning through models, where deduction occurs in five phases: Construction, Integration, Conclusion, Falsification, and Response. Second, we make an attempt, to analyze induction through the same phases. Our aim is an explorative evaluation of the mental processes possibly shared by deductive and inductive reasoning.
  7. The Problem of Basic Deductive Inference.Gordon Barnes - manuscript
    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. (...)
  8. Is the Self-Organizing Consciousness Framework Compatible with Human Deductive Reasoning?Pierre Barrouillet & Henry Markovits - 2002 - Behavioral and Brain Sciences 25 (3):330-331.
    As stressed by Perruchet & Vinter, the SOC model echoes Johnson-Laird's mental model theory. Indeed, the latter rejects rule-based processing and assumes that reasoning is achieved through the manipulation of conscious representations. However, the mental model theory as well as its modified versions resorts to the abstraction of complex schemas and some form of implicit logic that seems incompatible with the SOC approach.
  9. Narrowing Down Suspicion in Inconsistent Premise Sets.Diderik Batens - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):185-209.
    Inconsistency-adaptive logics isolate the inconsistencies that are derivable from a premise set, and restrict the rules of Classical Logic only where inconsistencies are involved. From many inconsistent premise sets, disjunctions of contradictions are derivable no disjunct of which is itself derivable. Given such a disjunction, it is often justified to introduce new premises that state, with a certain degree of confidence, that some of the disjuncts are false. This is an important first step on the road to consistency: it narrows (...)
  10. The Metaphoric Fallacy to a Deductive Inference.Michael P. Berman & Brian A. Lightbody - 2010 - Informal Logic 30 (2):185-193.
    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.
  11. Norms, Reasons and Reasoning: A Guide Through Lewis Carroll’s Regress Argument.Corine Besson - 2016 - In Daniel Star (ed.), The Oxford Handbook of Reasons and Normativity.
    This paper concerns connection between knowing or accepting a logical principle such as Modus Ponens and actions of reasoning involving it. Discussions of this connection typically mention the so-called ‘Lewis Carroll Regress’ and there is near consensus that the regress shows something important about it. Also, although the regress explicitly concerns logic, many philosophers think that it establishes a more general truth, about the structurally similar connection between epistemic or practical principles and actions involving them. This paper’s first aim is (...)
  12. Evaluating Dialectical Structures with Bayesian Methods.Gregor Betz - 2008 - Synthese 163 (1):25-44.
    This paper shows how complex argumentation, analyzed as dialectical structures, can be evaluated within a Bayesian framework by interpreting them as coherence constraints on subjective degrees of belief. A dialectical structure is a set of arguments (premiss-conclusion structure) among which support- and attack-relations hold. This approach addresses the observation that some theses in a debate can be better justified than others and thus fixes a shortcoming of a theory of defeasible reasoning which applies the bivalence principle to argument evaluations by (...)
  13. Situations in Which Disjunctive Syllogism Can Lead From True Premises to a False Conclusion.S. V. Bhave - 1997 - Notre Dame Journal of Formal Logic 38 (3):398-405.
    Disjunctive Syllogism, that is, the inference from 'not-A or B' and 'A', to 'B' can lead from true premises to a false conclusion if each of the sentences 'A' and 'not-A' is a statement of a partial truth such that affirming one of them amounts to denying the other, without each being the contradictory of the other. Such sentences inevitably occur whenever a situation which for its proper precise description needs the use of expressions such as 'most probably true' and (...)
  14. Justifying Deduction.Jerome E. Bickenbach - 1979 - Dialogue 18 (4):500-516.
  15. Believing Epistemic Contradictions.Beddor Bob & Simon Goldstein - 2018 - Review of Symbolic Logic (1):87-114.
    What is it to believe something might be the case? We develop a puzzle that creates difficulties for standard answers to this question. We go on to propose our own solution, which integrates a Bayesian approach to belief with a dynamic semantics for epistemic modals. After showing how our account solves the puzzle, we explore a surprising consequence: virtually all of our beliefs about what might be the case provide counterexamples to the view that rational belief is closed under logical (...)
  16. Blind Reasoning.Paul Boghossian - 2003 - Aristotelian Society Supplementary Volume 77 (1):225–248.
    The paper asks under what conditions deductive reasoning transmits justification from its premises to its conclusion. It argues that both standard externalist and standard internalist accounts of this phenomenon fail. The nature of this failure is taken to indicate the way forward: basic forms of deductive reasoning must justify by being instances of ‘blind but blameless’ reasoning. Finally, the paper explores the suggestion that an inferentialist account of the logical constants can help explain how such reasoning is possible.
  17. The Logical Process of Model-Based Reasoning.Joseph E. Brenner - 2010 - In W. Carnielli L. Magnani (ed.), Model-Based Reasoning in Science and Technology. pp. 333--358.
  18. The Epistemic Significance of Valid Inference – A Model-Theoretic Approach.Constantin C. Brîncuș - 2015 - In Sorin Costreie & Mircea Dumitru (eds.), Meaning and Truth. Bucharest: PRO Universitaria Publishing. pp. 11-36.
    The problem analysed in this paper is whether we can gain knowledge by using valid inferences, and how we can explain this process from a model-theoretic perspective. According to the paradox of inference (Cohen & Nagel 1936/1998, 173), it is logically impossible for an inference to be both valid and its conclusion to possess novelty with respect to the premises. I argue in this paper that valid inference has an epistemic significance, i.e., it can be used by an agent to (...)
  19. Is Gödelian Model-Based Deductive Reasoning Computational?Selmer Bringsjord - 1998 - Philosophica 61.
  20. Deductive Justification.Catherine M. Canary & Douglas Odegard - 1989 - Dialogue 28 (2):305-.
  21. Prototypicaiity and Deductive Reasoning.Chris Topher Cherlqlav - unknown
    lt is hypothesized that people use formally incorrect deductive procedures, and this is sometimes advisable. The particular "prototypicaiity heuristic" investigated is: to determine validity of a proof, (a) work out an example, and (b) pick a "good" rather than arbitrary example. An interaction was predicted betv;een validity of inference and proto-typicality of example. Experiment 1, although quite sensitive to "calibration' variables, does not reveal the interaction in reaction times. However, Experiment 2, in which subjects' time was limited, seems to elicit (...)
  22. Review: George Boole, The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning. [REVIEW]Alonzo Church - 1948 - Journal of Symbolic Logic 13 (4):216-216.
  23. Linguistic Processes in Deductive Reasoning.Herbert H. Clark - 1969 - Psychological Review 76 (4):387-404.
  24. Is Imperative Inference Impossible? The Argument From Permissive Presuppositions.Hannah Clark-Younger - 2012 - In James Maclaurin (ed.), Rationis Defensor.
    Standard definitions of validity are designed to preserve truth from the premises to the conclusion. However, it seems possible to construct arguments that contain sentences in the imperative mood. Such sentences are incapable of being true or false, so the standard definitions cannot capture the validity of these imperative arguments. Bernard Williams offers an argument that imperative inference is impossible: two imperatives will always have different permissive presuppositions, so a speaker will have to change his mind before uttering a second (...)
  25. Can Human Irrationality Be Experimentally Demonstrated?L. Jonathan Cohen - 1981 - Behavioral and Brain Sciences 4 (3):317-370.
    The object of this paper is to show why recent research in the psychology of deductive and probabilistic reasoning does not have.
  26. Convergence of the Inductive and Deductive Models in the Measurement of Reasoning Abilities.Magda Colber, Mary Anne Neste & Marvin H. Trattner - 1985 - Journal of Applied Psychology 70:681-694.
  27. Aristotle's Natural Deduction System.John Corcoran - 1974 - In Ancient Logic and its Modern Interpretations. Boston: Reidel. pp. 85--131.
    This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".
  28. Deduktive Begründung. Zu einem Explikationsvorschlag von Reinhard Kleinknecht.Moritz Cordes, Jens Glatzer, Friedrich Reinmuth & Geo Siegwart - 2010 - Conceptus: Zeitschrift Fur Philosophie 39 (95):31-60.
    In his paper "Deduktive Begründung und deduktive Ableitung" Reinhard Kleinknecht offers an explication of the concepts of deduetive reason and deductive argument respectively. To this end, he provides seven conditions that he sees as individually necessary and jointly sufficient for being a deductive reason. We argue that some of his conditions are far too restrictive and that his concept of deductive argument is therefore to narrow to capture the usual practice of deductively establishing propositions as true. We also show that (...)
  29. A Speech Act Calculus. A Pragmatised Natural Deduction Calculus and its Meta-Theory.Moritz Cordes & Friedrich Reinmuth - manuscript
    Building on the work of Peter Hinst and Geo Siegwart, we develop a pragmatised natural deduction calculus, i.e. a natural deduction calculus that incorporates illocutionary operators at the formal level, and prove its adequacy. In contrast to other linear calculi of natural deduction, derivations in this calculus are sequences of object-language sentences which do not require graphical or other means of commentary in order to keep track of assumptions or to indicate subproofs. (Translation of our German paper "Ein Redehandlungskalkül. Ein (...)
  30. Ein Redehandlungskalkül. Ein pragmatisierter Kalkül des natürlichen Schließens nebst Metatheorie.Moritz Cordes & Friedrich Reinmuth - manuscript
    Building on the work of Peter Hinst and Geo Siegwart, we develop a pragmatised natural deduction calculus, i.e., a natural deduction calculus that incorporates illocutionary operators at the formal level, and prove its adequacy. In contrast to other linear calculi of natural deduction, derivations in this calculus are sequences of object-language sentences which do not require graphical or other means of commentary in order to keep track of assumptions or to indicate subproofs.
  31. Ein Redehandlungskalkül: Folgern in einer Sprache.Moritz Cordes & Friedrich Reinmuth - 2011 - XXII. Deutscher Kongress Für Philosophie.
    Wir stellen einen pragmatisierten Kalkül des natürlichen Schließens vor, der sich dadurch auszeichnet, dass Ableitungen reine Folgen objektsprachlicher Sätze sind und ohne graphische oder andere Kommentarmittel auskommen.
  32. A Modern Malignant Demon? Hume's Scepticism with Regard to Reason (Partly) Vindicated.George Couvalis - 2011 - In Craig Taylor Stephen Buckle (ed.), Hume and the Enlightenment. Chatto & Pickering. pp. 105-115.
  33. The Enduring Scandal of Deduction.Marcello D'Agostino & Luciano Floridi - 2009 - Synthese 167 (2):271-315.
    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 (...)
  34. Semantic Information and the Trivialization of Logic: Floridi on the Scandal of Deduction.Marcello D'Agostinoemail - 2013 - Information 4 (1):33-59.
    In this paper we discuss Floridi’s views concerning semantic information in the light of a recent contribution (in collaboration with the present author) [1] that defies the traditional view of deductive reasoning as “analytic” or “tautological” and construes it as an informative, albeit non-empirical, activity. We argue that this conception paves the way for a more realistic notion of semantic information where the “ideal agents” that are assumed by the standard view can be indefinitely approximated by real ones equipped with (...)
  35. Deductive Cogency, Understanding, and Acceptance.Finnur Dellsén - 2018 - Synthese 195 (7):3121-3141.
    Deductive Cogency holds that the set of propositions towards which one has, or is prepared to have, a given type of propositional attitude should be consistent and closed under logical consequence. While there are many propositional attitudes that are not subject to this requirement, e.g. hoping and imagining, it is at least prima facie plausible that Deductive Cogency applies to the doxastic attitude involved in propositional knowledge, viz. belief. However, this thought is undermined by the well-known preface paradox, leading a (...)
  36. Inference Errors in Deductive Reasoning.Louis S. Dickstein - 1980 - Bulletin of the Psychonomic Society 16 (6):414-416.
  37. Why Is a Valid Inference a Good Inference?Sinan Dogramaci - 2017 - Philosophy and Phenomenological Research 94 (1):61-96.
    True beliefs and truth-preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth-preserving, but truth-preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: the orthodox definition given (...)
  38. Reasoning Without Blinders: A Reply to Valaris.Sinan Dogramaci - 2016 - Mind 125 (499):889-893.
    I object to Markos Valaris’s thesis that reasoning requires a belief that your conclusion follows from your premisses. My counter-examples highlight the important but neglected role of suppositional reasoning in the basis of so much of what we know.
  39. Communist Conventions for Deductive Reasoning.Sinan Dogramaci - 2015 - Noûs 49 (4):776-799.
    In section 1, I develop epistemic communism, my view of the function of epistemically evaluative terms such as ‘rational’. The function is to support the coordination of our belief-forming rules, which in turn supports the reliable acquisition of beliefs through testimony. This view is motivated by the existence of valid inferences that we hesitate to call rational. I defend the view against the worry that it fails to account for a function of evaluations within first-personal deliberation. In the rest of (...)
  40. Intuitions for Inferences.Sinan Dogramaci - 2013 - Philosophical Studies 165 (2):371-399.
    In this paper, I explore a question about deductive reasoning: why am I in a position to immediately infer some deductive consequences of what I know, but not others? I show why the question cannot be answered in the most natural ways of answering it, in particular in Descartes’s way of answering it. I then go on to introduce a new approach to answering the question, an approach inspired by Hume’s view of inductive reasoning.
  41. La Justification de la Déduction.Michael Dummett - 2002 - Philosophie 72 (1):36.
  42. The Justification of Deduction.Michael A. E. Dummett - 1974 - In Michael Dummett (ed.), Truth and Other Enigmas. Oxford University Press.
  43. The Justification of Deduction.Henry E. Kyburg - 1958 - Review of Metaphysics 12 (1):19-25.
  44. Logic, Reasoning and the Logical Constants.Pascal Engel - 2006 - Croatian Journal of Philosophy 6 (2):219-235.
    What is the relationship between logic and reasoning? How do logical norms guide inferential performance? This paper agrees with Gilbert Harman and most of the psychologists that logic is not directly relevant to reasoning. It argues, however, that the mental model theory of logical reasoning allows us to harmonise the basic principles of deductive reasoning and inferential perfomances, and that there is a strong connexion between our inferential norms and actual reasoning, along the lines of Peacocke’s conception of inferential role.
  45. Qualified Reasoning Approaching Deductive Validity.Robert H. Ennis - unknown
  46. Logic and Human Reasoning: An Assessment of the Deduction Paradigm.Jonathan Evans - 2002 - Psychological Bulletin 128 (6):978-996.
    The study of deductive reasoning has been a major paradigm in psychology for approximately the past 40 years. Research has shown that people make many logical errors on such tasks and are strongly influenced by problem content and context. It is argued that this paradigm was developed in a context of logicist thinking that is now outmoded. Few reasoning researchers still believe that logic is an appropriate normative system for most human reasoning, let alone a model for describing the process (...)
  47. The Psychology of Deductive Reasoning.Jonathan St B. T. Evans - 1982
  48. Rationality in Reasoning: The Problem of Deductive Competence.Jonathan Evans & David E. Over - unknown - Current Psychology of Cognition 16 (1-2):3-38.
  49. Deductive Reasoning.Jsbt Evans - 2005 - In K. Holyoak & B. Morrison (eds.), The Cambridge Handbook of Thinking and Reasoning. Cambridge University Press.
  50. The Universality of Logic: On the Connection Between Rationality and Logical Ability.Simon J. Evnine - 2001 - Mind 110 (438):335-367.
    I argue for the thesis (UL) that there are certain logical abilities that any rational creature must have. Opposition to UL comes from naturalized epistemologists who hold that it is a purely empirical question which logical abilities a rational creature has. I provide arguments that any creatures meeting certain conditions—plausible necessary conditions on rationality—must have certain specific logical concepts and be able to use them in certain specific ways. For example, I argue that any creature able to grasp theories must (...)
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