Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable (...) to manipulation than “premise-based voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

Writing strategic documents is a major practice of many actors striving to see their educational ideas realised in the curriculum. In these documents, arguments are systematically developed to create the legitimacy of a new educational goal and competence to make claims about it. Through a qualitative analysis of the writing strategies used in these texts, I show how two of the main actors in the Czech educational discourse have developed a proof that a new educational goal is needed. I draw (...) on the connection of the relational approach in the sociology of education with Lyotard’s analytical semantics of instances in the event. The comparison of the writing strategies in the two documents reveals differences in the formation of a particular pattern of justification. In one case the texts function as a herald of pure reality, and in the other case as a messenger of other witnesses. This reveals different regimens of proof, although both of them were written as prescriptive directives – normative models of the educational world. (shrink)

In the following paragraphs, I will describe ten strategies through which we can show the weaknesses of every form of theism based on the "One God", while postulating that the Trinity is a good solution. This approach follows up on Swinburne’s claims about the existence of a priori and a posteriori proofs for the existence of the Trinity (his proofs are part of the sixth strategy). Clearly, these strategies are not “new”: they have been advocated by many thinkers in (...) the past and in the present. I merely revived them, and brought them together in a kind of cumulative reasoning: the strength of them arises when these strategies are considered together, showing that the Trinity is a reasonable hypothesis even though it is contradictory. The proposed strategies lead to the conclusion that there must exist in God something similar to what we call ‘real relations’ and ‘multiplicity’; and in order for God to be relational, there must exist in Him some “distincts” that relate to one another. This is postulated by philosophical reasoning, not just by Revelation, and regardless of the choice to support a process metaphysics. As Trinitarian theology contains the mystery of eternal generation, the strategies do account for the fact that in philosophy we contemplate the mystery of eternal self-distinction and of all the other ‘self-actions’ of the One. The eternal generation remains mysterious, but it is the idea that best helps us describe how God is (One and Triune) and how he creates the world. God must be Triune in every theistic system. The One God is, as One, also Triune. The Unity-Trinity of the Principle is the only apophatic point that we can reach from many quarters. Once autonomous paths of reason have established that God is a Person and Persons, One-Multiple, Creator (communicated), Free, Relational and Infinite possibility, it therefore emerges that our most reliable hypothesis is that of the Trinitarian God. (shrink)

Gentzen’s approach by transfinite induction and that of intuitionist Heyting arithmetic to completeness and the self-foundation of mathematics are compared and opposed to the Gödel incompleteness results as to Peano arithmetic. Quantum mechanics involves infinity by Hilbert space, but it is finitist as any experimental science. The absence of hidden variables in it interpretable as its completeness should resurrect Hilbert’s finitism at the cost of relevant modification of the latter already hinted by intuitionism and Gentzen’s approaches for completeness. This paper (...) investigates both conditions and philosophical background necessary for that modification. The main conclusion is that the concept of infinity as underlying contemporary mathematics cannot be reduced to a single Peano arithmetic, but to at least two ones independent of each other. Intuitionism, quantum mechanics, and Gentzen’s approaches to completeness an even Hilbert’s finitism can be unified from that viewpoint. Mathematics may found itself by a way of finitism complemented by choice. The concept of information as the quantity of choices underlies that viewpoint. Quantum mechanics interpretable in terms of information and quantum information is inseparable from mathematics and its foundation. (shrink)

We develop a reading of Moore’s “Proof of an External World” that emphasizes the connections between this paper and Moore’s earlier concerns and strategies. Our reading has the benefit of explaining why the claims that Moore advances in “Proof of an External World” would have been of interest to him, and avoids attributing to him arguments that are either trivial or wildly unsuccessful. Part of the evidence for our view comes from unpublished drafts which, we believe, contain important clues concerning (...) Moore’s aims and intent. While our approach to PEW may be classified alongside other broadly "metaphysical" readings, we believe that a proper recognition of the continuity in Moore’s philosophical concerns and strategies across his philosophical career shows that the customary distinction between "epistemological" and "metaphysical" interpretative approaches to PEW is at best superficial. (shrink)

The widely discussed "discursive dilemma" shows that majority voting in a group of individuals on logically connected propositions may produce irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds a given threshold, where different thresholds may be used for different propositions. After characterizing quota rules, we prove necessary and sufficient conditions on the required thresholds for various collective rationality requirements. We also consider sequential (...) quota rules, which ensure collective rationality by adjudicating propositions sequentially and letting earlier judgments constrain later ones. Sequential rules may be path-dependent and strategically manipulable. We characterize path-independence and prove its essential equivalence to strategy-proofness. Our results shed light on the rationality of simple-, super-, and sub-majoritarian decision-making. (shrink)

A probability aggregation rule assigns to each profile of probability functions across a group of individuals (representing their individual probability assignments to some propositions) a collective probability function (representing the group's probability assignment). The rule is “non-manipulable” if no group member can manipulate the collective probability for any proposition in the direction of his or her own probability by misrepresenting his or her probability function (“strategic voting”). We show that, except in trivial cases, no probability aggregation rule satisfying two mild (...) conditions (non-dictatorship and consensus preservation) is non-manipulable. (shrink)

A Mathematical Review by John Corcoran, SUNY/Buffalo -/- Macbeth, Danielle Diagrammatic reasoning in Frege's Begriffsschrift. Synthese 186 (2012), no. 1, 289–314. ABSTRACT This review begins with two quotations from the paper: its abstract and the first paragraph of the conclusion. The point of the quotations is to make clear by the “give-them-enough-rope” strategy how murky, incompetent, and badly written the paper is. I know I am asking a lot, but I have to ask you to read the quoted passages—aloud (...) if possible. Don’t miss the silly attempt to recycle Kant’s quip “Concepts without intuitions are empty; intuitions without concepts are blind”. What the paper was aiming at includes the absurdity: “Proofs without definitions are empty; definitions without proofs are, if not blind, then dumb.” But the author even bollixed this. The editor didn’t even notice. The copy-editor missed it. And the author’s proof-reading did not catch it. In order not to torment you I will quote the sentence as it appears: “In a slogan: proofs without definitions are empty, merely the aimless manipulation of signs according to rules; and definitions without proofs are, if no blind, then dumb.”[sic] The rest of my review discusses the paper’s astounding misattribution to contemporary logicians of the information-theoretic approach. This approach was cruelly trashed by Quine in his 1970 Philosophy of Logic, and thereafter ignored by every text I know of. The paper under review attributes generally to modern philosophers and logicians views that were never espoused by any of the prominent logicians—such as Hilbert, Gödel, Tarski, Church, and Quine—apparently in an attempt to distance them from Frege: the focus of the article. On page 310 we find the following paragraph. “In our logics it is assumed that inference potential is given by truth-conditions. Hence, we think, deduction can be nothing more than a matter of making explicit information that is already contained in one’s premises. If the deduction is valid then the information contained in the conclusion must be contained already in the premises; if that information is not contained already in the premises […], then the argument cannot be valid.” Although the paper is meticulous in citing supporting literature for less questionable points, no references are given for this. In fact, the view that deduction is the making explicit of information that is only implicit in premises has not been espoused by any standard symbolic logic books. It has only recently been articulated by a small number of philosophical logicians from a younger generation, for example, in the prize-winning essay by J. Sagüillo, Methodological practice and complementary concepts of logical consequence: Tarski’s model-theoretic consequence and Corcoran’s information-theoretic consequence, History and Philosophy of Logic, 30 (2009), pp. 21–48. The paper omits definitions of key terms including ‘ampliative’, ‘explicatory’, ‘inference potential’, ‘truth-condition’, and ‘information’. The definition of prime number on page 292 is as follows: “To say that a number is prime is to say that it is not divisible without remainder by another number”. This would make one be the only prime number. The paper being reviewed had the benefit of two anonymous referees who contributed “very helpful comments on an earlier draft”. Could these anonymous referees have read the paper? -/- J. Corcoran, U of Buffalo, SUNY -/- PS By the way, if anyone has a paper that has been turned down by other journals, any journal that would publish something like this might be worth trying. (shrink)

Developing a suggestion of Wittgenstein, I provide an account of truth tables as formulas of a formal language. I define the syntax and semantics of TPL (the language of Tabular Propositional Logic), and develop its proof theory. Single formulas of TPL, and finite groups of formulas with the same top row and TF matrix (depiction of possible valuations), are able to serve as their own proofs with respect to metalogical properties of interest. The situation is different, however, for groups of (...) formulas whose top rows differ. For them I provide (i) a tree-style system of ‘row tree proofs’, which is shown to be sound and complete, and (ii) an alternative, re-writing strategy. (shrink)

The paper studies a cluster of systems for fully disquotational truth based on the restriction of initial sequents. Unlike well-known alternative approaches, such systems display both a simple and intuitive model theory and remarkable proof-theoretic properties. We start by showing that, due to a strong form of invertibility of the truth rules, cut is eliminable in the systems via a standard strategy supplemented by a suitable measure of the number of applications of truth rules to formulas in derivations. Next, (...) we notice that cut remains eliminable when suitable arithmetical axioms are added to the system. Finally, we establish a direct link between cut-free derivability in infinitary formulations of the systems considered and fixed-point semantics. Noticeably, unlike what happens with other background logics, such links are established without imposing any restriction to the premisses of the truth rules. (shrink)

This paper describes a decision procedure for disjunctions of conjunctions of anti-prenex normal forms of pure first-order logic (FOLDNFs) that do not contain V within the scope of quantifiers. The disjuncts of these FOLDNFs are equivalent to prenex normal forms whose quantifier-free parts are conjunctions of atomic and negated atomic formulae (= Herbrand formulae). In contrast to the usual algorithms for Herbrand formulae, neither skolemization nor unification algorithms with function symbols are applied. Instead, a procedure is described that rests on (...) nothing but equivalence transformations within pure first-order logic (FOL). This procedure involves the application of a calculus for negative normal forms (the NNF-calculus) with A -||- A & A (= &I) as the sole rule that increases the complexity of given FOLDNFs. The described algorithm illustrates how, in the case of Herbrand formulae, decision problems can be solved through a systematic search for proofs that reduce the number of applications of the rule &I to a minimum in the NNF-calculus. In the case of Herbrand formulae, it is even possible to entirely abstain from applying &I. Finally, it is shown how the described procedure can be used within an optimized general search for proofs of contradiction and what kind of questions arise for a &I-minimal proof strategy in the case of a general search for proofs of contradiction. (shrink)

Research suggests that interventions involving extensive training or counterconditioning can reduce implicit prejudice and stereotyping, and even susceptibility to stereotype threat. This research is widely cited as providing an “existence proof” that certain entrenched social attitudes are capable of change, but is summarily dismissed—by philosophers, psychologists, and activists alike—as lacking direct, practical import for the broader struggle against prejudice, discrimination, and inequality. Criticisms of these “debiasing” procedures fall into three categories: concerns about empirical efficacy, about practical feasibility, and about the (...) failure to appreciate the underlying structural-institutional nature of discrimination. I reply to these criticisms of debiasing, and argue that a comprehensive strategy for combating prejudice and discrimination should include a central role for training our biases away. (shrink)

This book tells the story of modern ethics, namely the story of a discourse that, after the Renaissance, went through a methodological revolution giving birth to Grotius’s and Pufendorf’s new science of natural law, leaving room for two centuries of explorations of the possible developments and implications of this new paradigm, up to the crisis of the Eighties of the eighteenth century, a crisis that carried a kind of mitosis, the act of birth of both basic paradigms of the two (...) following centuries: Kantian ethics and utilitarianism. The new science of natural law carried a fresh start for ethics, resulting from a mixture of the Old and the New. It was, as suggested by Schneewind, an attempt at rescuing the content of Scholastic and Stoic doctrines on a new methodological basis. The former was the claim of existence of objective and universal moral laws; the latter was the self-aware attempt at justifying a minimal kernel of such laws facing skeptical doubt. What Bentham and Kant did was precisely carrying this strategy further on, even if restructuring it each of them around one out of two alternative basic claims. The nineteenth- and twentieth-century critics of the Enlightenment attacked both not on their alleged failure in carrying out their own projects, but precisely on having adopted Grotius’s and Pufendorf’s project. What counter-enlightenment has been unable to spell out is which alternative project could be carried out facing the modern condition of pluralism, while on the contrary, if we takes a closer look at developments in twentieth-century ethics or at on-going discussions on practical issues, we might feel inclined to believe that Grotius’s and Pufendorf’s project is as up-to-date as ever. -/- Table of Contents -/- Preface I. Fathers of the Reformation and Schoolmen 1.1. Luther: passive justice and the good deeds; 1.2. Calvin: voluntarism and predestination; 1.3. Baroque Scholasticism; 1.4. Casuistry and Institutiones morales -/- II Neo-Platonists, neo-Stoics, neo-Sceptics 2.1. Aristotelian, neo-Platonic, neo-Epicurean and neo-Cynic Humanists; 2.2. Oeconomica and the art of living; 2.3. Neo-Stoics; 2.4. Neo-Sceptics; 2.5. Moralistic literature -/- III Neo-Augustinians 3.l. The Jansenists on natura lapsa, sufficient grace, pure love; 3.2. Nicole on the impossibility of self-knowledge; 3.3. Nicole on self-love and charity; 3.4. Nicole against civic virtue, for Christian civility; 3.5. Malebranche on general laws and necessary evil; 3.6. Malebranche on Neo-Augustinianism and Platonism. -/- IV Grotius, Pufendorf and the new moral science 4.1. Grotius against Aristotle and the sceptics; 4.2. Mersenne and Gassendi; 4.3. Descartes on ethics as the last branch of philosophy’s tree; 4.4. Hobbes on scepticism and the new moral science; 4.5. Spinoza on the new moral science as a descriptive science;4.6. Locke on voluntarism and probabilism; 4.7. Pufendorf on natural law as an exact science; 4.8. Pufendorf on physical and moral entities; 10. Pufendorf on self-preservation -/- V The empiricist version of the new moral science: from Cumberland to Paley 5.1. Cumberland against Hobbesian voluntarism; 5.2. Cumberland and theological consequentialism; 5.3. Cumberland on universal benevolence and self-love; 5.4. Shaftesbury on the moral sense; 5.5. Hutcheson on natural law and moral faculties; 5.6. Gay, Brown, Paley and theological consequentialism. -/- VI The rationalist version of the new moral science: from Cudworth to Price 6.1. The Cambridge Platonists; 6.2. Shaftesbury on the moral sense; 6.3. Butler and a third way between voluntarism and scepticism; 6.4. Price and the rational character of moral truths; -/- VII Leibniz’s compromise between the new moral science and Aristotelianism 1.Leibniz against voluntarism; 2.Leibniz against the division between the physical and the moral good; 3.Leibniz on la place d’autrui and theological consequentialism; 4.Thomasius, Wolff, Crusius -/- VIII French eighteenth-century philosophers without the new moral science 8.1. The genealogy of our ideas of virtue and vice; 8.2. Maupertuis and moral arithmetic 8.3. The philosophes and the harmony of interests; 8.4. Rousseau on corruption, self-love, and virtue; 8.5. Sade on the merits of vice -/- IX Experimental moral science: Hume and Adam Smith 9.1. Mandeville’s paradox; 9.2. Hutcheson on the law of nature and moral faculties; 9.3. Hume on experimental moral philosophy and the intermediate principles; 9.4. Hume’s Law; 9.5. Hume on the fellow-feeling; 9.6. Hume on natural and artificial virtues and disinterested pleasure for utility; 9.7. Adam Smith’s anti-realist metaethics; 9.8. Adam Smith on self-deception and the paradox of happiness; 9.9. Adam Smith on sympathy and the impartial spectator; 9.10. Adam Smith on the twofold criterion for moral judgement and its paradox; 9.11. Reid on the refutation of scepticism and the self-evidence of duty -/- X Kantian ethics 10.1. Kantian metaethics: moral epistemology; 10.2. Kantian metaethics: moral ontology; 10.3. Kantian metaethics: moral psychology; 10.4. Kantian normative ethics; 10.5. Kant on the impracticability of applied ethics; 10.6. Kantian moral anthropology; 10.7. Civilisation and moralisation; 10.8. Theology on a moral basis and the origins of evil; 10.9. Fichte and the transformation of theoretical philosophy into practical philosophy XI Bentham and utilitarianism 11.1. Bentham’s linguistic theory; 11.2. Bentham’s moral ontology, psychology, and theory of action; 11.3. The principle of greatest happiness; 11.4. The critique of religious ethics; 11.5. The new morality; 11.6. Interest and duty; 11.7. Virtues; 11.8. Private ethics and legislation -/- XII Followers of the Enlightenment: liberal Judaism and Liberal Theology 12.1. Mendelssohn; 12.2. Salomon Maimon; 12.3. Haskalā and liberal Judaism; 12.4. Liberal Theology. -/- XIII Counter-Enlighteners 13.1.Romanticism and the fulfilment of individuality as the Summum Bonum; 13.2. Hegel on history as the making of liberty; 13.3. Hegel on the unhappy consciousness and the beautiful soul; 13.4. Hegel on Morality and Sittlichkeit; 13.5. Marx on ideology, alienation, and praxis; 13.6. Schopenhauer on compassion; 13.7. Kierkegaard on faith beyond ethics. -/- XIV Followers of the Enlightenment: intuitionists and utilitarian 14.1 Whewell‘s criticism of utilitarianism; 14.2 Whewell on morality and the philosophy of morality; 14.3 Whewell on the Supreme Norm; 14.4 Whewell on the conflict between duties; 14.5 Mill and the proof of the principle of utility; 14.6 Mill’s eudemonistic utilitarianism; 14.7 Mill on rules -/- XV Followers of the Enlightenment: neo-Kantians and positivists 15.1. French spiritualism; 15.2. Neo-Kantians: the Marburg school; 15.3. Neo-Kantians: the Marburg school; 15.4. Comte’s positivism and the invention of altruism; 15.5. Social Darwinism; 15.6. Wundt and an ethic of humankind -/- XVI Post-enlighteners: Sidgwick 16.1. Criticism of intuitionism; 16.2. On ethical egoism; 16.3. Criticism of utilitarianism -/- XVII Post-enlighteners: Durkheim 17.1. Sociology as physics of customs; 17.2. Morality as physics of customs and as practical science; 17.3. On Kantian ethics and utilitarianism; 17.4. The variability of moralities;17.5. Social solidarity as end and justification of morality; 17.6. Secular morality as “sociodicy”; XVIII Post-enlighteners: Nietzsche 18.1. On the Dionysian; 18.2. On the deconstruction of the world of values 18.3 On the twofold genealogy of moralities; 18.4. On ascetics and nihilism; 18.5. Normative ethics of self-fulfilment -/- Bibliography / Index of names / Index of concepts -/- . (shrink)

An old and well-known objection to non-classical logics is that they are too weak; in particular, they cannot prove a number of important mathematical results. A promising strategy to deal with this objection consists in proving so-called recapture results. Roughly, these results show that classical logic can be used in mathematics and other unproblematic contexts. However, the strategy faces some potential problems. First, typical recapture results are formulated in a purely logical language, and do not generalize nicely to (...) languages containing the kind of vocabulary that usually motivates non-classical theories—for example, a language containing a naïve truth predicate. Second, proofs of recapture results typically employ classical principles that are not valid in the targeted non-classical system; hence, non-classical theorists do not seem entitled to those results. In this paper, we analyze these problems and provide solutions on behalf of non-classical theorists. To address the first problem, we provide a novel kind of recapture result, which generalizes nicely to a truth-theoretic language. As for the second problem, we argue that it relies on an ambiguity and that, once the ambiguity is removed, there are no reasons to think that non-classical logicians are not entitled to their recapture results. (shrink)

Epistemic decision theory produces arguments with both normative and mathematical premises. I begin by arguing that philosophers should care about whether the mathematical premises (1) are true, (2) are strong, and (3) admit simple proofs. I then discuss a theorem that Briggs and Pettigrew (2020) use as a premise in a novel accuracy-dominance argument for conditionalization. I argue that the theorem and its proof can be improved in a number of ways. First, I present a counterexample that shows that one (...) of the theorem’s claims is false. As a result of this, Briggs and Pettigrew’s argument for conditionalization is unsound. I go on to explore how a sound accuracy-dominance argument for conditionalization might be recovered. In the course of doing this, I prove two new theorems that correct and strengthen the result reported by Briggs and Pettigrew. I show how my results can be combined with various normative premises to produce sound arguments for conditionalization. I also show that my results can be used to support normative conclusions that are stronger than the one that Briggs and Pettigrew’s argument supports. Finally, I show that Briggs and Pettigrew’s proofs can be simplified considerably. (shrink)

The emphasis on the limitations of objectivity, in specific guises and networks, has been a continuing theme of contemporary analytic philosophy for the past few decades. The popular sport of baiting feminist philosophers — into pointing to what's left out of objective knowledge, or into describing what methods, exactly, they would offer to replace the powerful objective methods grounding scientific knowledge — embodies a blatant double standard which has the effect of constantly putting feminist epistemologists on the defensive, on the (...) fringes, on the run.This strategy can only work if objectivity is transparent, simple, stable, and clear in its meaning. It most certainly is not. In fact, taking objectivity as a sort of beautiful primitive, self-evident in its value, and all-powerful in its revelatory power, requires careless philosophy, and the best workers in metaphysics, epistemology, and philosophy of science have made reworked definitions of objectivity absolutely central to their own projects. In fact, classic feminist concerns with exploring the impact of sex and gender on knowledge, understanding, and other relations between human beings and the rest of the world fall squarely within the sort of human and social settings thatare already considered central in most current analytic metaphysics, epistemology, and philosophy of science. I argue that the burden of proof is clearly on those who wish toreject the centrality and relevance of sex and gender to our most fundamental philosophical work on knowledge and reality. (shrink)

Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation into conditional connectives may (...) show that there is no conditional operator that has all the properties native speaker intuitions suggest if has. Indicative conditionals have famously been the source of one such tension, ever since the triviality proofs of both Lewis (1976) and Gibbard (1981) established conclusions which are in prima facie tension with ordinary judgments about natural language indicative conditionals. In a recent series of papers, Branden Fitelson has strengthened both triviality results (Fitelson 2013, 2015, 2016), revealing a common culprit: a logical schema known as IMPORT-EXPORT. Fitelson’s results focus the tension between the logical results and ordinary judgments, since IMPORT-EXPORT seems to be supported by intuitions about natural language. In this paper, we argue that the intuitions which have been taken to support IMPORT-EXPORT are really evidence for a closely related, but subtly different, principle. We show that the two principles are independent by showing how, given a standard assumption about the conditional operator in the formal language in which IMPORT-EXPORT is stated, many existing theories of indicative conditionals validate one, but not the other. Moreover, we argue that once we clearly distinguish these principles, we can use propositional anaphora to show that IMPORT-EXPORT is in fact not valid for natural language indicative conditionals (given this assumption about the formal conditional operator). This gives us a principled and independently motivated way of rejecting a crucial premise in many triviality results, while still making sense of the speaker intuitions which appeared to motivate that premise. We suggest that this strategy has broad application and an important lesson: in theorizing about the logic of natural language, we must pay careful attention to the translation between the formal languages in which logical results are typically proved, and natural languages which are the subject matter of semantic theory. (shrink)

Monsters lurk within mathematical as well as literary haunts. I propose to trace some pathways between these two monstrous habitats. I start from Jeffrey Jerome Cohen’s influential account of monster culture and explore how well mathematical monsters fit each of his seven theses. The mathematical monsters I discuss are drawn primarily from three distinct but overlapping domains. Firstly, late nineteenth-century mathematicians made numerous unsettling discoveries that threatened their understanding of their own discipline and challenged their intuitions. The great French mathematician (...) Henri Poincaré characterised these anomalies as ‘monsters’, a name that stuck. Secondly, the twentieth-century philosopher Imre Lakatos composed a seminal work on the nature of mathematical proof, in which monsters play a conspicuous role. Lakatos coined such terms as ‘monster-barring’ and ‘monster-adjusting’ to describe strategies for dealing with entities whose properties seem to falsify a conjecture. Thirdly, and most recently, mathematicians dubbed the largest of the sporadic groups ‘the Monster’, because of its vast size and uncanny properties, and because its existence was suspected long before it could be confirmed. (shrink)

The first learning game to be developed to help students to develop and hone skills in constructing proofs in both the propositional and first-order predicate calculi. It comprises an autotelic (self-motivating) learning approach to assist students in developing skills and strategies of proof in the propositional and predicate calculus. The text of VALIDITY consists of a general introduction that describes earlier studies made of autotelic learning games, paying particular attention to work done at the Law School of Yale University, called (...) the ALL Project (Accelerated Learning of Logic). Following the introduction, the game of VALIDITY is described, first with reference to the propositional calculus, and then in connection with the first-order predicate calculus with identity. Sections in the text are devoted to discussions of the various rules of derivation employed in both calculi. Three appendices follow the main text; these provide a catalogue of sequents and theorems that have been proved for the propositional calculus and for the predicate calculus, and include suggestions for the classroom use of VALIDITY in university-level courses in mathematical logic. (shrink)

A specific soul of the times appears to require a survey of brain research as a study of the psyche and conduct as most settled definition. Two significant developments have emerged freely, one in the core of the American Mental Affiliation itself with Division 5 as of late renamed Quantitative and Subjective Techniques, remembering the General public for Subjective Request for Brain research and the Diary of Subjective Brain research and the other in the European custom with The Yokohama Proclamation (...) for a Brain research as the Study of Person. Both expect an open pluralistic move in the direction of the Mind as "perplexing, abstract, significant, and strange" "no act of request is precluded deduced; numerous objectives of request are delivered conceivable and different pathways might guarantee an arranged authenticity Following this contention, certain implied transcendentalism comprising of a dualistic cosmology with criticism from the regular logical strategy would be at the premise of the persevering dualism in brain research. It is perceived that the distinguishing proof of brain research as an inherent science was likely due more to its esteem than to its own intricacy as suggested by its review. The time has come to reconceive brain research as a human science (social, conduct), without a "complex". To do as such, an ontological inquiry ought to be raised concerning the spot of brain research in a pluralistic metaphysics, not dualistic or monistic. (shrink)

Some recent defenses of the 'ought' implies 'can' (OIC) principle try to derive that principle from uncontroversial claims about reasons for action. Reasons for action, it's said, are reasons only for 'potential' actions, which are actions that an agent can perform. Given that 'ought' implies 'reasons', it seems we have our proof of OIC. In this paper, I argue that this latest strategy for defending OIC fails.

It is commonly held that Kant ventured to derive morality from freedom in Groundwork III. It is also believed that he reversed this strategy in the second Critique, attempting to derive freedom from morality instead. In this paper, I set out to challenge these familiar assumptions: Kant’s argument in Groundwork III rests on a moral conception of the intelligible world, one that plays a similar role as the ‘fact of reason’ in the second Critique. Accordingly, I argue, there is (...) no reversal in the proof-structure of Kant’s two works. (shrink)

In the first half, I suggest that Kant’s conception of our moral life goes through a significant shift after 1793, with reverberations in his eschatology. The earlier account, based on the postulate of immortality, describes our moral life as an endless pursuit of the highest good, but all this changes in the later account, and I point out three possible reasons for this change of heart. In the second half, I explore how the considerations Kant brings up to argue for (...) his accounts can inform our process of formulating positions with respect to the afterlife. I argue that, in the absence of a convincing theoretical proof for or against the afterlife as well as apodictically certain knowledge of how demanding the moral law is, the Kantian strategy would be to ask which account of our moral life delivers the kind of contentment that can sustain our moral resolve. I also point out a way theists might be able to find contentment despite their moral failures by imagining God’s moral kenosis. (shrink)

Presuppositions are at the same time a crucial and almost neglected dimension of arguments and fallacies. Arguments involve different types of presuppositions, which can be used for manipulative purposes in distinct ways. However, what are presuppositions? What is their dialectical function? Why and how can they be dangerous? This paper intends to address these questions by developing the pragmatic approaches to presupposition from a dialectical perspective. The use of presuppositions will be analyzed in terms of presumptive conclusions concerning the interlocutor’s (...) acceptance of a proposition, which can be assessed as reasonable or unacceptable. Their dialectical function is described in terms of dark side commitments attributed to a collective "voice" representing what is commonly shared. For this reason, they count as attempts to include the presupposed contents into the hearer’s commitment store, which in some circumstances can reverse the burden of proof. The different manipulative strategies grounded on controversial presuppositions will be examined by showing the distinct roles that the latter play and the relationship between the degrees of presuppositional implicitness and the speaker’s burden of retraction. (shrink)

A sorites argument is a symptom of the vagueness of the predicate with which it is constructed. A vague predicate admits of at least one dimension of variation (and typically more than one) in its intended range along which we are at a loss when to say the predicate ceases to apply, though we start out confident that it does. It is this feature of them that the sorites arguments exploit. Exactly how is part of the subject of this paper. (...) The majority of philosophers writing on vagueness take it to be a kind of semantic phenomenon. If we are right, they are correct in this assumption, which is surely the default position, but they have not so far provided a satisfactory account of the implications of this or a satisfactory diagnosis of the sorites arguments. Other philosophers have urged more exotic responses, which range from the view that the fault lies not in our language, but in the world, which they propose to be populated with vague objects which our semantics precisely reflects, to the view that the world and language are both perfectly in order, but that the fault lies with our knowledge of the properties of the words we use (epistemicism). In contrast to the exotica to which some philosophers have found themselves driven in an attempt to respond to the sorites puzzles, we undertake a defense of the commonsense view that vague terms are semantically vague. Our strategy is to take fresh look at the phenomenon of vagueness. Rather than attempting to adjudicate between different extant theories, we begin with certain pre-theoretic intuitions about vague terms, and a default position on classical logic. The aim is to see whether (i) a natural story can be told which will explain the vagueness phenomenon and the puzzling nature of soritical arguments, and, in the course of this, to see whether (ii) there arises any compelling pressure to give up the natural stance. We conclude that there is a simple and natural story to be told, and we tell it, and that there is no good reason to abandon our intuitively compelling starting point. The importance of the strategy lies in its dialectical structure. Not all positions on vagueness are on a par. Some are so incredible that even their defenders think of them as positions of last resort, positions to which we must be driven by the power of philosophical argument. We aim to show that there is no pressure to adopt these incredible positions, obviating the need to respond to them directly. If we are right, semantic vagueness is neither surprising, nor threatening. It provides no reason to suppose that the logic of natural languages is not classical or to give up any independently plausible principle of bivalence. Properly understood, it provides us with a satisfying diagnosis of the sorites argumentation. It would be rash to claim to have any completely novel view about a topic so well worked as vagueness. But we believe that the subject, though ancient, still retains its power to inform and challenge us. In particular, we will argue that taking seriously the central phenomenon of predicate vagueness—the “boundarylessness” of vague predicates—on the commonsense assumption that vagueness is semantic, leads ineluctably to the view that no sentences containing vague expressions (henceforth ‘vague sentences’) are truth-evaluable. This runs counter to much of the literature on vagueness, which commonly assumes that, though some applications of vague predicates to objects fail to be truth-evaluable, in clear positive and negative cases vague sentences are unproblematically true or false. It is clarity on this, and related points, that removes the puzzles associated with vagueness, and helps us to a satisfying diagnosis of why the sorites arguments both seem compelling and yet so obviously a bit of trickery. We give a proof that semantically vague predicates neither apply nor fail-to-apply to anything, and that consequently it is a mistake to diagnose sorites arguments, as is commonly done, by attempting to locate in them a false premise. Sorites arguments are not sound, but not unsound either. We offer an explanation of their appeal, and defend our position against a variety of worries that might arise about it. The plan of the paper is as follows. We first introduce an important distinction in terms of which we characterize what has gone wrong with vague predicates. We characterize what we believe to be our natural starting point in thinking about the phenomenon of vagueness, from which only a powerful argument should move us, and then trace out the consequences of accepting this starting point. We consider the charge that among the consequences of semantic vagueness are that we must give up classical logic and the principle of bivalence, which has figured prominently in arguments for epistemicism. We argue there are no such consequences of our view: neither the view that the logic of natural languages is classical, nor any plausible principle of bivalence, need be given up. Next, we offer a diagnosis of what has gone wrong in sorites arguments on the basis of our account. We then present an argument to show that our account must be accepted on pain of embracing (in one way or another) the epistemic view of “vagueness”, i.e., of denying that there are any semantically vague terms at all. Next, we discuss some worries that may arise about the intelligibility of our linguistic practices if our account is correct. We argue none of these worries should force us from our intuitive starting point. Finally, we cast a quick glance at other forms of semantic incompleteness. (shrink)

Eternalism is the view that the past, the present and the future exist simpliciter. A typical argument in favor of this view leans on the relativity of simultaneity. The ‘equally real with’ relation is assumed to be transitive between spacelike separated events connected by hyperplanes of simultaneity. This reasoning is in tension with the conventionality of simultaneity. Conventionality indicates that, even within a specific frame, simultaneity is based on the choice of the synchronization parameter. Hence the argument for eternalism is (...) compromised. This paper lays out alternative eternalist strategies which do not hinge on hyperplanes. While we lack a rigorous proof for eternalism, there are still cogent reasons to prefer eternalism over presentism. (shrink)

Part of the Elements Philosophy of Religion series, this short book focuses on the spiritual dimensions of life’s meaning as they have been discussed in the recent English and mainly analytic philosophical literature. The overarching philosophical question that this literature has addressed is about the extent to which, and respects in which, spiritual realities such as God or a soul would confer meaning on our lives. There have been four broad answers to the question, namely: God or a soul is (...) necessary for meaning in our lives; they are not necessary for it; one or both would enhance the meaning in our lives; and they would detract from it. These views have been largely advanced in chronological order through the history of Western philosophy, with the view that life would be meaningless without God and a soul having been most prominent in the medieval period, the rejection of this claim having arisen in the modern era, and then sophisticated positions about enhancement or reduction having appeared in earnest only in the past 20 years. This book addresses all four positions, paying particular attention to the more recent views. Beyond familiarizing readers with these positions, it presents prima facie objections to them, points out gaps in research agendas, and suggests argumentative strategies that merit development. (shrink)

The implicit dimension of enthymemes is investigated from a pragmatic perspective to show why a premise can be left unexpressed, and how it can be used strategically. The relationship between the implicit act of taking for granted and the pattern of presumptive reasoning is shown to be the cornerstone of kairos and the fallacy of straw man. By taking a proposition for granted, the speaker shifts the burden of proving its un-acceptability onto the hearer. The resemblance of the tacit premise (...) with what is commonly acceptable or has been actually stated can be used as a rhetorical strategy. (shrink)

In this paper, I shall evaluate a strategy recently used to try to demonstrate the impossibility of behaviorally undetectable spectrum inversion. After showing that the impossibility proof proves too much, I shall identify where it goes wrong. In turn, I shall explain why someone attracted to functionalist and representationalist assumptions might rightly remain agnostic about the possibility of inversion.

When we use a word, we face a crucial epistemic gap: we ground our move on the fact that our interlocutor knows the meaning of the word we used, and therefore he can interpret our dialogical intention. However, how is it possible to know the other’s mind? Hamblin explained this dialogical problem advancing the idea of dialectical meaning: on his view, the use of a word is based on a set of presumptions. Building on this approach, the use of a (...) word in a dialogue can be analyzed in terms of presumptive reasoning, while the manipulative strategies based on slanted or loaded terms or redefinitions can be conceived as forms of conflicts of presumptions. A presumptive approach to meaning can also ground different dialectical strategies to solve misunderstanding or definitional disagreements, or tactics to undermine the interlocutor’s arguments by advancing charges of equivocation. (shrink)

In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions, and equivalence classes of coextensional properties. Part I focuses on Cantor’s theorem, its proof, how it can be used to manufacture (...) paradoxes, Frege’s diagnosis of the core difficulty, and several broad categories of strategies for offering solutions to these paradoxes. (shrink)

Development has been themain strategy in addressing the problemof sustainability since at least the mid-1980s. The results of this strategy have been mixed, if not disappointing. In their objections to this approach, critics frequently invoke constraints imposed by physical reality of which the most important one is entropy production. They question the belief that technological innovations are capable of solving the problem of sustainability. Is development the right response to this problem and is the current course capable of (...) attaining sustainability? The article examines closely and critiques the principal theoretical objection to sustainable development that emphasizes physical constraints, and more specifically entropy production. It also offers a critique of the current approach to sustainable development. The article advocates a systems approach as a way to anchor a broad consensus in the ongoing sustainability debates. (shrink)

n the spatialized Prisoner’s Dilemma, players compete against their immediate neighbors and adopt a neighbor’s strategy should it prove locally superior. Fields of strategies evolve in the manner of cellular automata (Nowak and May, 1993; Mar and St. Denis, 1993a,b; Grim 1995, 1996). Often a question arises as to what the eventual outcome of an initial spatial configuration of strategies will be: Will a single strategy prove triumphant in the sense of progressively conquering more and more territory without (...) opposition, or will an equilibrium of some small number of strategies emerge? Here it is shown, for finite configurations of Prisoner’s Dilemma strategies embedded in a given infinite background, that such questions are formally undecidable: there is no algorithm or effective procedure which, given a specification of a finite configuration, will in all cases tell us whether that configuration will or will not result in progressive conquest by a single strategy when embedded in the given field. The proof introduces undecidability into decision theory in three steps: by (1) outlining a class of abstract machines with familiar undecidability results, by (2) modelling these machines within a particular family of cellular automata, carrying over undecidability results for these, and finally by (3) showing that spatial configurationns of Prisoner’s Dilemma strategies will take the form of such cellular automata. (shrink)

The interpretation and the indirect reporting of a speaker’s communicative intentions lie at the crossroad between pragmatics, argumentation theory, and forensic linguistics. Since the leading case Masson v. New Yorker Magazine, Inc., in the United States the legal problem of determining the truth of a quotation is essentially equated with the correctness of its indirect reporting, i.e. the representation of the speaker’s intentions. For this reason, indirect reports are treated as interpretations of what the speaker intends to communicate. Theoretical considerations, (...) aimed at establishing the pragmatic meaning of an utterance and differentiating between presumptive and non-presumptive interpretation, are thus interwoven with the practical legal need of distinguishing a correct indirect report from an indirect one or a misquotation. An incorrect report or a misquotation has the dialectical effect of attributing to the misquoted party commitments that he never held, which the latter needs to rebut. This shifting of the burden of persuasion can be increased by using strategically the conflict between the presumptive interpretation of an utterance and the non-presumptive one, i.e. the different types of pragmatic ambiguity. When an interpreter is confronted with an utterance taken out of its dialogical context, his interpretative process is not guided by the actual context or intention, but rather the most frequent or prototypical dialogical setting or the most typical individual purpose that it could have served to achieve. This presumptive reconstruction can be used to provide a prima facie case that the other party needs to reject. The stronger the interpretative presumptions a speaker needs to rebut, the more effective the misquotation strategy. The conflict between the systematic and the presumptive process of interpretation can be represented as an argumentative mechanism of reconstruction of the individual intention, which allows one to assess the reasonableness of the interpretative reasoning. (shrink)

In this dissertation we present proof systems for several modal logics. These proof systems are based on analytic (or semantic) tableaux. -/- Modal logics are logics for reasoning about possibility, knowledge, beliefs, preferences, and other modalities. Their semantics are almost always based on Saul Kripke’s possible world semantics. In Kripke semantics, models are represented by relational structures or, equivalently, labeled graphs. Syntactic formulas that express statements about knowledge and other modalities are evaluated in terms of such models. -/- This dissertation (...) focuses on modal logics with dynamic operators for public announcements, belief revision, preference upgrades, and so on. These operators are defined in terms of mathematical operations on Kripke models. Thus, for example, a belief revision operator in the syntax would correspond to a belief revision operation on models. -/- The ‘dynamic’ semantics of dynamic modal logics are a clever way of extending languages without compromising on intuitiveness. We present ‘dynamic’ tableau proof systems for these dynamic semantics, with the express aim to make them conceptually simple, easy to use, modular, and extensible. This we do by reflecting the semantics as closely as possible in the components of our tableau system. For instance, dynamic operations on Kripke models have counterpart dynamic relations between tableaux. -/- Soundness, completeness, and decidability are three of the most important properties that a proof system may have. A proof system is sound if and only if any formula for which a proof exists, is true in every model. A proof system is complete if and only if for any formula that is true in all models, a proof exists. A proof system is decidable if and only if any formula can be proved to be a theorem or not a theorem in a finite number of steps. All proof systems in this dissertation are sound, complete, and decidable. -/- Part of our strategy to create modular tableau systems is to delay concerns over decidability until after soundness and completeness have been established. Decidability is attained through the operations of folding and through operations on ‘tableau cascades’, which are graphs of tableaux. -/- Finally, we provide a proof-of-concept implementation of our dynamic tableau system for public announcement logic in the Clojure programming language. (shrink)

According to the “paradox of knowability”, the moderate thesis that all truths are knowable – ... – implies the seemingly preposterous claim that all truths are actually known – ... –, i.e. that we are omniscient. If Fitch’s argument were successful, it would amount to a knockdown rebuttal of anti-realism by reductio. In the paper I defend the nowadays rather neglected strategy of intuitionistic revisionism. Employing only intuitionistically acceptable rules of inference, the conclusion of the argument is, firstly, not (...) ..., but .... Secondly, even if there were an intuitionistically acceptable proof of ..., i.e. an argument based on a different set of premises, the conclusion would have to be interpreted in accordance with Heyting semantics, and read in this way, the apparently preposterous conclusion would be true on conceptual grounds and acceptable even from a realist point of view. Fitch’s argument, understood as an immanent critique of verificationism, fails because in a debate dealing with the justification of deduction there can be no interpreted formal language on which realists and anti-realists could agree. Thus, the underlying problem is that a satisfactory solution to the “problem of shared content” is not available. I conclude with some remarks on the proposals by J. Salerno and N. Tennant to reconstruct certain arguments in the debate on anti-realism by establishing aporias. (shrink)

In the Treatise of Human Nature, David Hume mounts a spirited assault on the doctrine of the infinite divisibility of extension, and he defends in its place the contrary claim that extension is everywhere only finitely divisible. Despite this major departure from the more conventional conceptions of space embodied in traditional geometry, Hume does not endorse any radical reform of geometry. Instead Hume espouses a more conservative approach, claiming that geometry fails only “in this single point” – in its purported (...) proofs of infinite divisibility – while “all of its other arguments” remain intact. -/- In this paper, after laying out the prima facie case for Hume’s radical challenge to traditional geometry, I consider five strategies for blocking the arguments for infinite divisibility while conserving most of geometry. I show that each of these interpretive strategies suffers from serious substantive problems, and so none of them delivers an interpretation of Hume’s account that provides him with a way of blocking the geometric arguments for infinite divisibility while sustaining his geometric conservatism. (shrink)

For more than one decade, Andy Clark has defended the now-famous extended mind thesis, the idea that cognitive processes leak into the world. In this paper I analyse Clark’s theoretical justification for the thesis: explanatory simplicity. I argue that his way of justifying the thesis leads into contradiction, either at the level of propositional attitude ascriptions or at the theoretical level. I evaluate three possible strategies of dealing with this issue, concluding that they are all likely to fail and that (...) therefore, as regards explanatory simplicity, the burden of proof is on Clark’s side. The paper divides into two main sections: in “Simplicity and Coherence”, I define the two concepts that are important in this context (simplicity and explanatory coherence). In “How to Cope with Coherence”, these two concepts are applied to the central thought experiment, the Inga/Otto case. It will be shown that justifying the extended mind thesis by reference to simplicity may cause trouble, because ‘extended’ behavioural descriptions are likely to yield rather complicated explanations. (shrink)

My objections are: first, we may ask whether the achievement of The Wealth of Nations has been that of creating a new and more encompassing conceptual framework where already existing theoretical elements could be integrated and whether the growth of knowledge could have originated from a growth in the consistency of a theoretical framework which synthesized already existing individual elements; secondly, we may ask whether Smith's "tendentious" presentation of the positions of both predecessors and opponents might be some kind of (...) unavoidable sin and he might have been guilty of that sin because this was a price to be paid to his rhetorical strategy; thirdly, whether the fact that a text has been canonized at a certain moment in history for quite contingent reasons is no decisive proof of the intrinsic worth or lack of worth of the text in itself. (shrink)

The so called “elenctic” defense of the principle of non-contradiction in Metaphysics Γ4 will succed if only the opponent will say something. The strategy consists in showing that, in speaking, the opponent has al- ready accepted the principle. Given the structure of the argument, the only way to avoid begging the question is not to ask from the opponent any commitment exceeding the conditions of mere meanigfullness of speech. In particular, it is specially important to avoid any reliance on (...) Aristotelian essentialism. A reading which is in accordance with these requirements will hold that the core of the proof consists in showing that meaning something amounts to singling out a meaning. The mere aim of telling what is within from what is without the bounds imposed on speech of any complexity is enough to show that the speaker accepts the principle of non-contradiction. One is thereby not required to commit oneself to any particular description of reality. Nonetheless, the extention of this result to the conditions of predication will pave the way for the develop- ment of the science of being as being. (shrink)

There are at least two discussions about Pythagoreans in Aristotle’s works that can be related to paradigm, both in Book A of Metaphysics. In the first, Aristotle says that for Pythagoreans all the things are modeled after numbers (τὰ μὲν ἄλλα τοῖς ἀριθμοῖς ἐφαίνετο τὴν φύσιν ἀφωμοιῶσθαι πᾶσιν). (Met., A, 985b32-33) In the second, Aristotle tells us that Pythagoreans take ‘the first subject of which a given term would be predicable (ᾧ πρώτῳ ὑπάρξειεν ὁ λεχθεὶς ὃρος)’ as the substance of (...) the thing. His example is double and two: since two is the first thing of which double is predicated, double will be the substance of two. (Met., A, 987a22-25) 1) Forms as paradigms Some of the critiques of platonic Forms in Aristotle’s works are paradigm-oriented: they attack Plato’s theory on the basis that Platonians considered Forms as paradigms. The core of all Aristotle’s objections is that calling Forms paradigms is a mere poetical strategy and does not have any real effect. (Met., 991a20-22; M, 1079b24-26) We can recognize four reasons for Aristotle’s objections of forms as paradigms: a) To consider something as the paradigm of another thing to which it is like does not have any ontological effect: ‘For what it is that works, looking to the ideas? Anything can either be, or become, like another without being copied from it, so that whether Socrates exists or not a man might come to be like Socrates.’ (Met., A, 991a22-26; M, 1079b26-29) Therefore, paradigms are ontologically unnecessary: ‘It is quite unnecessary to set up a form as a paradigm … the begetter is adequate to the making of the product and the causing of the form in the matter.’ (Met., Z, 1034a2-5) Don’t these cases imply that Aristotle did have more the ontological necessity of paradigm in thought instead of its epistemological necessity? b) To consider Forms as paradigms means that a thing must have several paradigms; e.g. animal and too-footed and man will be paradigms of the same thing. (Met., A, 991a27-29; M, 1079b31-33) c) The theory that Forms are paradigms not only of sensible things but also of themselves makes the same thing both a paradigm and a copy (ἐικών). (Met., A, 991a29-b1; M, 1079b33-35) 2) Reasoning by paradigm Aristotle compares the arguments using paradigms to his own theory of syllogism: ‘We have an ‘example’ (παράδειγμα) when the major term is proved to belong to the middle by means of a term which resembles the third. It ought to be known that the middle belongs to the third term, and that the first belongs to that which resembles the third. For example, let A be evil, B making war against neighbors, C Athenians against Thebians, D Thebians against Phocians. If then we wish to prove that to fight against Thebians is an evil, we must assume that to fight against neighbors is an evil. Evidence of this is obtained from similar cases, e.g. that the war against the Phocians was an evil to Thebians. …Now it is clear that B belongs to C and to D (for both are cases of making war upon one’s neighbors) and that A belongs to D (for the war against the Phocians did not turn out well for the Thebians); but that A belongs to B will be proved through D.’ (PsA., B, 24, 66b38-69a11) An ‘example’ can also be made by several similar cases. (PrA., B, 24, 69a11-13) Aristotle notes (PrA., B, 24, 69a13-24) that reasoning by paradigm is ‘neither like reasoning from part to whole nor like reasoning from whole to part but is rather a reasoning from part to part, when both particulars are subordinate to the same term, and one of them is known.’ And it differs from induction in two ways: a) While induction uses all the particular cases to prove that the major term belongs to the middle, reasoning by paradigm does not draw its proof from all the particular cases. b) While induction does not apply the syllogistic conclusion to the minor term, reasoning by paradigm does make this application. (PrA., B, 24, 69a13-24) . (shrink)

Im Zentrum von Vallas Umgestaltung der Dialektik als rhetorischer Methode steht ein neues Verständnis von certum, das aus Quintilians Institutio oratoria stammt. Diesem Verständnis zufolge ist Gewissheit in dem begründet, was allgemein akzeptiert wird, nicht in dem, was wahr ist. Damit trennt Valla certum und verum. In den Dialecticae disputationes stellt er Dialektik nicht als eine logische oder philosophische Methode zum Beweis von Wahrheiten dar, sondern als Praxis Geständnisse herbeizuführen und als juristische Produktion konsensueller Gewissheiten. Auch in anderen Werken, etwa (...) den Elegantiae und seinem Kommentar zu Quintilians Institutio, verbindet er durchweg certum mit Konsens, insbesondere Konsens im Sinne der rhetorischen Strategie der status-Theorie. (shrink)

What It’s Like to Chill Out With Whom the Rest of the World Considers As The Most Ruthless Men: Ratko Mladic, Goran Hadzic and Radovan Karadzic (+) Confessions of a Female War Crimes Investigator By Jill Louise Starr NJ USA -/- Read My Entire Book Here (True Story) http://sites.google.com/site/thelawprojectscenternycoffices/what-it-s-like-to-chill-out-with-whom-th e-rest-of-the-world-considers-as-the-most-ruthless-men-ratko-mladic-goran-hadzic-and-radovan-karadzi c-confessions-of-a-female-war-crimes-investigator -/- Retrospectively, it was all so simple, natural and matter of fact being on a boat restaurant in Belgrade, sitting with, laughing, drinking a two hundred bottle of wine and chatting about (...) war and peace while Ratko Mladic held my hand. Mladic, a man considered the world’s most ruthless war criminal since Adolf Hitler, still at large and currently having a five million dollar bounty on his head for genocide by the international community. Yet there I was with my two best friends at the time, a former Serbian diplomat, his wife, and Ratko Mladic just chilling. There was no security, nothing you’d ordinarily expect in such circumstances. Referring to himself merely as, Sharko; this is the story of it all came about. Diplomatic / International Relations Consultant & War Crimes Investigator - War - Peace - Preventive Diplomatic Strategies - International Law - Charitable Causes - International Business - International Political Economy - Human Rights - Politics - War Crimes Investigations - Anti-Terrorism - Law Projects Center Funded Projects (YCICC) Internationally LPCYU Home Website -/- Irrefutable Proof ICTY Is Corrupt Court/Irrefutable Proof the Hague Court Cannot Legitimately Prosecute Karadzic Case By Jill Starr I want to stress, in this particular meeting , there was no observer status at the ICC Preparatory Meetings at the United Nations in New York City in 2001. What I did, made a historical precedent. I was asked by, Darko Trifunovic 1st Secretary of the Bosnian MIssion, to take his place, in a CLOSED DOOR UNITED NATIONS MEETING. This means, ONLY HEADS OF AMBASSADORIAL MISSIONS WERE ALLOWED IN THE MEETING. There was no "Observer Status for say NGO's such as Amnesty International." I represented a Country as an American Citizen that day; the Repuklika Srpska. This never occurred before to my knowledge ever. It was an error. My former professor, Arnold Stark, walked me in, A former State Dept. man chosen to be the former Ambassador from the USA to Bonn/Germany (and he declined years back because of his wife at the time). He knew it was illegal. It said on these paper I picked up in the meeting, Anyone, Richard Holbrooke, sat across from me, discussing this meeting outside the meeting itself thereafter , "would be prosecuted to the fullest extent of int'l law." I heard the Ambassadors of the world ALL DISCUS TRADING MONEY FOR ICC AND ICTY COURT VERDICT AS WELL AS FUTURE JUDICIAL APPOINTMENTS -/- http://sites.google.com/site/thelawprojectscenternycoffices/home/irrefutable-proof-icty-is-corrupt-c ourt-irrefutable-proof-the-hague-court-cannot-legitimately-prosecute-karadzic-case -/- http://picasaweb.google.com/lpcyusa/IrrefutableProofICTYIsCorruptCourtIrrefutabl# (The Documentary Secret United Nations ICC Meeting Papers Scanned Images) OR http://community.jigsaw.com/t5/media/gallerypage/user-id/903610# -/- Rea dMore Here _> Read the entire story here My testimonial video on Youtube _> http://www.youtube.com/watch?v=dKe-5LORsGs -/- http://www.youtube.com/watch?v=dKe-5LORsGs (My YouTube VIDEO) -/- This legal technicality indicates the Hague must dismiss charges against Dr Karadzic and others awaiting trials in the Hague jail; like it or not. -/- Unfortunately for the Signatures Of the Rome Statute United Nations member states instituting the ICC & ICTY housed at the Hague, insofar as the, Radovan Karadzic, as with the other Hague cases awaiting trial there, I personally witnessed these United Nations member states having a substantial conversations, and, openly speaking about trading judicial appointments and verdicts for financial funding when I attended the 2001 ICC Preparatory Meetings at the UN in Manhattan making the iCTY and ICC morally incapable trying Radovan Karazdic and others. -/- I witnessed with my own eyes and ears when attending the 2001 Preparatory Meetings to establish an newly emergent International Criminal Court, the exact caliber of criminal corruption running so very deeply at the Hague, that it was a perfectly viable topic of legitimate conversation in those meetings I attended to debate trading verdicts AND judicial appointments, for monetary funding. -/- Jilly wrote:*The rep from Spain became distraught and when her country’s proposal was not taken to well by the chair of the meeting , then Spain argued in a particularly loud and noticably strongly vocal manner, “Spain (my country) strongly believes if we contribute most financial support to the Hague’s highest court, that ought to give us and other countries feeding it financially MORE direct power over its decisions.” -/- ((((((((((((((((((((((((( ((((((((((((((((((((((((( Instead of censoring the country representative from Spain for even bringing up this unjust, illegal and unfair judicial idea of bribery for international judicial verdicts and judicial appointments, all country representatives present in the meeting that day all treated the Spain proposition as a ”totally legitimate topic” discussed and debated it between each other for some time. I was quite shocked! The idea was “let’s discuss it.” "It’s a great topic to discuss." -/- Some countries agreed with Spain’s propositions while others did not. The point here is, bribery for judicial verdicts and judicial appointments was treated as a totally legitimate topic instead of an illegitimate topic which it is in the meeting that I attended in 2001 that day to establish the ground work for a newly emergent international criminal court.)))))))))))))))))))))))))))) -/- In particular., since “Spain” was so overtly unafraid in bringing up this topic of trading financial funding the ICC for influence over its future judicial appointments and verdicts in front of every other UN member state present that day at the UN, “Spain” must have already known by previous experience the topic of bribery was “socially acceptable” for conversation that day. They must have previously spoke about bribing the ICTY and ICC before in meetings; this is my take an international sociological honor student. -/- SPAIN’s diplomatic gesture of international justice insofar as, Serbia, in all of this is, disgusting morally!SPAIN HAS TAUGHT THE WORLD THE TRUE DEFINITION OF AN “INTERNATIONAL CRIMINAL COURT.” -/- I represented the state interests’ of the Former Yugoslavia, in Diplomat Darko Trifunovic’s absence in those meetings and I am proud to undertake this effort on Serbia’s behalf. http://picasaweb.google.com/lpcyusa (My Political Satire Blog) Diplomatic / International Relations Consultant & War Crimes Investigator - War - Peace - Preventive Diplomatic Strategies - International Law - Charitable Causes - International Business - International Political Economy - Human Rights - Politics - War Crimes Investigations - Anti-Terrorism - Law Projects Center Funded Projects (YCICC) Internationally http://sites.google.com/site/jillstarrsite -/- -/- . 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The management of Higher Education Systems has continued to suffer from plethora of concerns and issues, cardinal amongst them, is the application of conventional administrative strategies and leadership patterns, sometimes without appropriate modifications so much so, that the management effectiveness of higher education systems is gradually being eroded. This is evident in the increasing distasteful gamut of multidimensional outcomes arising from the used of dogmatic and stereotype variants of managerial principles or nothing at all, in the circumstance. Given this premise, (...) there is an urgent desire to rejig and re-engineer learning experiences that will culminate into dynamic, goal oriented and robust management packages for higher education systems with results for global acclamations, thereby, chatting new directions to fill this existing gap in the management of higher education systems in Nigeria. With humility, I introduce to you this book titled: Management of Higher Education Systems, a collection of well-researched essays. The essays in this book promises to deliver on the deliverables of its raison d’tre of job specifications and management dynamics of higher education landscape, reflecting on the global realities. This is because scholarly evidences abound, to proof that looking into the National Universities Commission’s Bench Mark Minimum Academic Standard (BMAS) of the curriculum for Educational Management as a discipline, it is obvious, that the BMAS has fallen short of global expectations and appears to be revolving within neo-colonial conventional administrative theorizing, with little or no emphasis on the practical demonstration of acquired skills, competences and capabilities for trained educational administrators, to deal with peculiarities of the moment, especially in the developing world. This felt need pushes for a paradigm shift in our curricula endeavours. It is even worse off, when experiences have continued to show, that there are deficiencies noticeable in the understanding of job requirements of educational managers of higher education systems in Nigeria. -/- It is this gap therefore, that the current effort is geared towards building this literature which seeks to address this lacuna by re-chiseling and retooling educational management practices through equipping this sophisticated discipline with up-to-date information and knowledge that will enhance the full optimaization of the job specifications, of higher educational managers, to bring into a perfect nexus of the man, job and social milieu. It is also in public domain, that managers of higher educational systems with such limitations are very often left with no option than to resort to on -the- job training by bureaucrats, who are in themselves their acolytes ab-initio and who sometimes take over leadership of the organization, owing to the existing gaps that manifest in the knowledge of educational managers, thereby reducing substantive higher education executive head to a titular head or at best ceremonial heads. -/- This book brings together articles and chapters to be published in these directions by researchers, policy makers and practitioners to re-inform, reeducate and reorient higher educational managers on their job expectations. The volume also offers a rich and relevant literature of the dynamic state of higher education in global perspective. While this publication will be freely available online, the essays in this volume are carefully selected and they will provide a basis for thematic and analytical perspectives on the concerns of management of contemporary higher education systems. -/- The book is divided into twelve thematic sections with each addressing the demands of its Kernel, as it is reflected in Historical development of higher education systems and its organs, Gloabilization of higher education, Internationalization and the labour market, Funding of higher education systems, Proliferations of higher education systems, Corruption in higher education systems and the deterioration of its estate, Internationalization and massification, Politics and leadership in higher educational systems, Academic freedom and access to higher education, Academic planning and affiliation relationship of higher education systems, Conflict management in higher education systems, Research and training in higher education systems and Inclusivity in higher education. -/- Another striking feature of this book is in its efforts at globalizing the curriculum of management of higher education and providing opportunity for scholars with different shades of opinion even on same issues but from different perspectives with the hope that it will guarantee overall effectiveness in the management of higher education systems. I recommemd this book to all with passion for the management of diferentiated higher education systems, and invite you to this intellectual feast prepared so deliciously like a meal for the gods. -/- Finally, let me reflect on what may appears to be an aberration in this context, by appreciating all authors who had found time to respond to this academic calling by their various chapter contributions. This singular act is in itself enough justification as show of interest and further demonstration of your continuous determination to address gaps in Nigerian educational landscape. Similarly, my gratitude is equally extended to all members of my editorial team for their thoughtfulness and very constructive criticisms which have shaped these scholarly presentations thereof. May the Almighty God continue to enrich the contents of your cerebrum most intellectually, for the benefit of man but to His glory. -/- The PDF contains just the preliminary pages of the book. You can order the full copy of the book by contacting the editor-in-chief, Professor John A. Undie, FNAEAP, KSM. (shrink)

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, in particular, (...) as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning. (shrink)

In this paper, I propose that applying the methods of data science to “the problem of whether mathematical explanations occur within mathematics itself” (Mancosu 2018) might be a fruitful way to shed new light on the problem. By carefully selecting indicator words for explanation and justification, and then systematically searching for these indicators in databases of scholarly works in mathematics, we can get an idea of how mathematicians use these terms in mathematical practice and with what frequency. The results of (...) this empirical study suggest that mathematical explanations do occur in research articles published in mathematics journals, as indicated by the occurrence of explanation indicators. When compared with the use of justification indicators, however, the data suggest that justifications occur much more frequently than explanations in scholarly mathematical practice. The results also suggest that justificatory proofs occur much more frequently than explanatory proofs, thus suggesting that proof may be playing a larger justificatory role than an explanatory role in scholarly mathematical practice. (shrink)

Should we use the same standard of proof to adjudicate guilt for murder and petty theft? Why not tailor the standard of proof to the crime? These relatively neglected questions cut to the heart of central issues in the philosophy of law. This paper scrutinises whether we ought to use the same standard for all criminal cases, in contrast with a flexible approach that uses different standards for different crimes. I reject consequentialist arguments for a radically flexible standard of proof, (...) instead defending a modestly flexible approach on non-consequentialist grounds. The system I defend is one on which we should impose a higher standard of proof for crimes that attract more severe punishments. This proposal, although apparently revisionary, accords with a plausible theory concerning the epistemology of legal judgments and the role they play in society. (shrink)

The impossibility results in judgement aggregation show a clash between fair aggregation procedures and rational collective outcomes. In this paper, we are interested in analysing the notion of rational outcome by proposing a proof-theoretical understanding of collective rationality. In particular, we use the analysis of proofs and inferences provided by linear logic in order to define a fine-grained notion of group reasoning that allows for studying collective rationality with respect to a number of logics. We analyse the well-known paradoxes in (...) judgement aggregation and we pinpoint the reasoning steps that trigger the inconsistencies. Moreover, we extend the map of possibility and impossibility results in judgement aggregation by discussing the case of substructural logics. In particular, we show that there exist fragments of linear logic for which general possibility results can be obtained. (shrink)

Smith argues that, unlike other forms of evidence, naked statistical evidence fails to satisfy normic support. This is his solution to the puzzles of statistical evidence in legal proof. This paper focuses on Smith’s claim that DNA evidence in cold-hit cases does not satisfy normic support. I argue that if this claim is correct, virtually no other form of evidence used at trial can satisfy normic support. This is troublesome. I discuss a few ways in which Smith can respond.

In this dissertation, we shall investigate whether Tennant's criterion for paradoxicality(TCP) can be a correct criterion for genuine paradoxes and whether the requirement of a normal derivation(RND) can be a proof-theoretic solution to the paradoxes. Tennant’s criterion has two types of counterexamples. The one is a case which raises the problem of overgeneration that TCP makes a paradoxical derivation non-paradoxical. The other is one which generates the problem of undergeneration that TCP renders a non-paradoxical derivation paradoxical. Chapter 2 deals with (...) the problem of undergeneration and Chapter 3 concerns the problem of overgeneration. Chapter 2 discusses that Tenant’s diagnosis of the counterexample which applies CR−rule and causes the undergeneration problem is not correct and presents a solution to the problem of undergeneration. Chapter 3 argues that Tennant’s diagnosis of the counterexample raising the overgeneration problem is wrong and provides a solution to the problem. Finally, Chapter 4 addresses what should be explicated in order for RND to be a proof-theoretic solution to the paradoxes. (shrink)