Used informally, the Reductio ad Absurdum (RAA) consists in reasoning appealing to the logically implied, absurd consequences of a hypothetical proposition, in order to refute it. This kind of reasoning resembles the Argument from Consequences, which appeals to causally induced consequences. These types of argument are sometimes confused, since it is not worked out how these different kinds of consequences should be distinguished. In this article it is argued that the logical consequences in RAA-argumentation can take different appearances and (...) that it therefore must be concluded that RAA cannot be characterised by a specific content, but must instead be characterised as an argument form. Furthermore, clues are provided to distinguish RAA reasoning from the Argument from Consequences. (shrink)

1. The Down Under Logical Disproof of the Theist's God 1.1 Plantinga's Attempted Refutation of the Logical Disproof 1.2 Plantinga Refuted and God Disproved: A Preview 2. Plantinga's Formal Presentation of his Free Will Defense 3. First Formal Flaw: A Non Sequitur Regarding the Consistency of (3) with (1) 4. Further Flaws Regarding the Joint Conditions of Consistency and Entailment 4.1 A Non Sequitur Regarding the Entailment Condition 4.2 Telling the Full Story in Order to Satisfy the (...) Entailment Condition 4.3 Two Non Sequiturs Involving the Consistency Condition 4.4 The Russell Scenario: A Refutation by Logical Analogy 5. Plantinga's Leibnizian Definition of Omnipotence 5.1 Logical Consequences of the Definition 5.2 Why Leibniz Didn't Lapse 5.3 A Fatal Equivocation Over the Scope of Transworld Depravity 5.4 It Was All "Up to God" 5.5 The Distinction Between Absolute and Consequential Modalities 5.6 Plantinga's Ploy 5.7 Plantinga's Modal Muddle 5.8 Interlude on the Prevalence of the Modal Muddle 5.9 Back to Plantinga's Modal Muddle 5.10 Interim Verdict 6. Judgment Day: God Almighty and All Knowing Not Morally Perfect.. (shrink)

In this paper I offered a friendly amendment to Paul Churchland’s a well-known criticism of Frank Jackson’s knowledge argument. According to Jackson’s argument, a hypothetical Mary, living in her darkened stimulus-impoverished environment, knows all information from physical science about the perception of color but still does not know everything, e.g., what it is like to experience the color red. Churchland offered a refutation by analogy whereby Mary is an ectoplasmologist who knows all the supposed nonphysical things that friends (...) of the hard problem of qualia believe about that phenomenon. So Mary knows everything ectoplasmic about the perception of color but still does not know everything – what it is like to experience the color red. I made a necessary adjustment whereby Mary is not just an ectoplasmologist but a dualist who knows everything physical and ectoplasmic about the perception of color. By the same reasoning, then, the Jackson-style argument would refute dualism too. I also offered a diagnosis of the problem much in the spirit of other criticisms, namely, that things like experiencing red or riding a bicycle can be fully physical even though Mary would not “know how” to experience red or ride a bicycle simply by possessing all the “know that”/propositional/book-learning about those things. (shrink)

Krabbe (2003, in F.H. van Eemeren, J.A. Blair, C.A. Willard and A.F. Snoeck Henkemans (eds.), Proceedings of the Fifth Conference of the International Society for the Study of Argumentation, Sic Sat, Amsterdam, pp. 641–644) defined a metadialogue as a dialogue about one or more dialogues, and a ground-level dialogue as a dialogue that is not a metadialogue. Similarly, I define a meta-argument as an argument about one or more arguments, and a ground-level argument as one which is not a meta-argument. (...) Krabbe (1995, in F.H van Eemeren, R. Grootendorst, J.A. Blair, C.A. Willard and A.F. Snoeck Henkemans (eds.), Proceedings of the Third ISSA Conference on Argumentation, Sic Sat, Amsterdam, pp. 333–344) showed that formal-fallacy criticism (and more generally, fallacy criticism) consists of metadialogues, and that such metadialogues can be profiled in ways that lead to their proper termination or resolution. I reconstruct Krabbe’s metadialogical account into monolectical, meta-argumentative terminology by describing three-types of meta-arguments corresponding to the three ways of proving formal invalidity he studied: the trivial logic-indifferent method; the method of counterexample situation; and the method of formal paraphrase. A fourth type of meta-argument corresponds to what Oliver (1967, Mind 76, 463–478), Govier (1985, Informal Logic 7, 27–33), and Copi (1986) call refutation by logical analogy. A fifth type of meta-argument represents my reconstruction of arguments by parity of reasoning studied by Woods and Hudak (1989, Informal Logic 11, 125–139). Other particular meta-arguments deserving future study are Hume’s critique of the argument from design in the Dialogues Concerning Natural Religion, and Mill’s initial argument in The Subjection of Women about the importance of established custom and general feeling vis-à-vis argumentation. (shrink)

Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre (...) Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations. (shrink)

This paper discusses the method when an argument is refuted by a parallel argument since the flaw of the parallel argument is clearly displayed. The method is explicated, examined and compared with two other general methods.

In his recent book Is a Good God Logically Possible? and article by the same name, James Sterba argued that the existence of significant and horrendous evils, both moral and natural, is incompatible with the existence of God. He advances the discussion by invoking three moral requirements and by creating an analogy with how the just state would address such evils, while protecting significant freedoms and rights to which all are entitled. I respond that his argument has important ambiguities (...) and that consistent application of his moral principles will require that God remove all moral and natural evils. This would deleteriously restrict not only human moral decision making, but also the knowledge necessary to make moral judgments. He replies to this critique by appealing to the possibility of limited divine intervention, to which I rejoin with reasons why his middle ground is not viable. (shrink)

Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of (...) mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations. (shrink)

We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the "determination rule", so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization of the different types of dependency relations defined in database theory. Specifically, we define determination as a relation between schemata (...) of first order logic that have two kinds of free variables: (1) object variables and (2) what we call "polar" variables, which hold the place of truth values. Determination rules facilitate sound rule inference and valid conclusions projected by analogy from single instances, without implying what the conclusion should be prior to an inspection of the instance. They also provide a way to specify what information is sufficiently relevant to decide a question, prior to knowledge of the answer to the question. (shrink)

Abstract In this paper, I investigate the purported dilemma between a symmetrical conception of time and the denial of what I call Universal Logical Determinateness (ULD). According to the dilemma, the timeless and universal application of logical laws to all propositions necessitates either the view that the past and future are both open, or that they are both closed. My investigation proceeds by way of an assessment of Taylor's argument for fatalism, then of Dummet's presentation and refutation (...) of the fatalistic argument, and finally of Dummet's analogous argument which attempts to prove the possibility of an open past. In all cases, we find that the arguments implicitly rely upon the assumption that there exists a necessary connection between the truth aptness of propositions and the fixity (or non-fixity) of events. I question this assumption and conclude that any argument for the symmetry of time which relies upon it begs the question against the asymmetry of time. (shrink)

This paper is a case study of how a few short lines in two of Aristotle’s logical works were read in the thirteenth century. I shall begin with a quick look at Aristotle’s own remarks about equivocation in the Categories and the Sophistical Refutations, as they were transmitted to the West by Boethius’s translations. I shall continue with an analysis of the divisions of equivocation and analogy to be found in an anonymous commentary, on the Sophistical Refutations written (...) in Paris between 1270 and 1280. I have chosen this author’s work to focus on, because it offers a remarkably full account which brings together the elements found in many other logical works from the second half of the thirteenth century. In the course of my analysis I shall attempt to show the part played by four different sources: the Greek commentators of late antiquity; the new translations of Aristotle’s Physics and Metaphysics; the reception of Arabic works, particularly the commentaries of Averroes; and new grammatical doctrines, notably that of modi significandi. At the same time, I hope to throw some light on the development of the doctrine of analogy as it was understood by late thirteenth-century logicians. (shrink)

In True enough,, Elgin argues against veritism, which is the view that truth is the paramount epistemic objective. Elgin’s argument against veritism proceeds from considering the role that models, idealizations, and thought experiments play in science to the conclusion that veritism is unacceptable. In this commentary, I argue that Elgin’s argument fails as an argument against veritism. I sketch a refutation by logical analogy of Elgin’s argument. Just as one can aim at gold medals and still find (...) approximations to gold, such as silver and bronze medals, to be acceptable and honest achievements in competitive sports, one can aim at full truths as the paramount epistemic objective and still find approximations to truth, such as models and idealizations, to be acceptable and honest achievements in scientific inquiry. (shrink)

One of Berkeley's best-known arguments for the view that there are no material objects is the so-called Master Argument. There are several good critical discussions of it. That invites the question: is there anything new to say? Well, it will be argued, there are a few things to say. First, although refutations by logical analogy have been advanced against the Master Argument, the strongest such refutation, one which demonstrates its incoherence, has not been. It is here. Second, (...) there are few formal reconstructions of the Master Argument – the great majority of discussions treat it discursively – but a formal reconstruction, and one not found elsewhere, is offered here. Third, the formal reconstruction makes possible identification of the essential mistake of the argument. That mistake is equivocation. The common complaint that Berkeley illicitly introduces the act of conceiving into the content of the concept conceived is not quite correct; but to the extent that it is correct, it's explicable in terms of an underlying equivocation. Fourth, the article presupposes no acquaintance with Berkeley's work and is written in a conversational, easy-to-read style. Given that Berkeley himself wrote in a similar style, he could at least agree that the fourth point is a merit of the article. (shrink)

There are good reasons for being dissatisfied with standard criticisms of the various arguments, all of which are referred to as being “The Ontological Argument”. While refutation by logical analogy is compelling, it merely teaches us that something is amiss. It does not specify the exact nature of the flaw. The first part of this paper examines and rejects several well-known attempts at refuting and clarifying the argument(s). The second part attempts to provide a principled uniform account (...) of what is wrong by treating the arguments as resting on definitions. Then, by bringing to bear Ajdukiewicz’s exhaustive classification of definitions, we arrive at a unified account of the flaw common to such arguments. In effect we have an explication of the dictum that one cannot define into existence. (shrink)

ABSTRACT 'The Duologue of King/Governor Pāyāsi' has long been recognised as a source for the proto-materialism current at the time of the Buddha. What needs to be stressed is the significance of the text as a pointer to the development of Logic in India. Perception, which is an accepted method of experimental enquiry, and reasoning from analogy, which can lead at best to a probable conclusion - these two are the only means employed to settle the dispute concerning the (...) existence of the other-world. The Jain version of the same duologue-cum-parable, though varying in minor details regarding the name and identity of the monk refuting the king/governor, contains the same contrast, namely, perception versus analogical reasoning. There can be little doubt that the original parable was conceived with a view to asserting the existence of the other-world. In the Kaṭha Upaniṣad, an earlier Brahmanical text, however, instead of argument by analogy, verbal testimony was invoked to settle the same point. Naciketas is assailed by doubt about the existence of a person after his or her death. The authority of Yama, the Pluto of Indian mythology, is invoked to convince him that the other-world does exist. Thus, the three parables taken together exhibit three means of knowledge in operation: verbal testimony and argument by analogy pitted against perception. RESUMO 'O duólogo do rei/governador Pāyāsi' há muito tempo é reconhecido como uma fonte da corrente protomaterialista da época do Buda. O que é necessário ressaltar é o significado desse texto como um indicador do desenvolvimento da lógica na Índia. Percepção, aceita como método de investigação experimental, e raciocínio por analogia, que no máximo pode conduzir a uma conclusão provável - apenas esses dois são os meios utilizados para dirimir a disputa que diz respeito à existência do outro-mundo. A versão jaina do mesmo duólogo-cum-parábola, mesmo com variações que concernem ao nome e à identidade do monge que se opõe ao rei/governador, contém o mesmo contraste, a dizer, percepção contra raciocínio por analogia. Não há muita dúvida de que a parábola original foi concebida com o intuito de afirmar a existência do outro-mundo. Entretanto, na Kaṭha Upaniṣad, um texto bramânico mais antigo, em vez do argumento por analogia, o testemunho verbal foi invocado para resolver o mesmo ponto. Naciketas é tomado pela dúvida sobre a existência da pessoa depois da sua morte. A autoridade de Yama, o Plutão da mitologia indiana, é invocada para convencê-lo que o outro-mundo existe. Portanto, as três parábolas juntas exibem três meios de conhecimento em função: testemunho verbal e argumento por analogia opostos à percepção. (shrink)

Gilbert Ryle and a number of other philosophers have argued that Descartes’ claim his senses could always deceive him is false. Ryle’s argument is the well-known ‘counterfeit coins’ argument. A similar argument, featuring forged paintings, has been advanced by Jay Rosenberg. Both Ryle’s and Rosenberg’s arguments are refutations by logical analogy. In this paper, their arguments are exposed and reconstructed, and it is shown and how and why their refutations by logical analogy fail. It is then (...) noted that, even so, they could be right about the invalidity of Descartes’ argument. A close examination of Descartes’ argument, however, shows that there is nothing wrong with it. (shrink)

Analogical reasoning projects a property taken to hold of something or things (the source) to something else (the target) on the basis of just those similarities premised in the analogy. Standard similarity-based accounts of analogical reasoning face the question: Under what conditions does a collection of similarities sufficiently warrant analogical projection? One answer is: When a thing’s having the premised similarities somehow determines its having the projected property. Standardly, this answer has been interpreted as claiming that a formally defined (...) determination relation exists between the variables of which the determining properties are values and the variable of which the determined property is a value. This paper supplies another answer: Analogical projection is warranted when an item’s having the projected property is grounded in its having the premised similarities. Drawing on the metaphysics of grounding, we propose a model of grounded analogy on which analogical reasoning is valid under metaphysical necessity. Our model thus provides one answer to John Stuart Mill’s question of how analogical reasoning based on limited information about a single source case can provide an indefeasible justification for analogical projection. Once a relation of total grounding is ascertained to hold between some similarities and the projected property, no other properties bear on the projectability of the projected property from the source to the target. (shrink)

Cover -- Half Title Page -- Title Page -- Copyright Page -- Original Title Page -- Original Copyright Page -- Contents -- Preface -- 1 Introduction -- 2 Probability And Possibility For Choice -- 1 Introductory -- 2 A Theory About Personal Power -- 3 A Criticism Of Keynes -- 4 Some More Theories About Personal Power -- 5 An Analogy Between Two Kinds Of Possibility -- 3 Probability And Natural Powers -- 1 Introductory -- 2 The Relation Between (...) Epistemic And Natural Possibility -- 3 A Criticism Of The Doctrine That 'Probable' Is Ambiguous -- 4 A Comparison Of Possibility With Probability -- 4 Some Unobservable Properties -- 1 Introductory -- 2 Certainty, Necessity And Hume -- 3 Epistemology And Determinism -- 4 An Analysis Proposed And Defended -- 5 Power And Law -- 5 Some Puzzles About Potentiality -- 1 Introductory -- 2 The idea of a 'circumstance' -- 3 The Distinction Between Intrinsic And Extrinsic Properties -- 4 The Refutation Of Actualism -- 5 The Refutation Of The Theory That 'All Power Is Conditional' -- 6 The Powers Of People Andthe Powers Of Things -- 1 Introductory -- 2 The Distinction Between Natural And Personal Power -- 3 The Refutation Of Ryle's Dispositionalist Account Of Human Capacities -- 7 IFS And Cans -- 1 Introductory -- 2 The Refutation Of The Theory That All Personal Power is Conditional -- 3 A Refutation Of The Orthodox Account Of 'I Can', As Equivalent To A Conditional Statement -- 4 A Contradiction In Dispositionalism -- 5 Further Objections To The Orthodox View -- 6 The Verification Of 'I Can': More About Trying -- 8 Deliberation, Freedom And Meaning -- 1 Introductory -- 2 More About Possibility And The Context Of Deliberation -- And About The Relation Between Power And Will -- 3 On Not Being Able To Help It: A: Discussion Of The Relationship Between Power And Responsibility -- 4 On The Meaning Of Words Like 'Can'. (shrink)

The reasoning process of analogy is characterized by a strict interdependence between a process of abstraction of a common feature and the transfer of an attribute of the Analogue to the Primary Subject. The first reasoning step is regarded as an abstraction of a generic characteristic that is relevant for the attribution of the predicate. The abstracted feature can be considered from a logic-semantic perspective as a functional genus, in the sense that it is contextually essential for the attribution (...) of the predicate, i.e. that is pragmatically fundamental (i.e. relevant) for the predica-tion, or rather the achievement of the communicative intention. While the transfer of the predicate from the Analogue to the analogical genus and from the genus to the Primary Subject is guaranteed by the maxims (or rules of inference) governing the genus-species relation, the connection between the genus and the predicate can be complex, characterized by various types of reasoning patterns. The relevance relation can hide implicit arguments, such as an implicit argument from classification , an evaluation based on values, consequences or rules, a causal relation, or an argument from practical reasoning. (shrink)

Axiomatic proof/refutation systems for the paraconsistent modal logics: KN4 and KN4.D are presented. The completeness proofs boil down to showing that every sequent is either provable or refutable. By constructing finite tree-type countermodels from refutations, the refined characterizations of these logics by classes of finite tree-type frames are established. The axiom systems also provide decision procedures for these logics.

The λ-continuum of inductive methods was derived from an assumption, called λ-condition, which says that the probability of finding an individual having property $x_{j}$ depends only on the number of observed individuals having property $x_{j}$ and on the total number of observed individuals. So, according to that assumption, all individuals with properties which are different from $x_{j}$ have equal weight with respect to that probability and, in particular, it does not matter whether any individual was observed having some property similar (...) to $x_{j}$ (the most complete proof of this result is presented in Carnap, 1980). The problem thus remained open to find some general condition, weaker than the λ-condition, which would allow for the derivation of probability functions which might be sensitive to similarity. Carnap himself suggested a weakening of the λ-condition which might allow for similarity sensitive probability functions (Carnap, 1980, p. 45) but he did not find the family of probability functions derivable from that principle. The aim of this paper is to present the family of probability functions derivable from Carnap's suggestion and to show how it is derived. In Section 1 the general problem of analogy by similarity in inductive logic is presented, Section 2 outlines the notation and the conceptual background involved in the proof, Section 3 gives the proof, Section 4 discusses Carnap's principle and the result, Section 5 is a brief review of the solutions which have previously been proposed. (shrink)

The Logic of Metaphor uses techniques from possible worlds semantics to provide formal truth-conditions for many grammatical classes of metaphors. It gives logically precise and practically useful syntactic and semantic rules for generating and interpreting metaphors. These rules are implemented in a working computer program. The book treats the lexicon as a conceptual network with semantics provided by an intensional predicate calculus. It gives rules for finding analogies in such networks. It shows how to syntactically and semantically analyze texts containing (...) metaphors and how to use structural similarities between parts of possible worlds to provide truth-conditions for metaphors. Meanings for metaphors are linked to the modal logics of identity and indiscernibility. The book shows how to extend deductive and abductive inference systems to handle metaphors. It shows how to handle novel metaphorical word-senses. The Logic of Metaphor will be useful to philosophers, logicians, linguists, and computer scientists. (shrink)

Given a 4-tuple of Boolean variables (a, b, c, d), logical proportions are modeled by a pair of equivalences relating similarity indicators ( \({a \wedge b}\) and \({\overline{a} \wedge \overline{b}}\) ), or dissimilarity indicators ( \({a \wedge \overline{b}}\) and \({\overline{a} \wedge b}\) ) pertaining to the pair (a, b), to the ones associated with the pair (c, d). There are 120 semantically distinct logical proportions. One of them models the analogical proportion which corresponds to a statement of the (...) form “a is to b as c is to d”. The paper inventories the whole set of logical proportions by dividing it into five subfamilies according to what they express, and then identifies the proportions that satisfy noticeable properties such as full identity (the pair of equivalences defining the proportion hold as true for the 4-tuple (a, a, a, a)), symmetry (if the proportion holds for (a, b, c, d), it also holds for (c, d, a, b)), or code independency (if the proportion holds for (a, b, c, d), it also holds for their negations \({{(\overline{a},\overline{b}, \overline{c}, \overline{d})}}\) ). It appears that only four proportions (including analogical proportion) are homogeneous in the sense that they use only one type of indicator (either similarity or dissimilarity) in their definition. Due to their specific patterns, they have a particular cognitive appeal, and as such are studied in greater details. Finally, the paper provides a discussion of the other existing works on analogical proportions. (shrink)

This paper considers logics which are formally dual to intuitionistic logic in order to investigate a co-constructive logic for proofs and refutations. This is philosophically motivated by a set of problems regarding the nature of constructive truth, and its relation to falsity. It is well known both that intuitionism can not deal constructively with negative information, and that defining falsity by means of intuitionistic negation leads, under widely-held assumptions, to a justification of bivalence. For example, we do not want to (...) equate falsity with the non-existence of a proof since this would render a statement such as “pi is transcendental” false prior to 1882. In addition, the intuitionist account of negation as shorthand for the derivation of absurdity is inadequate, particularly outside of purely mathematical contexts. To deal with these issues, I investigate the dual of intuitionistic logic, co-intuitionistic logic, as a logic of refutation, alongside intuitionistic logic of proofs. Direct proof and refutation are dual to each other, and are constructive, whilst there also exist syntactic, weak, negations within both logics. In this respect, the logic of refutation is weakly paraconsistent in the sense that it allows for statements for which, neither they, nor their negation, are refuted. I provide a proof theory for the co-constructive logic, a formal dualizing map between the logics, and a Kripke-style semantics. This is given an intuitive philosophical rendering in a re-interpretation of Kolmogorov’s logic of problems. (shrink)

This article criticizes an attempt by j. Brenton stearns to refute naturalism as an account of evaluative language ("a refutation of axiological naturalism," journal of value inquiry, I, No.2 (fall, 1967)). Stearns argued that if the goodness of a thing were, As naturalism claims, Equivalent to its possession of certain non-Evaluative properties, Then two things could differ from one another solely with respect to their goodness. And since this is impossible, Stearns concludes that naturalism is false. This argument is (...) criticized by logical analogy. It is argued that if this argument shows that a naturalistic account of "good" is false, Then it equally shows that a naturalistic account of "large" or "primary color" is false. (shrink)

Socrates’ expert-analogies is frequent both in Plato’s dialogues and in the Socratic writings of Xenophon, and is also ascribed to Socrates by Aristotle and Aeschines. Socrates makes an analogy from a non-controversial expert (or an expertise) like the cobbler or ship-captain, to another (often controversial) expert (or expertise) like the statesman. This paper defends an interpretation of the expert-analogy as valid deductions. It infers from one type of expert (such as the ship-captain) to another type of expert (such (...) as the statesman), and the attribute inferred (for instance ‘should not be selected by lot’) belongs to these types of experts because they are experts. The general logical form, which makes no mention of the expert and which is valid in virtue of its form, infers from one or more species to another species of the same genus, and the attribute inferred is presupposed to belong as such to the genus and only accidentally to the species. (shrink)

We investigate the relative probabilistic support afforded by the combination of two analogies based on possibly different, structural similarity (as opposed to e.g. shared predicates) within the context of Pure Inductive Logic and under the assumption of Language Invariance. We show that whilst repeated analogies grounded on the same structural similarity only strengthen the probabilistic support this need not be the case when combining analogies based on different structural similarities. That is, two analogies may provide less support than each would (...) individually. (shrink)

This paper deals with two issues in the field of reasoning by analogy in the law. The one issue is whether there exists such a thing as analogous rule application, or whether there is only the ‘normal’ application of a broadened rule. It is argued that if rules, as the entities made by a legislator, are distinguished from generalised solutions for cases, the idea of analogous application of rules makes sense. It is also shown how the so-called ‘reason-based model (...) of rule application’, in contrast to the traditional modus ponens or subsumption model, makes it easy to give a logical account of analogous rule application. The other issue is how to argue logically about whether two cases are sufficiently similar to adopt the outcome of the one case for the other case. Section 3 provides a general logical model to establish this. The model is based on the comparison of the reasons for and against a particular solution in the two cases. (shrink)

In the paper rejection systems for a system of nonsense-logic are investigated. The first rejection system consists of four rejected axioms and only one rejection rule  the rule of rejection by detachment. The second one consists of one rejected axiom and two rejection rules: the rule of rejection by detachment and the rule of rejection by substitution. The aim of the paper is to present also a proof of Ł-decidability for the considered systems.

The paper explores the handling of singular analogy in quantitative inductive logics. It concentrates on two analogical patterns coextensive with the traditional argument from analogy: perfect and imperfect analogy. Each is examined within Carnap’s λ-continuum, Carnap’s and Stegmüller’s λ-η continuum, Carnap’s Basic System, Hintikka’s α-λ continuum, and Hintikka’s and Niiniluoto’s K-dimensional system. Itis argued that these logics handle perfect analogies with ease, and that imperfect analogies, while unmanageable in some logics, are quite manageable in others. The paper (...) concludes with a modification of the K-dimensional system that synthesizes independent proposals by Kuipers and Niiniluoto. (shrink)

Argument by analogy has long been regarded as the characteristic way of arguing in ancient Chinese culture. Classic Chinese philosophers not only prefer to use analogy to argue for their own views, but also take efforts to theorize it in a systematic way. This paper aims to provide a careful study on the relevant ideas in ancient China in order to reconstruct the ancient Chinese theory of argument by analogy, and then to reveal some of its distinctive (...) features through a comparison with the Western counterpart account as developed by Aristotle. It is indicated that in ancient China analogical argument was conceived primarily as a way of arguing based on classification, with a unique mechanism of taking and giving according to kind. On that basis, it is argued that although such a characterization captures the logical structure of analogical argument in a similar way to Aristotle, the ancient Chinese theory stresses the foundational role of a particular notion of kind, thus makes the construction and application of analogical arguments become highly flexible and context-sensitive. Moreover, it is also contended that in ancient China the rationale of analogical arguments is explained from a general perspective of kind, relying upon the universal knowledge pertaining to the forming of kinds. Then it is further revealed that, unlike Aristotle who emphasizes the causal links between attributes in the physical world, ancient Chinese thinkers justify analogical argument by appealing to some normative metaphysical and epistemological principles. (shrink)

John Woods and Brent Hudak’s theory on arguments by analogy (1989), although correct in its meta-argumentative approach, gives rise to problems when we consider the possibility of weighing reasons. I contend that this is an outcome of construing the relationship between the premises and the conclusion of arguments compared in argumentation by analogy as inferences. An interpretation in terms of reasons is proposed here. The reasons-based approach solves these problems and allows the theory to be extended to account (...) for a particular variant of argumentation by analogy in which the subjects of comparison are not arguments, but weighings of reasons. (shrink)

John Woods and Brent Hudak’s theory on arguments by analogy (1989), although correct in its meta-argumentative approach, gives rise to problems when we consider the possibility of weighing reasons. I contend that this is an outcome of construing the relationship between the premises and the conclusion of arguments compared in argumentation by analogy as inferences. An interpretation in terms of reasons is proposed here. The reasons-based approach solves these problems and allows the theory to be extended to account (...) for a particular variant of argumentation by analogy in which the subjects of comparison are not arguments, but weighings of reasons. (shrink)

In refutation of Cajetan, the sixteenth century commentator who is still considered an authority on Thomas' doctrine of analogy, it is argued that "the analogy of names is, for St. Thomas, a logical intention, and in speaking of it we must observe the general rule that the logical and real orders must not be confused. St. Thomas does not see any peculiar significance of analogy for metaphysics--apart, i.e., from the significance it has for science (...) and ordinary discourse." The thesis is closely argued for and painstakingly documented.--A. P. D. M. (shrink)

The paper discusses some logical problems concerning analogy. The traditional understanding of analogy as _proportion_ (proportion) is inadequate, at least if proportionality is taken in mathematical sense. This situation is clear if we considered various special cases of analogy for instance _analogia legis_ and _analogia juris._ Since analogy assumes a similarity of analogata (items being or investigated) as analogical, a general analysis of analogical relation must begin with the concept of similarity. It can be defined (...) as possessing a common property. This idea is formalized by devices borrowed from logic and set theory. (shrink)

Since the first decade of the 14th Century, Thomas Aquinas’s disciples have struggled to explain and defend his doctrine of analogy. Analogy after Aquinas: Logical Problems, Thomistic Answers relates a history of prominent Medieval and Renaissance Thomists’ efforts to solve three distinct but interrelated problems arising from their reading both of Aquinas’s own texts on analogy, and from John Duns Scotus’s arguments against analogy and in favor of univocity in Metaphysics and Natural Theology. The first (...) of these three problems concerns Aquinas’s at least apparently disparate statements on whether a name is said by analogy through a single concept or through diverse concepts. The second problem concerns the model of analogy suited for predicating names analogously across the categories of being or about God and creatures. Is “being” said analogously about God and creatures, or substance and accidents, on the model of how “healthy” is said of medicine and an animal, or on the model of how “principle” is said of a point and a line? The third problem comes from outside challenges to Aquinas’s thought, in particular Scotus’ claims that univocal names alone can mediate valid demonstrations, and any demonstration that failed to use its mediating terms univocally would fail by the fallacy of equivocation. Analogy after Aquinas makes a unique contribution to the study of philosophical theology in the tradition of Thomas Aquinas by showing the historical and philosophical connection between these three problems, as well as the variety of solutions proposed by leading representatives of this tradition. Thomists considered in the book include: Hervaeus Natalis (1250-1323), Thomas Sutton (1250-1315), John Capreolus (1380-1444), Dominic of Flanders (1425-1479), Paul Soncinas (d. 1494), Thomas dio vio Cajetan (1469-1534), Francis Silvestri of Ferrara (1474-1528), and Chrysostom Javelli (1470-1538). (shrink)

This paper considers a topos-theoretic structure for the interpretation of co-constructive logic for proofs and refutations following Trafford :22–40, 2015). It is notoriously tricky to define a proof-theoretic semantics for logics that adequately represent constructivity over proofs and refutations. By developing abstractions of elementary topoi, we consider an elementary topos as structure for proofs, and complement topos as structure for refutation. In doing so, it is possible to consider a dialogue structure between these topoi, and also control their relation (...) such that classical logic is simulated where proofs and refutations are conclusive. (shrink)

Analogy making from examples is a central task in intelligent system behavior. A lot of real world problems involve analogy making and generalization. Research investigates these questions by building computer models of human thinking concepts. These concepts can be divided into high level approaches as used in cognitive science and low level models as used in neural networks. Applications range over the spectrum of recognition, categorization and analogy reasoning. A major part of legal reasoning could be formally (...) interpreted as an analogy making process. Because it is not the same as reasoning in mathematics or the physical sciences, it is necessary to use a method, which incorporates first the ability to specify likelihood and second the opportunity of including known court decisions. We use for modelling the analogy making process in legal reasoning neural networks and fuzzy systems. In the first part of the paper a neural network is described to identify precedents of immaterial damages. The second application presents a fuzzy system for determining the required waiting period after traffic accidents. Both examples demonstrate how to model reasoning in legal applications analogous to recent decisions: first, by learning a system with court decisions, and second, by analyzing, modelling and testing the decision making with a fuzzy system. (shrink)

Bi-intuitionistic logic is the union of intuitionistic and dual intuitionistic logic, and was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent ‘cut-free’ sequent calculus has recently been shown to fail cut-elimination. We present a new cut-free sequent calculus for bi-intuitionistic logic, and prove it sound and complete with respect to its Kripke semantics. Ensuring completeness is complicated by the interaction between intuitionistic implication and dual intuitionistic exclusion, similarly to future and past modalities in (...) tense logic. Our calculus handles this interaction using derivations and refutations as first class citizens. We employ extended sequents which pass information from premises to conclusions using variables instantiated at the leaves of refutations, and rules which compose certain refutations and derivations to form derivations. Automated deduction using terminating backward search is also possible, although this is not our main purpose. (shrink)

We discuss in this paper the question of the scope of the principle of tolerance about languages promoted in Carnap's The Logical Syntax of Language and the nature of the analogy between it and the rudimentary conventionalism purportedly exhibited in the work of Poincaré and Hilbert. We take it more or less for granted that Poincaré and Hilbert do argue for conventionalism. We begin by sketching Coffa's historical account, which suggests that tolerance be interpreted as a conventionalism that (...) allows us complete freedom to select whatever language we wish—an interpretation that generalizes the conventionalism promoted by Poincaré and Hilbert which allows us complete freedom to select whatever axiom system we wish for geometry. We argue that such an interpretation saddles Carnap with a theory of meaning that has unhappy consequences, a theory we believe he did not hold. We suggest that the principle of linguistic tolerance in fact has a more limited scope; but within that scope the analogy between tolerance and geometric conventionalism is quite tight. (shrink)