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 number of philosophers to conclude that Deductive Cogency has at best a very limited role to play in our epistemic lives. I argue here that Deductive Cogency is still an important epistemic requirement, albeit not as a requirement on belief. Instead, building on a distinction between belief and acceptance introduced by Jonathan Cohen and recent developments in the epistemology of understanding, I propose that Deductive Cogency applies to the attitude of treating propositions as given in the context of attempting to understand a given phenomenon. I then argue that this simultaneously accounts for the plausibility of the considerations in favor of Deductive Cogency and avoids the problematic consequences of the preface paradox. (shrink)

Hume's attempt to show that deduction is the only legitimate form of inference presupposes that enumerative induction is the only non-deductive form of inference. In actuality, enumerative induction is not even a form of inference: all supposed cases of enumerative induction are disguised cases of Inference to the Best Explanation (IBE), so far as they aren't simply cases of mentation of a purely associative kind and, consequently, of a kind that is non-inductive and otherwise non-inferential. The justification for IBE (...) lies in two truths, each analytic, viz. that good explanations eliminate anomalies and, second, that anomaly-elimination is identical with discontinuity-elimination. Given these truisms, along with the empirical data to which even skeptics must grant that we have access, it follows that induction is truth-conducive, a corrollary being that skepticism with regard to the veridicality of our senses is indefensible. Hume's erroneous beliefs about non-deductive inference are consequences of his belief that the world has a digital, as opposed to an analogue, structure--of, in other words, his belief that the spatiotemporal manifold decomposes into minimal units. This belief of his is not only false, but analytically so, and its negation has the consequence--for reasons additional to the one already given---that many forms of skepticism are non-starters. It also has the consequence, later given empirical confirmation by the (apparent) truth of Relativity Theory, that spatiotemporal relations are causal relations. Finally, it has the consequence that, contrary to what Hume argues, there are instances of causation. Additional reinforcemet for this claim is shown to lie in a fact first identified by Kant, viz. that we couldn't even ask whether or not there were instances of causation unless there were in fact such instances. Other, similarly 'transcendental' arguments of Kant's are put forth, sometimes in a modified form, so as to buttress the anti-skeptical positions advocated in thsi paper. (shrink)

Cogency is the central normative concept of informal logic. But it is a loose evaluative concept and I argue that a generic notion covering all of the qualities of a well-reasoned argument is the most plausible conception. It is best captured by the standard RSA criterion: in a good argument acceptable (A) and relevant (R) premises provide sufficient (S) grounds for the conclusion. Logical qualities in a broad sense are affected by the epistemic qualities of the premises and “consequence” (...) in a broad sense exhibits an interplay of form and content. There are four proposals for the premise—conclusion relation: (i) no strictly logical connection (“non-logical” consequence); (ii) one type of connection only (deductivism); (iii) a few types of connection (deduction, induction, perhaps conduction and analogical reasoning); (iv) many types of connection (argumentation schemes). Deductivism is a serious option but in its strong version, as the discussion about petitio shows, it fails to establish that arguments which are not cogent are thereby invalid. And weak deductivism, very attractive from the pedagogical point of view, has some deficiencies (implausible hidden premises; preservation of truth, not probability). I argue that the idea of a counterexample, when we regard certain components of the argument as fixed and others as variable, is the best approach to the analysis of the illative core of every-day arguments (the approach of David Hitchcock on material consequence). (shrink)

This paper aims to flesh out the celebrated notion of reflective equilibrium within a probabilistic framework for epistemic rationality. On the account developed here, an agent's attitudes are in reflective equilibrium when there is a certain sort of harmony between the agent's credences, on the one hand, and what the agent accepts, on the other hand. Somewhat more precisely, reflective equilibrium is taken to consist in the agent accepting, or being prepared to accept, all and only claims that follow from (...) a maximally comprehensive theory that is more probable than any other such theory. Drawing on previous work, the paper shows that when an agent is in reflective equilibrium in this sense, the set of claims they accept or are prepared to accept is bound to be logically consistent and closed under logical implication. The paper also argues that this account can explain various features of philosophical argumentation in which the notion of reflective equilibrium features centrally, such as the emphasis on evaluating philosophical theories holistically rather than in a piecemeal fashion. (shrink)

Given the standard dominance conditions used in accuracy theories for outright belief, epistemologists must invoke epistemic conservatism if they are to avoid licensing belief in both a proposition and its negation. Florian Steinberger (2019) charges the committed accuracy monist — the theorist who thinks that the only epistemic value is accuracy — with being unable to motivate this conservatism. I show that the accuracy monist can avoid Steinberger’s charge by moving to a subtly different set of dominance conditions. Having done (...) so, they no longer need to invoke conservatism. I briefly explore some ramifications of this shift. (shrink)

Some general, programmatic points about informal logic are addressed. The informal approach to argument analysis faces serious foundational problems which have been recognized by its practitioners – but informal logic has yet to come together as a clearly defined discipline. Another problem is the dilemma of the dialectician (Sextus Empiricus): informal logic is either trivial or powerless on its own (field expertise is needed). According to Johnson and Blair the central notion in theory of argument is cogency which replaces (...) soundness. An argument is cogent if and only if (i) its premises are rationally acceptable, (ii) its premises are relevant to its conclusion and (iii) its premises provide sufficient reason to accept the conclusion. I propose to understand cogency as a broader notion that includes deductively valid inferences. The criteria of cogency are simply the basic ideals of scientific methodology which requires a respect for available evidence and “reasonable” inference, an awareness of alternatives and a willingness to modify or reject those beliefs that fail to conform to the evidence. Informal logic in the sense of elementary scientific methodology is concerned with proper reasoning and not with proper dialogue. Informal logic involves non-trivial argumentativeskills and abilities applied to the subject area and accessible to every normally intelligent and educated person. (shrink)

John Rawls’ “reflective equilibrium” ranges amongst the most popular conceptions in contemporary ethics when it comes to the basic methodological question of how to justify and trade off different normative positions and attitudes. Even where Rawls’ specific contractualist account is not adhered to, “reflective equilibrium” is readily adopted as the guiding idea of coherentist approaches, seeking moral justification not in a purely deductive or inductive manner, but in some balancing procedure that will eventually procure a stable adjustment of relevant (...) doctrines and standpoints. However, it appears that the widespread use of this idea has led to some considerable deviations from its meaning within Rawls’ original framework and to a critical loss of conceptual cogency as an ethico-hermeneutical tool. This contribution identifies three kinds of “balancing” constellations that are frequently, but inadequately brought forth under the heading of Rawlsian “reflective equilibrium”: (a) balancing theoretical accounts against intuitive convictions; (b) balancing general principles against particular judgements; (c) balancing opposite ethical conceptions or divergent moral statements, respectively. It is argued that each of these applications departs from Rawls’ original construction of “reflective equilibrium” and also deprives the idea of its reliability in clarifying and weighing moral stances. (shrink)

There are two uses of randomization in efforts to control systematic bias in experimental design: (a) Alchemical uses seek to convert unavoidable systematic errors into random errors. (b) Hygienic uses seek to reduce the prospect of the experimenter's involvement with the implementation of the experiment contributing to bias. A few remarks are made at the end of the paper about the hygienic use of randomization as a preventative against sticky fingers. The bulk of the discussion addresses the alchemical applications. The (...) thesis is that attitudes towards the cogency of Fisher's alchemical use of randomization ought to depend on views concerning statistical deduction or direct inference. (shrink)

I discuss Smokrović’s work on the normativity of logic (Smokrović 2017, Smokrović 2018). I agree that the classical formal logic is not an adequate model for real-life reasoning. But I present some doubts about his notion of deductive logic and his proposal to model such reasoning in non-monotonic logic. No branch of formal logic by itself is likely to capture real-life inferential links (reasoned-inference). I use the logic of relevance as my case study and extend the pessimistic morals to (...) modern systems of non-classical logic. Finally, I propose a more lax conception of normativty: there is a connection between logical assessment in the broad sense (as sanctioned by the notion of cogency) and the evaluation and criticism of reasoning. (shrink)

When someone presents an argument on a charged topic and it is (credibly) alleged that the arguer has a strong personal interest and investment in the conclusion, the allegation, directed to the reception or evaluation of the argument, typically gives rise to two seemingly conflicting reactions:I. The allegation is an unwarranted diversion (a species ofargumentum ad hominemorgenetie fallacy).The prejudices or biases of the arguer are irrelevant to thecogencyof the argument. ('Cogency’ is used broadly to refer both to correct support (...) relations, validity, in the case of deductive arguments, and to the soundness, warrant, and relevance of the premises.) In particular, it is a distraction from the crucial judgment of whether the argument is cogent to press the question of whether the arguer truly holds his conclusion on the grounds that he offers, or whether he believes it on some illicit or suspect basis (prejudice, ideology, self-interest, wishful thinking, bias). (shrink)

'You shouldn't drink too much. The Earth is round. Milk is good for your bones.' Are any of these claims true? How can you tell? Can you ever be certain you are right? For anyone tackling philosophical logic and critical thinking for the first time, Critical Thinking: An Introduction to Reasoning Well provides a practical guide to the skills required to think critically. From the basics of good reasoning to the difference between claims, evidence and arguments, Robert Arp and Jamie (...) Carlin Watson cover the topics found in an introductory course. Now revised and fully updated, this Second Edition features a glossary, chapter summaries, more student-friendly exercises, study questions, diagrams, and suggestions for further reading. Topics include: the structure, formation, analysis and recognition of arguments deductive validity and soundness inductive strength and cogency inference to the best explanation truth tables tools for argument assessment informal and formal fallacies With real life examples, advice on graduate school entrance exams and an expanded companion website packed with additional exercises, an answer key and help with real life examples, this easy-to-follow introduction is a complete beginner's tool set to good reasoning, analyzing and arguing. Ideal for students in basic reasoning courses and students preparing for graduate school. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Plato's Political Analogy: Fallacy or Analogy? ROBERT W. HALL THE INTERPRETATIONOf the familiar political analogy between the state and the soul is crucial to a proper understanding of Plato's conception of the individual and his relation to the polls. Interpretations which, consciously or not, tend to identify the justice of the individual with that of the state result either in a subordination of justice of the individual to that (...) of the state, or in endowing the ordinary citizen with an inferior justice. These interpretations of the political analogy have beert adequately dealt with? Recently, Vlastos has stressed what he considers to be the logical or deductive character of the analogy." He finds defects or fallacies in Plato's logic, which, while not necessarily fatal to the significance of the analogy, seriously impair its cogency. What is of particular interest is Vlastos' claim that the primary goal of the analogy is a demonstration, unknown to most scholars, albeit an unsuccessful one, that the justice of the individual necessarily instantiates or entails ordinary acts of justice,a Vlastos has thus raised the question of what kind of approach is most fruitful in unlocking the meaning of the political analogy. My own conviction is that the political analogy can best be understood through a careful examination or observation of the two wholes, the state and the individual, and the character of their relationship. A consideration of the essentials of Vlastos' outlook on the analogy will be a useful introduction to what may be termed a "phenomenological" approach. Such a perspective may provide a better understanding of what Plato is attempting to establish in the analogy, and of how he goes about it. Vlastos' interpretation of the political analogy is strongly colored by his assessment of the central concern of the Republic, the proof that justice "pays." By this Vlastos means that what he terms "psychological justice," the correct, hierarchical arrangement of the three parts or aspects of the soul, must be proven to result in acts of external justice. It is this relationship between psychological justice and ordinary or social justice which sets the problem of logical consistency in Vlastos' account of the political analogy. As the definition of justice of the individual or psychological justice, Vlastos offers Socrates' statement, "In the case of each one of us, whoever is such that each of the three [psychic elements] in him does its own, he is a just man." The social description of justice is: What we laid down at the start as a general requirement when we were founding the polls this, or some form of it, is justice. We did lay down, and often stated, if you recall, that every single person ought to engage in the social function.., for which his own nature is I For exponents of these positions and their critics, cf. my "Plato's Theory of Justice in the Republic," Bucknell Review, XV, 2 (May, 1967), 60, n. I. G. Vlastos, "Justice and Psychic Harmony in the Republic," The 1ournal of Philosophy, LXVI, 16 (August 21, 1969), 505-521. All further references to this article will be by page number. s 506, 515. [419] 420 HISTORY OF PHILOSOPHY best fitted.uWe did say this.--And indeed that to do one's own and not to be meddlesome is justice, this we have often heard from many others, and have often said ourselves.-Wc have said it.--This, then, my friend, if taken in a certain way, appears to be justice: to do one's own. (433A-B) 4 Vlastos admits that this social description is not really a definition of the justice of the individual, "that 'doing one's own' was not meant to constitute a definition of the justice of an individual person.''~ Nonetheless, this social description functions for him as a definition of the individual's justice, and plays a prominent role in the supposed fallacy of equivocation in the meaning of justice. Vlastos argues for this social description on the grounds that "/or Plato every just man must have the disposition named by the 'doing one's own' formula.''e The basis for this claim is Socrates' declaration that "the same (moral) characters... (shrink)

Deductivism has been variously presented as an evaluative thesis and as an interpretive one. I argue that deductivism fails as a universal evaluative thesis, and as such that its value as an interpretive thesis must be supported on other grounds. As a reconstructive strategy, deductivism is justified only on the grounds that an arguer is, or ought to be, aiming at the deductive standard of evidence. As such, the reconstruction of an argument as deductive must be supported by (...) contextual and situational factors including facts about the arguer. Further, the plausibility of deductivism as a normative thesis is not tied to its plausibility as a descriptive or interpretive thesis. (shrink)

We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran's deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of (...) syllogistic, the goal is to offer a general discussion of the relations between informal notions—in this case, an informal notion of deductive validity—and logical apparatuses such as deductive systems and (model-theoretic or other) semantic systems that aim at offering technical, formal accounts of informal notions. Specifically, we will be interested in Kreisel's famous 'squeezing argument'; we shall ask ourselves what a plurality of semantic systems (understood as classes of mathematical structures) may entail for the cogency of specific applications of the squeezing argument. More generally, the analysis brings to the fore the need for criteria of adequacy for semantic systems based on mathematical structures. Without such criteria, the idea that the gap between informal and technical accounts of validity can be bridged is put under pressure. (shrink)

This essay (a revised version of my undergraduate honors thesis at Stanford) constructs a theory of analogy as it applies to argumentation and reasoning, especially as used in fields such as philosophy and law. The word analogy has been used in different senses, which the essay defines. The theory developed herein applies to analogia rationis, or analogical reasoning. Building on the framework of situation theory, a type of logical relation called determination is defined. This determination relation solves a puzzle about (...) analogy in the context of logical argument, namely, whether an analogous situation contributes anything logically over and above what could be inferred from the application of prior knowledge to a present situation. Scholars of reasoning have often claimed that analogical arguments are never logically valid, and that they therefore lack cogency. However, when the right type of determination structure exists, it is possible to prove that projecting a conclusion inferred by analogy onto the situation about which one is reasoning is both valid and non-redundant. Various other properties and consequences of the determination relation are also proven. Some analogical arguments are based on principles such as similarity, which are not logically valid. The theory therefore provides us with a way to distinguish between legitimate and illegitimate arguments. It also provides an alternative to procedures based on the assessment of similarity for constructing analogies in artificial intelligence systems. (shrink)

THE INDICATIVE CONDITIONAL. A PROBABILISTIC CRITERION OF SOUNDNESS FOR DEDUCTIVE INFERENCES Our objective in this section is to establish a prima facie case ...

The aim of this article is to present and discuss the language of the «givens», a typical stylistic resource of Greek mathematics and one of the major features of the proof format of analysis and synthesis. I shall analyze its expressive function and its peculiarities, as well as its general role as a deductive tool, explaining at the same time its particular applications in subgenres of a geometrical proposition like the locus theorems and the so-called «porisms». The main interpretative (...) theses of this study are the following: the language of the «givens» (1) is the standard idiom in which “existence and uniqueness” of a mathematical object was proved, (2) was conceived as an unified framework reducing to a strictly deductive format disparate argumentative steps such as deductions, constructions, and calculations. (shrink)

This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.

We are justified in employing the rule of inference Modus Ponens (or one much like it) as basic in our reasoning. By contrast, we are not justified in employing a rule of inference that permits inferring to some difficult mathematical theorem from the relevant axioms in a single step. Such an inferential step is intuitively “too large” to count as justified. What accounts for this difference? In this paper, I canvass several possible explanations. I argue that the most promising approach (...) is to appeal to features like usefulness or indispensability to important or required cognitive projects. On the resulting view, whether an inferential step counts as large or small depends on the importance of the relevant rule of inference in our thought. (shrink)

I address a type of circularity threat that arises for the view that we employ general basic logical principles in deductive reasoning. This type of threat has been used to argue that whatever knowing such principles is, it cannot be a fully cognitive or propositional state, otherwise deductive reasoning would not be possible. I look at two versions of the circularity threat and answer them in a way that both challenges the view that we need to apply general (...) logical principles in deductive reasoning and defuses the threat to a cognitivist account of knowing basic logical principles. (shrink)

Seldom does human reasoning fit the standards of deduction. Yet logicians have tended to use the strict standards of deductive validity for assessing all inferences. _Within Reason_ develops instead a way of assessing arguments and inferences that is directly appropriate to the non-deductive forms people regularly use. It uses analogy, and argument from analogy, to provide a thread that unites various forms: raising objections, inductions of various sorts, arguments to explanation, and arguments to action. The discussion is developed (...) progressively, at each stage building on the skills learned previously. And at each stage the book suggetss ways of assessing the strength of reasoning. Most of the examples are taken from the great texts of the Western tradition. In the exercises that form an integral part of each chapter an even broader range of writing is presented, offering instructors an extraordinary variety of texts at various levels ot assign to their students. The thesis implicit in the book is that induction, arguments to explanation and arguments to action are all sophisticated forms of arguments from analogy. Burbidge is concerned not simply to warn against the misuse of non-deductive reasoning but also to develop a more positive theory that allows us both to better udnerstand the workings of non-deductive reasoning, and to better employ it. (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)

We offer an interpretation of the words and works of Richard Dedekind and the David Hilbert of around 1900 on which they are held to entertain diverging views on the structure of a deductive science. Firstly, it is argued that Dedekind sees the beginnings of a science in concepts, whereas Hilbert sees such beginnings in axioms. Secondly, it is argued that for Dedekind, the primitive terms of a science are substantive terms whose sense is to be conveyed by elucidation, (...) whereas Hilbert dismisses elucidation and consequently treats the primitives as schematic. (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)

The main point for criticizing the Cartesians for Vico is the notion of method, interpreted as exceptionally discursive procedure, devoid of spontaneity and creative force which are necessary for discovering new truths. These qualities are embodied for Vico in the Latin term ingenium, loan translation of which is found in Italian (ingegno) and is absent in French. The criticism of Cartesianisn suggested by Vico does not consider the fundamental bilingualism of this philosophy and wide use of the term ingenium in (...) the corps of Descartes’ Latin works. The analysis of the latter proves that the early Descartes’ notion intuitus mentis, as well as the concept of natural light of mind are, in the end, based exactly on ingenium, but not on the discursive methodical procedures. Human soul, following Descartes, reveals its content in several hypostastes and each method of revelation corresponds to specific terminology. Soul as mens is not the same as soul as ingenium. But even the early Descartes’ study of soul is marked by peculiar nominalism, proclamation of the real existence of individual soul as a separate entity. Therefore later, stating his ego cogito, Descartes states exactly the individual substance, not thinking in general. The terminological couple ingenium/mens is not translatable already in the French texts of Descartes himself (both merge in the French esprit), however their Ukrainian translations do not consider neither this untranslatability nor obvious references of Descartes’ esprit to other Latin compliances which differ each time. The article also analyses frequency in usage of the terms ingenium and mens in early and late Descartes’ Latin works; it has been proved that the augmentation of the meaning of metaphysical problems gradually turned mens into the main subject of Descartes’ research and deactualised the problem of ingenium. (shrink)

Background As more people are living longer, they become frail and are affected by multi-morbidity, resulting in increased demands from the ambulance service. Being vulnerable, older patients may have reduced decision-making capacity, despite still wanting to be involved in decision-making about their care. Their needs may be complex and difficult to assess, and do not always correspond with ambulance assessment protocols. When needing an ambulance, older patients encounter ambulance clinicians who are under high workloads and primarily consider themselves as emergency (...) medical care providers. This situates them in the struggle between differing expectations, and ethical conflicts may arise. To resolve these, providing ethical care, focussing on interpersonal relationships and using ethical competence is needed. However, it is not known whether ambulance clinicians possess the ethical competence required to provide ethical care. Thus, the aim of this study was to deductively explore their ethical competence when caring for older patients with reduced decision-making ability. Methods A qualitative deductive and exploratory design was used to analyse dyadic interviews with ambulance clinicians. A literature review, defining ethical competence as comprising ethical sensitivity, ethical knowledge, ethical reflection, ethical decision-making, ethical action and ethical behaviour, was used as a structured categorization matrix for the analysis. Results Ambulance clinicians possess ethical competence in terms of their ethical knowledge, highlighting the need for establishing an interpersonal relationship with the older patients. To establish this, they use ethical sensitivity to interpret the patients’ needs. Doing this, they are aware of their ethical behaviour, signifying how they must act respectfully and provide the necessary time for listening and interacting. Conclusions Ambulance clinicians fail to see their gut feeling as a professional ethical competence, which might hinder them from reacting to unethical ways of working. Further, they lack ethical reflection regarding the benefits and disadvantages of paternalism, which reduces their ability to perform ethical decision-making. Moreover, their ethical knowledge is hampered by an ageist approach to older patients, which also has consequences for their ethical action. Finally, ambulance clinicians show deficiencies regarding their ethical reflections, as they reflect merely on their own actions, rather than on their values. (shrink)

In this paper we study interpretations and equivalences of propositional deductive systems by using a quantale-theoretic approach introduced by Galatos and Tsinakis. Our aim is to provide a general order-theoretic framework which is able to describe and characterize both strong and weak forms of interpretations among propositional deductive systems also in the cases where the systems have different underlying languages.

We show that a finitely generated protoalgebraic strict universal Horn class that is filter-distributive is finitely based. Equivalently, every protoalgebraic and filter-distributive multidimensional deductive system determined by a finite set of finite matrices can be presented by finitely many axioms and rules.

I express my dissatisfaction with the common ways to treat the semantic paradoxes. Not only do they give rise to revenge paradoxes, they ignore the wisdom contained in the ordinary reaction to paradoxes. I instead propose an account that vindicates the ordinary reaction to paradox by putting the blame on us philosophers. It is the wrong conception of what a valid inference is, one that is central to “the ideal of deductive logic” that gives rise to the problem. The (...) solution outlined gives us a new way to accept defeat in light of the paradoxes: the arguments that lead to them are based on valid forms of reasoning, but their conclusions are nonetheless rationally rejected. (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)