This paper explains how a five minute-segment from “Monty Python and the Holy Grail” can be an effective pedagogical tool for distinguishing validity from soundness and for explaining several other concepts relevant to critical thinking courses. After viewing the “We’ve found a witch” scene, students are given a transcript of the sketch and asked to put arguments into a valid form. Once these arguments have been represented, students are charged with determining whether the argument is sound and, if unsound, (...) with determining which of the premises is controversial. The author argues that using this segment has a number of pedagogical benefits as it encourages real live critical thinking, can be used to teach additional critical thinking concepts (e.g. reasoning with analogies), and can help students be more cautious about making over-reaching claims in their own arguments. (shrink)

A great deal of theorizing has emerged about the economic ramifications of increased automation. However, significantly less attention has been paid to the potential effects of AI-driven occupational replacement on less measurable metrics—in particular, what it feels like to be replaced. In politics, we see examples of nation-states and extremist groups invoking the concept of replacement as a motivator for political action, unrest, and, at times, violence. In the realm of workplace automation, and in particular, in the case of AI-driven (...) workplace automation, the replacement of human labor with artificial labor is an explicit goal. In this paper, we suggest that, given the effects that the experience of a sense of replacement has in political contexts and the potential for that sense of replacement to motivate unrest and violence, we should be concerned about the widely predicted replacement of workers over the coming decades beyond the potential economic challenges which may arise. (shrink)

Reasoning that compares two objects or situations to draw conclusions about previously unknown properties of one of them has traditionally been taken to be ampliative and probabilistic. I propose that it is apodeictic reasoning from a premise about isomorphic structures that is often uncertain, but which we may have good reasons to believe. I characterize the structures and their isomorphism, describe patterns of reasoning appropriate to them, and discuss some complications not immediately obvious.

I present three critical points against G.E.R. Lloyd's ‘The Fortunes of Analogy’. First, I argue that Lloyd unduly criticises Aristotle's view of analogies. Second, I argue that Lloyd needs to discuss the means of limiting the semantic stretch of terms, for instance through the distinction between fiat and bona fide boundaries. Third, I point out some terminological issues in Lloyd's account, especially concerning the applicability of validity, soundness, and fallaciousness to analogies.

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)

What are people who disagree about logic disagreeing about? The paper argues that (in a wide range of cases) they are primarily disagreeing about how to regulate their degrees of belief. An analogy is drawn between beliefs about validity and beliefs about chance: both sorts of belief serve primarily to regulate degrees of belief about other matters, but in both cases the concepts have a kind of objectivity nonetheless.

In this article I am concerned with analogical reasoning in ethics. There is no doubt that the use of analogy can be a powerful tool in our ethical reasoning. The importance of this mode of reasoning is therefore commonly accepted, but there is considerable debate concerning how its structure should be understood and how it should be assessed, both logically and epistemically. In this paper, I first explain the basic structure of arguments from analogy in ethics. I then discuss the (...) diversity of analogical arguments that can be found in ethics. I analyse their structure, assess them from a logical viewpoint, and show how they can be epistemically challenged and defended. The result of this investigation is that, contrary to a commonly held view, analogical reasoning can be a logically valid type of ethical reasoning that can provide reasons for action that are not worse than the reasons provided by any other kind of practical reasoning. (shrink)

How should we understand validity? A standard way to characterize validity is in terms of the preservation of truth (or truth in a model). But there are several problems facing such characterizations. An alternative approach is to characterize validity epistemically, for instance in terms of the preservation of an epistemic status. In this paper, I raise a problem for such views. First, I argue that if the relevant epistemic status is factive, such as being in a position to know or (...) having conclusive evidence for, then the account runs into trouble if we endorse certain familiar logical principles. Second, I argue that if the relevant epistemic status is non-factive, such as is rationally committed to or has justification for believing, then a similar problem arises if we endorse the logical principles as well as a sufficiently strong epistemic “level-bridging” principle. Finally, I argue that an analogous problem arises for the most natural characterization of validity in terms of rational credence. (shrink)

A number of recent works consider treating validity as a primitive notion rather than one defined in some standard manner. There seem to have been three motivations. First, to understand how truth and validity interact in potentially paradoxical settings. Second, to argue that validity is in fact afflicted with paradoxes analogous to the semantic paradoxes. Third, to develop a ‘deflationary’ conception of validity or consequence. This article treats the notion of validity as a primitive notion and shows how to provide (...) a consistent theory of classical validity (and self-applicative truth), conservative over Peano arithmetic. (shrink)

Light is the most important analogy for the Vijñānavādin in proving self-awareness, namely the cognition that cognizes itself. Recent studies show that two opponents of the doctrine of self-awareness, Kumārila and Bhaṭṭa Jayanta alleged that the Vijñānavādin has also used light as an analogy for the view that cognition must be perceived before the object is perceived. However, this is a modification of the actual view of the Vijñānavāda that cognition must be perceived in order for it to perceive its (...) object. Based on Kumārila’s such modified restatement, Taber argues that “Kumārila’s Buddhist” fails to establish the light as a valid analogy in their theory. Taber’s argument is subsequently referred to by Watson and Kataoka in their works, in which they defend Vijñānavāda’s light-analogy against Taber. However, their defence is also based on a similarly modified restatement by Jayanta and the defence is set out in the view of Naiyāyika philosophy. This paper examines all these arguments and shows that Watson’s and Kataoka’s thought of the light-analogy might still be problematic. It also goes back to the original view of the Vijñānavāda and observes to what extent the light-analogy serves as a strong support for the establishment of the self-awareness. (shrink)

The analogy between biological and cultural evolution is not perfect. Yet, as Mesoudi et al. show, many of the vaunted differences between cultural and genetic evolution (for example, an absence of discrete particles of cultural inheritance, and the blurred distinction between cultural replicators and cultural phenotypes) are, on closer inspection, either illusory or peripheral to the validity of the analogy. But what about horizontal transmission? We strongly agree with the authors that the potential for horizontal transmission of cultural traits does (...) not invalidate an evolutionary approach to culture. We suggest, however, that it does require a different evolutionary treatment. (Published Online November 9 2006). (shrink)

The Logic of Analogy is a study of the valid logical forms of qualitative and quantitative analogical argument, and the rules pertaining to them. It investigates equally valid conflicting arguments, statistics-based arguments and their utility in science, arguments from precedent used in law-making or law-application, and examines subsumption in analogical terms. Included for purposes of illustration is a large section on Talmudic use of analogical reasoning.

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)

In Part I of this paper, I argue that the arguments Plato offers for the tripartition of the soul are founded upon an equivocation, and that each of the valid options by which Plato might remove the equivocation will not produce a tripartite soul. In Part II, I argue that Plato is not wholly committed to an analogy of soul and state that would require either a tripartite state or a tripartite soul for the analogy to hold. It follows (...) that the heart of the analogy is not to be found in the comparison of the Kallipolis and its three parts to the soul conceived as tripartite, but rather must be supposed to reside in some other connection between the ways in which justice characterizes states and souls, and I will suggest what this other connection consists in. (shrink)

This paper presents a novel position in the philosophy of logic: I argue that _validity_ is a thick concept. Hence, I propose to consider _validity_ in analogy to other thick concepts, such as _honesty_, _selfishness_ or _justice_. This proposal is motivated by the debate on the normativity of logic: while logic textbooks seem simply descriptive in their presentation of logical truths, many have argued that logic has consequences for how we ought to reason, for what we ought to believe, or (...) for what we ought to infer. How can logic be normative, if it appears to be descriptive? According to the proposal of this paper, the normativity of logic can be explained because a thick concept is in play: _validity_. Thus, I argue that the debate on how to best characterize validity and the debate on logic’s normativity are more connected than we think, because _validity_ is a thick concept. (shrink)

Any theory of truth must find a way around Curry’s paradox, and there are well-known ways to do so. This paper concerns an apparently analogous paradox, about validity rather than truth, which JC Beall and Julien Murzi call the v-Curry. They argue that there are reasons to want a common solution to it and the standard Curry paradox, and that this rules out the solutions to the latter offered by most “naive truth theorists.” To this end they recommend a radical (...) solution to both paradoxes, involving a substructural logic, in particular, one without structural contraction. In this paper I argue that substructuralism is unnecessary. Diagnosing the “v-Curry” is complicated because of a multiplicity of readings of the principles it relies on. But these principles are not analogous to the principles of naive truth, and taken together, there is no reading of them that should have much appeal to anyone who has absorbed the morals of both the ordinary Curry paradox and the second incompleteness theorem. (shrink)

Although the use of possible worlds in semantics has been very fruitful and is now widely accepted, there is a puzzle about the standard definition of validity in possible-worlds semantics that has received little notice and virtually no comment. A sentence of an intensional language is typically said to be valid just in case it is true at every world under every model on every model structure of the language. Each model structure contains a set of possible worlds, and (...) models are defined relative to model structures, assigning truth-values to sentences at each world countenanced by the model structure. The puzzle is why more than one model structure is used in the definition of validity. There is presumably just one class of all possible worlds and just one model structure defined on this class that does correctly the things that model structures are supposed to do. (These include, but need not be limited to, specifying the set of individuals in each world as well as various accessibility relations between worlds.) Why not define validity simply as truth at every world under every model on this one model structure? What is the point of bringing in more model structures than just this one?

We investigate these questions in some detail and conclude that for many intensional languages the puzzle points to a genuine difficulty: the standard definition of validity is insufficiently motivated. We begin (Section 1) by showing that a plausible and natural account of validity for intensional languages can be based on a single model structure, and that validity so defined is analogous in important respects to the standard account of validity for extensional languages. We call this notion of validity "validity!", and in Section 2 we contrast it with the standard notion, which we call "validity2". Several attempts are made to discover a rationale for the almost universal acceptance of validity2, but in most of these attempts we come up empty-handed. So in Section 3 we investigate validity! for some intensional languages. Our investigation includes providing axiomatizations for several propositional and predicate logics, most of which are provably complete. The completeness proofs are given in the Appendix, which also contains a sketch of a compactness proof for one of the predicate logics. (shrink)

This article identifies and formalizes the logical features of analogous terms that justify their use in deduction. After a survey of doctrines in Aristotle, Aquinas, and Cajetan, the criteria of “analogy of proper proportionality” are symbolized in first-order predicate logic. A common genus justifies use of a common term, but does not provide the inferential link required for deduction. Rather, the respective differentiae foster this link through their identical proportion. A natural-language argument by analogy is formalized so as to exhibit (...) these criteria, thereby showing the validity of analogical deduction. (shrink)

This paper addresses several issues in argumentation theory. The over-arching goal is to discuss how a theory of analogical argument schemes fits the pragma-dialectical theory of argument schemes and argument structures, and how one should properly reconstruct both single and complex argumentation by analogy. I also propose a unified model that explains how formal valid deductive argumentation relates to argument schemes in general and to analogical argument schemes in particular. The model suggests “scheme-specific-validity” i.e. that there are contrasting species (...) of validity for each type of argument scheme that derive from one generic conception of validity. (shrink)

We can usefully draw an analogy between ethics and science, despite the significant differences between them. We can then see the ways in which moral theories can indeed be “tested,” not by empirical experience but by moral experience. This can be expected to lead to rival moral theories, but in science also we have rival theories. I argue that we should demand more than coherence of our moral theories, as we do of our scientific theories. I try to show how (...) the “testing” of moral theories can be carried out and how this can allow us to accept some moral theories as valid. (shrink)

In Mohist philosophy, the gnomon is a metaphor for the standard of valid arguments. This metaphor comes from the method of establishing due east and west by observing gnomon shadows at dusk and dawn. I argue that there is also an overlooked, implicit aspect of the gnomon metaphor that comes from its function of measuring the height of heaven indirectly through proportional calculation. The function of indirect measurement inspires a strategy of argumentation in Mohist ethics, which I call “analogical (...) upscaling.” Such an argument draws a parallel between small-scale and large-scale actions for the purpose of determining the Will of Heaven in a particular circumstance, just as the gnomon measures heaven’s physical height analogically. In the conclusion, I compare the epistemological status of light and shadow in the Mozi and Plato’s Republic. (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)

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)

A doctrine of analogy in various guises is the traditional medicine for the malady of theological meaninglessness; it supposedly cures both the anthropomorphism of univocation and the unintelligibility of equivocation. If Palmer is right, however, the cure is as bad as the disease. Analogy, he urges, is essential to traditional "descriptive" theology, i.e., to "a systematic presentation of our knowledge about God" which utilizes arguments and licenses inferences. Palmer indicates that analogy is required by anyone who "holds some beliefs about (...) the ultimate nature of the "universe", so that metaphysics as well as natural and revealed theology stands under the strictures of his argument. But his focus is on theology, and he says very little about the consequences for metaphysics. Palmer argues, the doctrine of analogy entails agnosticism with regard to the meaning of terms predicated of God; we cannot know what sense, if any, our theological terms possess. But if we cannot know the sense of our terms, or even whether they have any sense, we cannot know whether any term is being used in the same sense. Hence no inferences or arguments are possible in theology. More precisely, no arguments can be known to be valid in theology, which is to say that theology as traditionally conceived is impossible. (shrink)

Even though the concept of a 'validity claim' is central to Habermas's theory of communicative action, he has never given a precise definition of the term. He has stated only that truth is a type of validity claim, and that rightness and sincerity are analogous to truth. This paper explores the basis of this analogy, arguing that rightness and sincerity must share at least two characteristics with the truth predicate: each must be the designated value in an appropriate system of (...) logic, and each must serve as the 'central notion' in a theory of meaning for some corresponding class of speech acts. It is these two characteristics that establish the internal connec tion between understanding and justification that Habermas's more general project requires. However, there is an unnoticed tension between these two characteristics, since the relative autonomy of linguistic meaning from specific contexts of use appears to require that speech acts be governed by a uniform logic, and thus by a single validity claim. Key Words: communicative action • - Habermas • - pragmatics • - speech act theory • - truth • - validity claim. (shrink)

Participants were asked to draw inferences about correlation from single x,y observations. In Experiment 1 statistically sophisticated participants were given the univariate characteristics of distributions of x and y and asked to infer whether a single x, y observation came from a correlated or an uncorrelated population. In Experiment 2, students with a variety of statistical backgrounds assigned posterior probabilities to five possible populations based on single x, y observations, again given knowledge of the univariate statistics. In Experiment 3, statistically (...) naïve participants were given a problem analogous to that given in Experiment 1, framed verbally. Experiment 4 replicated Experiment 3 but added an “impossible to determine” response option. Models that rely on computing sample correlations make no predictions about these investigations. From a Bayesian perspective, participants’ inferences in all four experiments tended to make probabilistically valid inferences as long as the single datum was directional. The results are discussed in light of the Brunswikian notion of vicarious functioning. (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)

Blanchette and Dunbar have claimed that when participants are allowed to draw on their own source analogs in the service of analogical argumentation, retrieval is less constrained by surface similarity than traditional experiments suggest. In two studies, we adapted this production paradigm to control for the potentially distorting effects of analogy fabrication and uneven availability of close and distant sources in memory. Experiment 1 assessed whether participants were reminded of central episodes from popular movies while generating analogies for superficially (...) similar versus superficially dissimilar target situations. In Experiment 2, we modified this procedure to assess the retrieval of autobiographic memories, more familiar to participants than fictional episodes. Both studies revealed a strong effect of surface similarity on the retrieval of participants' own sources, thus suggesting that the superficial bias typically observed in experimental studies—and simulated by most computational models—does not originate in a lack of ecological validity. (shrink)

This article explains the problems with Alan Shewmon’s critique of brain death as a valid sign of human death, beginning with a critical examination of his analogy between brain death and severe spinal cord injury. The article then goes on to assess his broader argument against the necessity of the brain for adult human organismal integration, arguing that he fails to translate correctly from biological to metaphysical claims. Finally, on the basis of a deeper metaphysical analysis, I offer a (...) revised rationale for the validity of the neurological criterion of human death. (shrink)

Alethic pluralism holds that there are many truth properties. The view has been challenged to make sense of the notion of logical validity, understood as necessary truth preservation, when inferences involving different areas of discourse are concerned. I argue that the solution proposed by Edwards to solve the analogous problem of mixed compounds can straightforwardly be adapted to give alethic pluralists also a viable account of validity.

In 1976, The Hastings Center convened a conference to examine the validity of proposed parallels between Nazi and contemporary biomedical practices in moral argument. Charges that current medical and social practices and policies are analogous to or are the moral equivalent of Nazi programs are again in the air, and in this new feature of the Report, four commentators display and critique the use of this analogy.

An application and confirmation of the thesis of my book, "Kant's Model of the Mind", that, for Kant, space and time exist only in and for imagination, and the given of sense is atemporal and aspatial (=transcendental idealism). On previous interpretations of transcendental idealism, appearances already have temporal and spatial existence; on mine, they lack such existence, and the purpose of the Analogies is to show how they originally acquire it. Existence in space and time is constituted by a (...) priori principles of necessary connection (the Analogies), whose validity with respect to appearances is grounded on the demand for original apperception (i.e., a synthetic unitary sensibility). The implications vis-à-vis Kant's metaphysics of nature and his Euclideanism are then explored. (shrink)

There is a Barthian objection to the project of natural validation theology (i.e. to the attempt to establish, on purely natural bases, whether God exists) according to which, far from being required to engage in the project, the theologian is required to abstain from engaging in it. By considering the motivation for an analogous objection to validation projects in metaphysics and epistemology, voiced by representatives of the comman sense tradition in modern Western philosophy, I argue that this objection is plausibly (...) motivated by the thought that engaging in natural validation theology inappropriately commits one to the irrelevance of putatively nonnatural belief-sources. (shrink)

Consider the following argument written on the board in room 227: 1 = 1. So, the argument on the board in room 227 is not valid. This argument generates a paradox. The aim of this paper is to present a resolution of this paradox and related paradoxes of validity, including a version of the Curry paradox. The proposal stresses the close connections between these validity paradoxes and paradoxes of truth and paradoxes of denotation. So a more general aim is (...) to provide a unified response to semantic paradox. The positive proposal is in part inspired by a brief, tantalizing suggestion of Gödel’s, that the paradoxes might appear “as something analogous to dividing by zero”—so that the concept of validity, for example, is everywhere applicable except for certain singular points or singularities. A second central claim is that ‘valid’ is a context-sensitive predicate. The key notions of this contextual-singularity theory are presented and applied to a variety of cases. Any purported solution to paradox must deal with the phenomenon of revenge, and a response to revenge is outlined. The paper closes with remarks about the accommodation of Tarski’s claim that natural languages are universal. (shrink)

This article addresses the ability of Parallel Distributed Processing (PDP) networks to generate stagewise cognitive development in accordance with Piaget's theory of cognitive epigenesis. We carried out a replication study of the simulation experiments by McClelland (1989) and McClelland and Jenkins (1991) in which a PDP network learns to solve balance scale problems. In objective tests motivated from catastrophe theory, a mathematical theory of transitions in epigenetical systems, no evidence for stage transitions in network performance was found. It is concluded (...) that PDP networks lack the ability to recover the positive outcomes of analogous catastrophe analyses of real cognitive developmental data. In an attempt to further characterize the learning behaviour of PDP networks, we carried out a second simulation study using the discrimination‐shift paradigm. The results thus obtained indicate that PDP learning is compatible with the learning of stimulus‐response relationships, not with the acquisition of mediating rules such as conceived in (neo‐)Piagetian theory. In closing, we speculate about the feasibility of simulating stagewise development with alternative network architectures. (shrink)

Legal Reason describes and explains the process of analogical reasoning, which is the distinctive feature of legal argument. It challenges the prevailing view, urged by Edward Levi, Cass Sunstein, Richard Posner and others, which regards analogical reasoning as logically flawed or as a defective form of deductive reasoning. It shows that analogical reasoning in the law is the same as the reasoning used by all of us routinely in everyday life and that it is a valid form of reasoning (...) derived from the innate human capacity to recognize the general in the particular, on which thought itself depends. The use of analogical reasoning is dictated by the nature of law, which requires the application of rules to particular facts. Written for scholars as well as students and persons generally who are interested in law, Legal Reason is written in clear, accessible prose, with many examples drawn from the law and from everyday experience. (shrink)

The main goal of Kant’s Second Analogy of Experience was to answer Humean objectionsconcerning the aprioricity of the principle of “every-event-some-cause”. This paper intendsto suggest an interpretation of the Kantian argument that, even though cannot show thatHume should be satisfied with the answer, makes clear Kant’s reasons for that anti-Humeangoal. In the first part of this paper, I intend to discuss summarily Hume’s objection againstthe possibility of a demonstration of the principle “every-event-some-cause” and his thesisconcerning its validity. In the second (...) part, it is the turn of the Kantian answer to thesame question concerning the validity of the principle of “every-event-some-cause”. (shrink)

The main goal of Kant’s Second Analogy of Experience was to answer Humean objectionsconcerning the aprioricity of the principle of “every-event-some-cause”. This paper intendsto suggest an interpretation of the Kantian argument that, even though cannot show thatHume should be satisfied with the answer, makes clear Kant’s reasons for that anti-Humeangoal. In the first part of this paper, I intend to discuss summarily Hume’s objection againstthe possibility of a demonstration of the principle “every-event-some-cause” and his thesisconcerning its validity. In the second (...) part, it is the turn of the Kantian answer to thesame question concerning the validity of the principle of “every-event-some-cause”. (shrink)

The term ‘bioethics’ is commonly associated with debates prompted by innovations in medical technology, yet the issues raised by bioethics are not new. They concern the extent to which medicine and social morality exist in harmony or opposition — issues routinely addressed in the social history of medicine. This paper will argue that historical thinking, understood broadly, has a significant role to play in understanding relations between medicine and social morality, and therefore in contemporary bioethics. It explores past and present (...) uses of metaphor and analogy in shaping perceptions of scientific innovation, and argues for the validity of apparently anachronistic thinking in our judgments of the past. The aims of the paper are ultimately pedagogical: to enable students to look at media reports about developments in medicine and biotechnology in order to problematise what are presented as the self-evident terms of current debate. (shrink)

This article addresses the ability of Parallel Distributed Processing (PDP) networks to generate stagewise cognitive development in accordance with Piaget's theory of cognitive epigenesis. We carried out a replication study of the simulation experiments by McClelland (1989) and McClelland and Jenkins (1991) in which a PDP network learns to solve balance scale problems. In objective tests motivated from catastrophe theory, a mathematical theory of transitions in epigenetical systems, no evidence for stage transitions in network performance was found. It is concluded (...) that PDP networks lack the ability to recover the positive outcomes of analogous catastrophe analyses of real cognitive developmental data. In an attempt to further characterize the learning behaviour of PDP networks, we carried out a second simulation study using the discrimination‐shift paradigm. The results thus obtained indicate that PDP learning is compatible with the learning of stimulus‐response relationships, not with the acquisition of mediating rules such as conceived in (neo‐)Piagetian theory. In closing, we speculate about the feasibility of simulating stagewise development with alternative network architectures. (shrink)

Philosophy, political philosophy and legal philosophy are all concerned with issues of justice and the validity of law (also known as the force of law ). These two problem areas are discussed against the background of the intersection of traditional theories of natural law and legal positivism, mediated by the contribution of the historical school. In addition the influence of the two neo-Kantian schools of thought (Baden and Marburg) required attention, particularly because certain elements in the thought of Derrida, Dooyeweerd (...) and Habermas are (implicitly) influenced by these schools. Derrida positions the problem of justice within the context of distinguishing universality and singularity (what is unique) and he alludes to the difficulty of bridging the gap between the two. It turned out that modern nominalism had an important effect on all three of the mentioned thinkers, in spite of their willingness to recognize “extra-mental” forms of universality. The problem of legal validity (the “force of law”) appears to be an instance of the interconnectedness between different aspects of reality, namely the jural and the physical . In order to account for this coherence Dooyeweerd developed a theory in which both the uniqueness and coherence between different aspects are explained in terms of inter-modal analogies. On this basis the difference between law and justice is specified by distinguishing between constitutive legal principles and the regulatively deepened (disclosed) principles of legal morality (such as f ault, equity, bona fides and so on). It will be shown that the idea of positivization , shared by thinkers coming from different backgrounds, is an important ingredient of an understanding of the nature of legal validity . Explaining it will require a focus on the nature of state law, of the power of the state, and of the legal competence entailed in the office of government. (shrink)

This article addresses the ability of Parallel Distributed Processing (PDP) networks to generate stagewise cognitive development in accordance with Piaget's theory of cognitive epigenesis. We carried out a replication study of the simulation experiments by McClelland (1989) and McClelland and Jenkins (1991) in which a PDP network learns to solve balance scale problems. In objective tests motivated from catastrophe theory, a mathematical theory of transitions in epigenetical systems, no evidence for stage transitions in network performance was found. It is concluded (...) that PDP networks lack the ability to recover the positive outcomes of analogous catastrophe analyses of real cognitive developmental data. In an attempt to further characterize the learning behaviour of PDP networks, we carried out a second simulation study using the discrimination‐shift paradigm. The results thus obtained indicate that PDP learning is compatible with the learning of stimulus‐response relationships, not with the acquisition of mediating rules such as conceived in (neo‐)Piagetian theory. In closing, we speculate about the feasibility of simulating stagewise development with alternative network architectures. (shrink)

We briefly address three issues that might be important to evaluate the validity of the “emulation theory”: (1) Does it really say something new? (2) Are similar processes engaged in action, imagery, and perception? (3) Does a brain amodal emulator exist?

We study algebras whose elements are relations, and the operations are natural “manipulations” of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schröder . Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of n-ary relations, RPEAn of polyadic equality algebras of n-ary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be very complex in the following sense: (...) for every natural number k there is an equation in E containing more than k distinct variables and all the operation symbols, if 2 < n < ω. Completely analogous statement holds for the case n ω. This improves Monk's famous non-finitizability theorem for which we give here a simple proof. We prove analogous nonfinitizability properties of the larger varieties SNrnCAn + k. We prove that the complementation-free subreducts of RCAn do not form a variety. We also investigate the reason for the above “non-finite axiomatizability” behaviour of RCAn. We look at all the possible reducts of RCAn and investigate which are finitely axiomatizable. We obtain several positive results in this direction. Finally, we summarize the results and remaining questions in a figure. We carry through the same programme for RPEAn and for RRA. By looking into the reducts we also investigate what other kinds of natural algebras of relations are possible with more positive behaviour than that of the well known ones. Our investigations have direct consequences for the logical properties of the n-variable fragment Ln of first order logic. The reason for this is that RCAn and RPEAn are the natural algebraic counterparts of Ln while the varieties SNrnCAn + k are in connection with the proof theory of Ln. This paper appears in two parts. The first part contains the non-finite axiomatizability results. The present second part contains finite axiomatizations of some fragments together with a figure summarizing the finite and non-finite axiomatizability results in this area and the problems left open. (shrink)

There is little doubt that in the actual practice of science, models, metaphors, analogies, reasoning by similar cases, and other "parallel" forms of argument are often essential for the discovery of new phenomena and their theoretical interpretation. The author has assembled in five essays, culled and developed from previous ones, her ideas on some basic questions concerning models and analogies. The first chapter considers in dialogue form the role of models in science; the next section is an exploration (...) of the questions of what is an analogy and under what conditions analogical arguments are valid. The formal logic of analogy is then developed in the third part. The theory concerning analogy put forth by Aristotle is next discussed; the last chapter treats of the explanatory function of metaphor—we are brought back to our starting point, hopefully enlightened.—P. J. M. (shrink)

This article proposes an interpretation of the status of the Grundnorm in Hans Kelsen’s legal theory which addresses the broader philosophical problem of the ultimate foundation of normativity. It begins by reviewing the main objections that have been raised against Kelsen’s theory, pointing out that most of these can be met by a ‘transcendental’ interpretation of the Grundnorm as a condition of possibility for legal cognition. It then argues that in order to solve the problem of the ultimate foundation for (...) legal validity it is also necessary to read the Grundnorm in light of the parallel category of ‘nomo-dynamicity’, which Kelsen introduced in all his legal writings beginning with the Pure Theory of Law of 1933. This yields a conception of legal validity as an ‘essentially temporal’ category, from the point of view of which the problem of ultimate foundations cannot emerge because the beginning is by definition not situated conceptually within time. The broader conclusion is therefore that overcoming the problem of the ultimate foundation of normativity requires abandoning the theologico-political assumption that valid norms are posited through a sovereign gesture analogous to that through which God is supposed to have created the universe ex nihilo. Construing normativity as ‘essentially temporal’ implies that the search for ultimate foundations must run into a category that is entirely foreign to political theology but well known to phenomenology: that of an ‘always-already’. (shrink)

What formulas are tense-logically valid depends on the structure of time, for example on whether it has a beginning. Logicians have investigated what formulas correspond to what physical hypotheses about time. Analogously, we can investigate what formulas of modal logic correspond to what metaphysical hypotheses about necessity. It is widely held that physical hypotheses about time may be contingent. If so, tense-logical validity may be contingent. In contrast, validity in modal logic is typically taken to be non-contingent, as reflected (...) by the general acceptance of the so-called “rule of necessitation.” But as has been argued by various authors in recent years, metaphysical hypotheses may likewise be contingent. If, in particular, hypotheses about the extent of possibility are contingent, we should expect modal-logical validity to be contingent too. Let “contingentism” be the view that everything that is not ruled out by logic is possible. I shall investigate what the right system of modal logic is, if contingentism is true. Given plausible assumptions, the system contains the McKinsey principle, and is thus not even contained in S5. It also contains simple and elegant iteration principles for the contingency operator: something is contingent if and only if it is contingently contingent. (shrink)