Peter van Inwagen's Direct Argument (DA) for incompatibilism purports to establish incompatibilism with respect to moral responsibility and determinism without appealing to assumptions that compatibilists usually consider controversial. Recently, Michael McKenna has presented a novel critique of DA. McKenna's critique raises important issues about philosophical dialectics. In this article, we address those issues and contend that his argument does not succeed.

Not focusing on the history of classical logic, this book provides discussions and quotes central passages on its origins and development, namely from a philosophical perspective. Not being a book in mathematical logic, it takes formal logic from an essentially mathematical perspective. Biased towards a computational approach, with SAT and VAL as its backbone, this is an introduction to logic that covers essential aspects of the three branches of logic, to wit, philosophical, mathematical, and computational.

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)

The relation of normic support offers a novel solution to the proof paradox: a paradox in evidence law arising from legal cases involving merely statistical evidence (Smith 2018). Central to the normic support solution has been the thesis that merely statistical evidence cannot confer normic support. However, it has been observed that there are exceptions to this: there exist cases where merely statistical evidence can give rise to normic support (Blome-Tillmann 2020). If correct, this fact seems to undermine the normic (...) support solution to the proof paradox. This paper explores a resolution: normic support can resolve the proof paradox even though merely statistical evidence sometimes gives rise to normic support. The key to understanding this resolution lies with a source of evidential support that arises out of bodies of evidence that involve *character evidence* (Colyvan, et al. 2001). It turns out that character evidence can provide normic support when it is grounded in our knowledge of a certain kind of disposition individuals can have: *goal-directed dispositions*. The upshot is the recovery of the normic support solution to the puzzle of whether statistical evidence can meet legal standards of proof. (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)

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

We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt.

When an agent’s motivation is sensitive to how his supervisor thinks about the agent’s competence, the supervisor has to take into account both informational and expressive contents of her message to the agent. This paper shows that the supervisor can credibly express her trust in the agent’s ability only by being un- clear about what to do. Suggesting what to do, i.e., “directives,” could reveal the supervisor’s “distrust” and reduce the agent’s equilibrium effort level even though it provides useful information (...) about the decision environment. There is also an equilibrium in which directives are neutral in expressive content. However, it is shown that neologism proofness favors equilibria in which directives are double- edged swords. (shrink)

Peter van Inwagen's Direct Argument (DA) purports to establish the incompatibility of determinism and moral responsibility, without appealing to the notion of avoidability, a notion on whose analysis compatibilists and incompatibilists disagree. Van Inwagen intended DA to refute compatibilism, or at least to shift the burden of proof onto the compatibilist. In this paper, we offer a critical assessment of DA. We examine a variety of objections to DA due to John Fischer and Mark Ravizza, Ishtiyaque Haji, Seth Shabo, (...) Michael McKenna, and David Widerker. We divide these objections into those based on dialectical considerations (section 1), and objections in the form of counterexamples to a central principle which the Direct Argument employs (sec 2). The conclusion we reach is that the proponent of DA can deal plausibly with these objections, thus establishing DA as a powerful argument in favor of incompatibilism. (shrink)

This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means ‘The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown to be (...) sound and complete for the semantics. The system has a number of novel features and is briefly compared to the usual approach of formalising ‘the F ’ by a term forming operator. It does not coincide with Hintikka’s and Lambert’s preferred theories, but the divergence is well-motivated and attractive. (shrink)

According to a widely held view in the philosophy of mathematics, direct inferential justification for mathematical propositions (that are not axioms) requires proof. I challenge this view while accepting that mathematical justification requires arguments that are put forward as proofs. I argue that certain fallacious putative proofs considered by the relevant subjects to be correct can confer mathematical justification. But mathematical justification doesn’t come for cheap: not just any argument will do. I suggest that to successfully transmit (...) justification an argument must satisfy specific standards, some of which are social. I contrast my view with Huemer’s inferential conservatism, which makes mathematical justification too easy to get. Although in this article I focus on mathematical inferential beliefs, the view on offer generalizes to other inferential beliefs. (shrink)

The aim of this paper is to provide a proof-theoretic characterization of relevant logics including fusion and fission connectives, as well as Ackermann’s truth constant. We achieve this by employing the well-established methodology of labelled sequent calculi. After having introduced several systems, we will conduct a detailed proof-theoretic analysis, show a cut-admissibility theorem, and establish soundness and completeness. The paper ends with a discussion that contextualizes our current work within the broader landscape of the proof theory of relevant logics.

ABSTRACT This paper explores the role of aesthetic judgements in mathematics by focussing on the relationship between the epistemic and aesthetic criteria employed in such judgements, and on the nature of the psychological experiences underpinning them. I claim that aesthetic judgements in mathematics are plausibly understood as expressions of what I will call ‘aesthetic-epistemic feelings’ that serve a genuine cognitive and epistemic function. I will then propose a naturalistic account of these feelings in terms of sub-personal processes of representing and (...) assessing the relation between cognitive processes and certain properties of the stimuli at which they are directed. (shrink)

Leibniz proposed the ‘Most Determined Path Principle’ in seventeenth century. According to it, ‘ease’ of travel is the end purpose of motion. Using this principle and his calculus method he demonstrated Snell’s Laws of reflection and refraction. This method shows that light follows extremal (local minimum or maximum) time path in going from one point to another, either directly along a straight line path or along a broken line path when it undergoes reflection or refraction at plane or spherical (concave (...) or convex) surfaces. The extremal time path avoided the criticism that Fermat’s least time path was subjected to, by Cartesians who cited examples of reflections at spherical surfaces where light took the path of longest time. Thereby it became the standard method of demonstration of Snell’s Laws. Ptolemy’s theorem is a fundamental theorem in geometry. A special case of it offers a method of finding the minimum sum of the two distances of a point from two given fixed points. We show in this paper that Leibniz’s calculus proof of Snell’s Laws violates Ptolemy’s theorem, whereby Leibniz’s proof becomes invalid. (shrink)

In a previous paper, an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n (...) = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the two linked semigroups originating from addition and multiplication and from the Peano axioms in the final analysis can be postulated algebraically as independent of each other in a “Hamilton” modification of arithmetic supposedly equivalent to Peano arithmetic. The inductive proof of FLT can be deduced absolutely precisely in that Hamilton arithmetic and the pransfered as a corollary in the standard Peano arithmetic furthermore in a way accessible in Fermat’s epoch and thus, to himself in principle. A future, second part of the paper is outlined, getting directed to an eventual proof of the case “n=3” based on the qubit Hilbert space and the Kochen-Specker theorem inferable from it. (shrink)

Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to deductive conclusions without any need for other representations.

Gödel's incompleteness theorems establish the stunning result that mathematics cannot be fully formalized and, further, that any formal system containing a modicum of number or set theory cannot establish its own consistency. Wilfried Sieg and Clinton Field, in their paper Automated Search for Gödel's Proofs, presented automated proofs of Gödel's theorems at an abstract axiomatic level; they used an appropriate expansion of the strategic considerations that guide the search of the automated theorem prover AProS. The representability conditions that (...) allow the syntactic notions of the metalanguage to be represented inside the object language were taken as axioms in the automated proofs. The concrete task I am taking on in this project is to extend the search by formally verifying these conditions. Using a formal metatheory defined in the language of binary trees, the syntactic objects of the metatheory lend themselves naturally to a direct encoding in Zermelo's theory of sets. The metatheoretic notions can then be inductively defined and shown to be representable in the object-theory using appropriate inductive arguments. Formal verification of the representability conditions is the first step towards an automated proof thereof which, in turn, brings the automated verification of Gödel's theorems one step closer to completion. (shrink)

The Earth is positioned at the center of the universe in the Ptolemaic model of the universe. The center of the Earth is at the same time the center of the universe in this model. This system, which was constructed according to Aristotelian physics, was accepted as the prevailing theory up to the adoption of the heliocentric universal model in the 16th century. The Earth was at the same time assumed to be completely stationary in the geocentric theory. Movement around (...) its own axis or around another celestial body was out of the question for it. In Antiquity and the Middle Ages when observational instruments like the telescope were not yet in use, this theory was seen to be rationally based on data obtained directly from the senses. In this context, various justifications had been provided about the world being stationary and existing at the center. Representatives from the Peripatetic philosophy in the Muslim world also were seen to accept the geocentric model. In The Book of Healing, Ibn Sīnā (d. 1038 CE) subjected the proofs that had come to him about the Earth being stationary by distinguishing an independent chapter. The 14th century follower of Ibn Sīnā’s philosophy, Najm al-Dīn al-Kātibī addressed this topic in Ḥikmat al-‘ain, and the work’s principle commentators also commented on his assessments. This study will address Ibn Sīnā’s assessments on the Earth being stationary in the geocentric model of the universe and will discuss the reflections of these assessments in Ḥikmat al-‘ain as an Avicennan text. (shrink)

In the later Fichte the reflection splits the world into a fivefoldness of its possible view. To get through all the a priori arranged levels from sensuality to the Doctrine of Science means to use up all the possibilities of the views of the world. I will examine whether Fichte can offer us a direct proof of completeness of the standpoints or at least show indirectly that there must be exactly five of them. Which answer would he give us (...) if we argued that history, skepticism and nonentity could complement the array? -/- Keywords Fivefoldness-worldviews-completeness-proof-history-skepticism -/- Die Reflexion spaltet nach Fichte die Welt in eine Fünffachheit ihrer möglichen Ansicht. Das Durchlaufen der a priori geordneten Stufen von der Sinnlichkeit bis zur Wissenschaftslehre stellt zugleich ein Ausschöpfen der Möglichkeiten dar, sich zur Welt zu verhalten. Ich werde prüfen, ob Fichte uns einen direkten Beweis der Vollständigkeit der Standpunkte geben oder zumindest indirekt dafür argumentieren kann, dass es genau fünf sein müssen. Was würde er uns antworten, wenn wir behaupteten, die Geschichte, der Skeptizismus und die Nullität könnten die Reihe ergänzen? -/- Schlüsselbegriffe Fünffachheit-Weltansichten-Vollständigkeit-Beweis-Geschichte-Skeptizismus. (shrink)

The depth-bounded approach seeks to provide realistic models of reasoners. Recognizing that most useful logics are idealizations in that they are either undecidable or likely to be intractable, the approach accounts for how they can be approximated in practice by resource-bounded agents. The approach has been applied to Classical Propositional Logic (CPL), yielding a hierarchy of tractable depth-bounded approximations to that logic, which in turn has been based on a KE/KI system. -/- This Thesis shows that the approach can be (...) naturally extended to useful nonclassical logics such as First-Degree Entailment (FDE), the Logic of Paradox (LP), Strong Kleene Logic (K3 ) and Intuitionistic Propositional Logic (IPL). To do this, we introduce a KE/KI-style system for each of those logics such that: is formulated via signed formulae, consist of linear operational rules and branching structural rule(s), can be used as a direct-proof and a refutation method, and is interesting independently of the approach in that it has an exponential speed-up on its tableau system counterpart. The latter given that we introduce a new class of examples which we prove to be hard for all tableau systems sharing the V/& rules with the classical one, but easy for their analogous KE-style systems. Then we focus on showing that each of our KE/KI-style systems naturally yields a hierarchy of tractable depth-bounded approximations to the respective logic, in terms of the maximum number of allowed nested applications of the branching rule(s). The rule(s) express(es) a generalized rule of bivalence, is (are) essentially cut rule(s) and govern(s) the manipulation of virtual information, which is information that an agent does not hold but she temporarily assumes as if she held it. Intuitively, the more virtual information needs to be invoked via the branching rule(s), the harder the inference is for the agent. So, the nested application the branching rule(s) provides a sensible measure of inferential depth. We also show that each hierarchy approximating FDE, LP, and K3 , admits of a 5-valued non-deterministic semantics; whereas, paving the way for a semantical characterization of the hierarchy approximating IPL, we provide a 3-valued non-deterministic semantics for the full logic that fixes the meaning of the connectives without appealing to “structural” conditions. -/- Moreover, we show a super-polynomial lower bound for the strongest possible version of clausal tableaux on the well-known class of “truly fat” expressions (which are easy for KE), settling a problem left open in the literature. Further, we investigate a hierarchy of tractable depth-bounded approximations to CPL based only on KE. Finally, we propose a refinement of the p-simulation relation which is adequate to establish positive results about the superiority of a system over another with respect to proof-search. (shrink)

We show how a semantics based on Aristotle’s texts and ecthetic proofs can be reconstructed. All truth conditions are given by means of set inclusion. Perfect syllogisms reveal to be valid arguments that deserve a validity proof. It turns out of these proofs that transitivity of set inclusion is the necessary and sufficient condition for the validity and perfection of a syllogism. The proofs of validity for imperfect syllogisms are direct proofs without conversion in a (...) calculus of natural deduction. Transitivity of set inclusion turns out to be a necessary condition for the validity of imperfect syllogisms. As a consequence, it can be established what the main metalogical difference between a perfect and an imperfect syllogism is. The validity of the laws of conversion is also obtained by direct proofs. Finally, it is shown that and explained why some imperfect syllogisms satisfy the definition of a perfect syllogism. (shrink)

In Metaphysics M.2, 1077a9-14, Aristotle appears to argue against the existence of Platonic Forms on the basis of there being certain universal mathematical proofs which are about things that are ‘beyond’ the ordinary objects of mathematics and that cannot be identified with any of these. It is a very effective argument against Platonism, because it provides a counter-example to the core Platonic idea that there are Forms in order to serve as the object of scientific knowledge: the universal of (...) which theorems of universal mathematics are proven in Greek mathematics is neither Quantity in general nor any of the specific quantities, but Quantity-of-type-x. This universal cannot be a Platonic Form, for it is dependent on the types of quantity over which the variable ranges. Since for both Plato and Aristotle the object of scientific knowledge is that F which explains why G holds, as shown in a ‘direct’ proof about an arbitrary F (they merely disagree about the ontological status of this arbitrary F, whether a Form or a particular used in so far as it is F), Plato cannot maintain that Forms must be there as objects of scientific knowledge - unless the mathematics is changed. (shrink)

We advance a theory of the representational role of Euclidean diagrams according to which they are samples of co-exact features. We contrast our theory with two other conceptions, the instantial conception and Macbeth’s iconic view, with respect to how well they accommodate three fundamental constraints on theories of the Euclidean diagrammatic practice— that Euclidean diagrams are used in proofs whose results are wholly general, that Euclidean diagrams indicate the co-exact features that the geometer is allowed to infer from them (...) and that Euclidean diagrams play the same role in both direct proofs and indirect proofs by reductio—and argue that our view is the one best suited to account for them. We conclude by illustrating the virtues of our conception of Euclidean diagrams as samples by means of an analysis of Saccheri’s quadrilateral. (shrink)

DEFINING OUR TERMS A “paradox" is an argumentation that appears to deduce a conclusion believed to be false from premises believed to be true. An “inconsistency proof for a theory" is an argumentation that actually deduces a negation of a theorem of the theory from premises that are all theorems of the theory. An “indirect proof of the negation of a hypothesis" is an argumentation that actually deduces a conclusion known to be false from the hypothesis alone or, more commonly, (...) from the hypothesis augmented by a set of premises known to be true. A “direct proof of a hypothesis" is an argumentation that actually deduces the hypothesis itself from premises known to be true. Since `appears', `believes' and `knows' all make elliptical reference to a participant, it is clear that `paradox', `indirect proof' and `direct proof' are all participant-relative. PARTICIPANT RELATIVITY In normal mathematical writing the participant is presumed to be “the community of mathematicians" or some more or less well-defined subcommunity and, therefore, omission of explicit reference to the participant is often warranted. However, in historical, critical, or philosophical writing focused on emerging branches of mathematics such omission often invites confusion. One and the same argumentation has been a paradox for one mathematician, an inconsistency proof for another, and an indirect proof to a third. One and the same argumentation-text can appear to one mathematician to express an indirect proof while appearing to another mathematician to express a direct proof. WHAT IS A PARADOX’S SOLUTION? Of the above four sorts of argumentation only the paradox invites “solution" or “resolution", and ordinarily this is to be accomplished either by discovering a logical fallacy in the “reasoning" of the argumentation or by discovering that the conclusion is not really false or by discovering that one of the premises is not really true. Resolution of a paradox by a participant amounts to reclassifying a formerly paradoxical argumentation either as a “fallacy", as a direct proof of its conclusion, as an indirect proof of the negation of one of its premises, as an inconsistency proof, or as something else depending on the participant's state of knowledge or belief. This illustrates why an argumentation which is a paradox to a given mathematician at a given time may well not be a paradox to the same mathematician at a later time. -/- The present article considers several set-theoretic argumentations that appeared in the period 1903-1908. The year 1903 saw the publication of B. Russell's Principles of mathematics, [Cambridge Univ. Press, Cambridge, 1903; Jbuch 34, 62]. The year 1908 saw the publication of Russell's article on type theory as well as Ernst Zermelo's two watershed articles on the axiom of choice and the foundations of set theory. The argumentations discussed concern “the largest cardinal", “the largest ordinal", the well-ordering principle, “the well-ordering of the continuum", denumerability of ordinals and denumerability of reals. The article shows that these argumentations were variously classified by various mathematicians and that the surrounding atmosphere was one of confusion and misunderstanding, partly as a result of failure to make or to heed distinctions similar to those made above. The article implies that historians have made the situation worse by not observing or not analysing the nature of the confusion. -/- RECOMMENDATION This well-written and well-documented article exemplifies the fact that clarification of history can be achieved through articulation of distinctions that had not been articulated (or were not being heeded) at the time. The article presupposes extensive knowledge of the history of mathematics, of mathematics itself (especially set theory) and of philosophy. It is therefore not to be recommended for casual reading. AFTERWORD: This review was written at the same time Corcoran was writing his signature “Argumentations and logic”[249] that covers much of the same ground in much more detail. https://www.academia.edu/14089432/Argumentations_and_Logic . (shrink)

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting to (...) embeddings, semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants. (shrink)

Redictio ad absurdum is an important part of Aristotle’s syllogistic. It is connected with direct proof and they are complementary methods. All moods of Aristotle are provable by direct methods and redictio ad absurdum. In this paper, I have studied on the bases and principles of redictio ad absurdum, I showed how to prove by redictio ad absurdum, and how to prove Aristotle by redictio ad absurdum. By redictio ad absurdum, all forms of Aristotle’s method proved in the (...) first figure can be reduced to the perfect forms. (shrink)

Aristotle’s points about circle and vicious circle are as follows: 1. Aristotle criticizes some thinkers because ‘they see no difficulty in holding that all truths are demonstrated, on the ground that demonstration may be circular and reciprocal.’ (PsA., A, 3, 72b16-18) 2. ‘Not all knowledge is demonstrative’ and ‘knowledge of the immediate premises is independent of demonstration.’ Aristotle brings two reasons for this: ‘Since we must know the prior premises from which the demonstration is drawn, and since the regress must (...) end in immediate truths, those truths must be indemonstrable.’ (PsA., A, 3, 72b18-22) 3. Demonstration in the unqualified sense cannot be circular: ‘Demonstration must be based on premises prior to and better known than the conclusion; and the same things cannot simultaneously be both prior and posterior to one another: so circular demonstration is clearly not possible in the unqualified sense of demonstration, but only possible if ‘demonstration be extended to include that other method of argument which rests on a distinction between truths prior to us and truths without qualification prior, i.e. the method by which induction produces knowledge. But if we accept this extension of meaning, our definition of unqualified knowledge will prove faulty; for there seem to be two kinds of it. Perhaps, however, the second form of demonstration, that which proceeds from truths better known to us, is not demonstration in the unqualified sense of the term.’ (PsA., A, 3, 72b23-32) 4. The theory of circular demonstration ‘reduces to the mere statement that if a thing exists, then it does exist- an easy way of providing anything.’ (psA., A, 3, 72b32-34) 5. ‘To constitute the circle it makes no difference whether many terms or few or even only one is taken. Thus by direct proof, if A is, B must be; if B is, C must be; therefore, if A is, C must be. Since then- by the circular proof- if A is, B must be, and if B is, A must be. A may be substituted for C above. Then ‘if B is, A must be’ = ‘if B is, C must be.’ But C and A have been identified. Consequently, the upholders of circular demonstration are in the position of saying that if A is, A must be- a simple way of proving anything. Moreover, even such circular demonstration is impossible except in the case of attributes that imply one another, viz. ‘peculiar’ properties.’ (PsA, A, 3, 72b34-73a7) . (shrink)

This essay is an accessible introduction to the proof paradox in legal epistemology. -/- In 1902 the Supreme Judicial Court of Maine filed an influential legal verdict. The judge claimed that in order to find a defendant culpable, the plaintiff “must adduce evidence other than a majority of chances”. The judge thereby claimed that bare statistical evidence does not suffice for legal proof. -/- In this essay I first motivate the claim that bare statistical evidence does not suffice for legal (...) proof. I then introduce and motivate a knowledge-centred explanation of this fact. The knowledge-centred explanation rests on two premises. The first is that legal proof requires knowledge of culpability. The second is that one cannot attain knowledge that p from bare statistical evidence that p. To motivate the second premise, I suggest that beliefs based on bare statistical evidence fail to be safe—they could easily be wrong—and bare statistical evidence cannot eliminate relevant alternatives. -/- I then cast doubt on the first premise; I argue that legal proof does not require knowledge. I thereby dispute the knowledge-centred explanation of the inadequacy of bare statistical evidence for legal proof. Instead of appealing to the nature of knowledge, I suggest we should seek a more direct explanation by appealing to those more foundational epistemic properties, such as safety or eliminating relevant alternatives. (shrink)

Without directly addressing the Demarcation Problem for logic—the problem of distinguishing logical vocabulary from others—we focus on distinctive aspects of logical vocabulary in pursuit of a second goal in the philosophy of logic, namely, proposing criteria for the justification of logical rules. Our preferred approach has three components. Two of these are effectively Belnap’s, but with a twist. We agree with Belnap’s response to Prior’s challenge to inferentialist characterisations of the meanings of logical constants. Belnap argued that for a logical (...) constant to exist, its rules must be conservative over a previously given consequence relation and guarantee the uniqueness of the constant. The twist is that we require logical vocabulary to be provably conservative, not over a previously given formal consequence relation, but over a previously given meaningful vocabulary of a language. Uniqueness is also a feature defined in terms of provability: if two syntactically distinguished expressions are governed by the same rules, then formulas with them as main operators are interderivable. Belnap’s criteria are not only those for the existence of a logical constant, but more: they are what distinguishes logical vocabulary from all other expressions. It is the defining mark of a logical constant that it is provably conservative over the fragment of the language which excludes it and that its rules guarantee its uniqueness. The third component is the topic neutrality of logic. The provable conservativeness of logic over a previously given vocabulary of a language is motivated, in part, by appeal to molecularism in the theory of meaning. Molecularity is a feature endorsed by the theory of meaning as a whole, so it does not distinguish logical constants from other expressions. The same is true for conservativeness. We argue that molecularity, and hence conservativeness, are implicit presuppositions of speakers’ use of language: the addition of new vocabulary to a language is presupposed to be conservative. But this presupposition is one that we should be able reflectively to endorse (such as when attempting a rational reconstruction of the use of the vocabulary). Thus, where conservativeness is found to fail, this defect should be remedied and the use of the vocabulary corrected (as in classical negation) or excised altogether (as in pejoratives). We go on to characterise a notion of topic neutrality, which we argue applies to logical vocabulary. We then note that reflective endorsement of the conservativeness of a topic neutral vocabulary requires a proof that the vocabulary is conservative relative to any base vocabulary. Thus we require that logical vocabulary be demonstrably conservative. Allying this requirement, distinctive of logic, to a general consideration about the commitments of assertion yields a mode of justification for logical constants akin to some conceptions of Harmony, i.e., to the idea that the consequences of assertion of a logical complex need to be warranted by the grounds and ought to be the strongest consequences warranted by the grounds. Intuitionistic logic acquires a somewhat familiar justification but emanating from a new motivation. (shrink)

According to an influential view about directed expressive duties (e.g., duties to express gratitude to benefactors, remorse to victims, forgiveness to wrongdoers), these duties do not have rights as their correlates, because they are not demandable and enforceable. The chapter argues that this view is mistaken. Like other directed duties, directed expressive duties are demandable and enforceable. While this does not entail that these duties have rights as their correlates, it does create a strong presumption of this being the case. (...) This shifts the burden of proof from those who hold that expressive duties correlate with rights to those who deny it. (shrink)

This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as (...) completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics. (shrink)

In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic, or multiple-conclusion calculi for classical logic). -/- The sequent derivations and proofnets are both simple extensions of sequents and proofnets for classical propositional logic, in which the new machinery—to take account of the modal vocabulary—is directly motivated (...) in terms of the simple, universal Kripke semantics for S5. The sequent system is cut-free and the circuit proofs are normalising. (shrink)

Is it right to convict a person of a crime on the basis of purely statistical evidence? Many who have considered this question agree that it is not, posing a direct challenge to legal probabilism – the claim that the criminal standard of proof should be understood in terms of a high probability threshold. Some defenders of legal probabilism have, however, held their ground: Schoeman (1987) argues that there are no clear epistemic or moral problems with convictions based on (...) purely statistical evidence, and speculates that our aversion to such convictions may be nothing more than an irrational bias. More recently, Hedden and Colyvan (2019, section VI) describe our reluctance to convict on the basis of purely statistical evidence as an ‘intuition’, but suggest that there may be no ‘in principle’ problem with such convictions (see also Papineau, forthcoming, section 6). In this paper, I argue that there is, in some cases, an in principle problem with a conviction based upon statistical evidence alone – namely, it commits us to a precedent which, if consistently followed through, could lead to the deliberate conviction of an innocent person. I conclude with some reflections on the idea that the criminal justice system should strive to maximise the accuracy of its verdicts – and the related idea that we should each strive to maximise the accuracy of our beliefs. (shrink)

Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein’s philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein’s distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation or theorem (...) and its proof. An attempt is made to meet directly some of Wittgenstein’s critical comments on the mathematical treatment of infinity and irrational numbers. (shrink)

Should people include beef in their diet? This chapter argues that the answer is “no” by reviewing what is known and not known about the presence in cattle of three psychological traits: pain, desire, and self-consciousness. On the basis of behavioral and neuroanatomical evidence, the chapter argues that cattle are sentient beings who have things they want to do in the proximal future, but they are not self-conscious. The piece rebuts three important objections: that cattle have injury information but not (...) pain; that cattle have goal-directed behavior but not desire; and that the absence of evidence for bovine self-consciousness should not be taken as evidence that cattle lack self-consciousness. In sum, what is known about cattle cognition shifts the moral burden of proof on to the beef eaters. (shrink)

This paper analyzes the incisive counter-arguments against Gaṅgeśa’s defense of non-conceptual perception offered by the Dvaita Vedānta scholar Vyāsatīrtha in his Destructive Dance of Dialectic. The details of Vyāsatīrtha’s arguments have gone largely unnoticed by subsequent Navya Nyāya thinkers, as well as by contemporary scholars engaged in a debate over the role of non-conceptual perception in Nyāya epistemology. Vyāsatīrtha thoroughly undercuts the inductive evidence supporting Gaṅgeśa’s main inferential proof of non-conceptual perception, and shows that Gaṅgeśa has no basis for thinking (...) that non-conceptual perception has any necessary causal role in generating concept-laden perceptual awareness. He further raises a number of internal inconsistencies and undesirable consequences for Gaṅgeśa’s claim that non-conceptual states are introspectively invisible. His own causal theory of perception is more parsimonious than the Nyāya account, and is equally compatible with direct realism. I conclude by noting several striking parallels between Vyāsatīrtha’s views and the conceptualism of John McDowell, while also suggesting that Vyāsatīrtha's own conceptualism is not unduly constrained by some of McDowell’s limiting assumptions about concepts and perceptual contents. (shrink)

The proof of God’s existence, known as Ratio Anselmi, is being analyzed. Four first-order theories are constructed to mirror versions of Anselm’s reasoning. God’s existence is shown to be provable in all of them. A traditional objection to the employment of a concept of God is overruled. And yet, Anselm’s proof is eventually found to be incorrect. The error attributed to Anselm consists in an illegitimate use of the words “greater‘ and “conceivable‘, and is identified as quaternio terminorum or petitio (...) principii, depending on circumstances. It is claimed that there is no direct way to improve the argument. (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)

There are passages in Kant’s writings according to which empirical intuitions have to be (a) singular, (b) object-dependent, and (c) immediate. It has also been argued that empirical intuitions (d) are not truth-apt, and (e) need to provide the subject with a proof of the possibility of the cognized object. Having relied on one or another of the a-e constraints, the naïve realist readers of Kant have argued that it is not possible for empirical intuitions to be representations. Instead they (...) have argued for a relationalist reading of empirical intuitions in terms of an acquaintance relation between the subject and the intuited object. -/- For the sake of argument, I will grant the naïve realist reader of Kant that empirical intuitions should satisfy all the a-e constraints. Nevertheless, by incorporating these constraints, one by one, into a representationalist theory of empirical intuitions, I will show that not only doesn’t a naïve realist reading of empirical intuitions follow, but also that the naïve realist has hastily overlooked a range of perfectly representationalist readings of intuitions available to Kant and his representationalist allies. On the positive side, I will argue that there is an extra constraint on intuitions—i.e., that givenness does not require presence to consciousness—that directly goes against any naïve realist account of intuitions. (shrink)

The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined even if it is not sufficiently formal and precise to belong to mathematics proper (in a narrow sense)—and even if (as many have asserted) for that reason the Church–Turing thesis is unprovable. It is proved logically that the class of effective procedures is not decidable, i.e., that no effective procedure is possible for ascertaining whether a given procedure is effective. This (...) undecidability result is proved directly from the notion itself of an effective procedure, without reliance on any (partly) mathematical lemma, conjecture, or thesis invoking recursiveness or Turing-computability. In fact, there is no reliance on anything very mathematical. The proof does not even appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of an effective procedure. Though the result that effectiveness is undecidable is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure invariably terminates with the correct verdict. (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)

The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...) of the reasons why CDs form a good notation is that they are highly mathematically tractable: experts can obtain valid results by ‘calculating’ with CDs. These calculations, take the form of ‘diagram chases’. In order to draw inferences, experts move algebraic elements around the diagrams. It will be argued that these diagrams are dynamic. It is thanks to their dynamicity that CDs can externalize the relevant reasoning and allow experts to draw conclusions directly by manipulating them. Lastly, it will be shown that CDs play essential roles in the context of proof as well as in other phases of the mathematical enterprise, such as discovery and conjecture formation. (shrink)

The Sure-Thing Principle famously appears in Savage’s axiomatization of Subjective Expected Utility. Yet Savage introduces it only as an informal, overarching dominance condition motivating his separability postulate P2 and his state-independence postulate P3. Once these axioms are introduced, by and large, he does not discuss the principle any more. In this note, we pick up the analysis of the Sure-Thing Principle where Savage left it. In particular, we show that each of P2 and P3 is equivalent to a dominance condition; (...) that they strengthen in different directions a common, basic dominance axiom; and that they can be explicitly combined in a unified dominance condition that is a candidate formal statement for the Sure-Thing Principle. Based on elementary proofs, our results shed light on some of the most fundamental properties of rational choice under uncertainty. In particular they imply, as corollaries, potential simplifications for Savage’s and the Anscombe- Aumann axiomatizations of Subjective Expected Utility. Most surprisingly perhaps, they reveal that in Savage’s axiomatization, P3 can be weakened to a natural strengthening of so-called Obvious Dominance. (shrink)

In Book 10 of the Republic, Plato launches an extensive critique of art, claiming that it can have no legitimate role within the well-ordered state. While his reasons are multifac- eted, Plato’s primary objection to art rests on its status as a mere shadow of a shadow. Such shadows inevitably lead the human mind away from the Good, rather than toward it. How- ever, after voicing his many objections, Plato concedes that if art “has any arguments to show it should (...) have a place in a well-governed city, [he] would gladly welcome it back.” Over two millennia later, the nineteenth-century Russian philosopher Vladimir Solov’ev implicitly responded to this challenge in his Lectures on Godmanhood (1881). Solov’ev cited the phenomenon of art as additional proof in favor of his model of the metaphysical foundations of reality. According to Solov’ev, art is not three steps removed from ultimate reality; rather, an artist creates true art only when he has experienced a vision of the univer- sal and substantial ideas that stand over and above particular things, and then conveys them to the viewer directly, via the artistic medium. Hence, the artist is able to sidestep the in- termediate shadow and produce something that is more than a shadow—a clear reflection of that higher reality. If Solov’ev is correct, the artist should enjoy the elevated status of sage, per- haps even philosopher-king, rather than face exile from Plato’s republic, because the artist both knows the Good and guides the less enlightened toward it. After a brief sketch of the metaphysical grounds for Plato’s critique of art, I provide an analysis of Solov’ev’s ontology, as represented in his Lectures on Godmanhood. Next, I describe Solov’ev’s concept of the three-fold mission of art and its relationship to human nature, drawing both from the Lectures and from The Universal Meaning of Art (1890). Finally, in the last section, I demonstrate how the afore-mentioned account comprises Solov’ev’s robust and successful response to Plato’s challenge, from within a platonic framework. (shrink)

This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (2005), and the dependence digraph by Beringer & Schindler (2015). Unlike the usual discussion about self-reference of paradoxes centering around Yablo's paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb's dependence relation. They are called 'locally finite paradoxes', satisfying that any sentence in these paradoxes can depend on finitely many sentences. I prove (...) that all locally finite paradoxes are self-referential in the sense that there is a directed cycle in their dependence digraphs. This paper also studies the 'circularity dependence' of paradoxes, which was introduced by Hsiung (2014). I prove that the locally finite paradoxes have circularity dependence in the sense that they are paradoxical only in the digraph containing a proper cycle. The proofs of the two results are based directly on König's infinity lemma. In contrast, this paper also shows that Yablo's paradox and its nested variant are non-self-referential, and neither McGee's paradox nor the omega-cycle liar paradox has circularity dependence. (shrink)

In her seminal article ‘Modern Moral Philosophy’ (1958) Elizabeth Anscombe argued that we need a new ethics, one that uses virtue terms to generate absolute prohibitions against certain act-types. Leading contemporary virtue ethicists have not taken up Anscombe's challenge in justifying absolute prohibitions and have generally downplayed the role of rule-following in their normative theories. That they have not done so is primarily because contemporary virtue ethicists have focused on what is sufficient for characterizing the deliberation and action of the (...) fully virtuous person, and rule-following is inadequate for this task. In this article, I take up Anscombe's challenge by showing that rule-following is necessary for virtuous agency, and that virtue ethics can justify absolute prohibitions. First, I offer a possibility proof by showing how virtue ethics can generate absolute prohibitions in three ways: by considering actions that directly manifest vice or that cannot be performed virtuously; actions that are prohibited by one's institutional roles and practical identities; and actions that are prohibited by the prescriptions of the wise. I then seek to show why virtue ethicists should incorporate rule-following and absolute prohibitions into their theories. I emphasize the central role that rules have in the development of virtue, then motivate the stronger view that fully virtuous agents follow moral rules by considering the importance of hope, uncertainty about consequences, and taking responsibility for what eventuates. Finally, I provide an account of what Anscombe called a ‘corrupt mind’, explaining how our understanding of virtue is corrupted if we think that virtue may require us to do vicious actions. (shrink)

Techne and Truth. The problem of techne in the dispute between Gorgias and Plato -/- The source of the problem matter of the book is the Plato’s dialogue „Gorgias”. One of the main subjects of the discussion carried out in this multi-aspect work is the issue of the art of rhetoric. In the dialogue the contemporary form of the art of rhetoric, represented by Gorgias, Polos and Callicles, is confronted with Plato’s proposal of rhetoric and concept of art (techne). The (...) ingenuous and dramatic structure of the dialogue composed of three acts, in each of which Socrates’ consecutive interlocutors emerge, is difficult to interpret. It seems, however, that even though the first conversation between Socrates and Gorgias constitutes a small part of the dialogue, it forms the foundations for the discussion. This part, dealing with such important issues as the subject of art, knowledge, power and relation between art and good, is the starting point for the conversations which follow. What do the differences between the Gorgias’ and Plato’s concepts of art consist in? Any attempt to answer the question requires presentation of the background for the discussion taking place in Plato’s work as well as the reconstruction of Gorgias’ vision of the art of rhetoric and art in general, defining the relation between art and knowledge. The latter may be undertaken on the basis of two paraphrases of the treatise “On Non-existence”, two epideictic speeches entitled “Helen” and “Palamedes” and some smaller fragments which have been preserved from Gorgias’ creative output. The treatise “On Non–existence”, very paradoxical in its philosophical meaning, testifies to new, sophistic thinking represented by Gorgias of Leontinoi. The treatise is the polemic and attack on Eleatism based on certain principles and methods elaborated by the Eleatics themselves. It also shows that Gorgias – using traditional Eleatic schemes – is opposed to this tradition. Even though the treatise does not discuss the problem of art directly, it anticipates the considerations from epideictic speeches. “Helen” and “Palamedes” constitute further stages in the development of Gorgias’ thought and concept of art combining typically epideictic elements with some philosophical convictions. Gorgias refers to the Eleatic theme considering the issues of truth, knowledge and belief, yet defining them in the empirical spirit. Solutions in the cognitive sphere determine the horizon of Gorgias’ rhetoric. The word is separated from the existence. Human cognition is limited and therefore the word and visual images affect the belief. This promotes the great importance of rhetoric, painting and sculpture, i.e. the areas which influence in a specific way – creating the “delusion” (ἀπάτη). Through idealization art provides pleasure, which is its objective. Therefore the task of art is to create delusion. The rhetor of Leontinoi discusses the issue of “how?” to use the word ‘rhetoric’. Gorgias is aware that rhetoric may be used to talk about what is unknown and that technical correctness of a rhetoric statement is not identical with the truthfulness of the proclaimed message. Mentioning it, Gorgias shows his respect to the truth as a value which should be respected in speech on the one hand, and on the other emphasizes that the truth in itself has no persuasive power. For this reason it is not enough to proclaim the truth, but, to convince the listeners, the orator should possess the skill of speaking. What is then the relation between truth and art emerging from epideictic speeches? Gorgias undoubtedly emphasizes the formal aspect of speech, as rhetoric is art, thus an ability based on certain principles. According to Gorgias, the truth is the value which should be respected in speeches. Rhetoric is able to create a fictive world, as a great range of reality remains outside direct human experience. Rhetoric does not oppose the truth but discussing not only what is directly given concerns the area outside the sphere of direct experience. This concept of rhetoric is the basis of the discussion about art carried out in the dialogue “Gorgias”. Even though the first of the discussions in the dialogue – the conversation between Socrates and Gorgias – is directly concerned with rhetoric itself, numerous remarks testify to its much wider character. This is best exemplified by the way of carrying out the conversation by Socrates, who, asking questions about rhetoric practised by Gorgias, throughout the whole conversation compares it with other skills. Additionally, the manner and the structure of the conversation prove that Plato considers the issue of rhetoric from a wider perspective determined by the issue of art. The specific feature of the conversation is ordering it around main issues – such notions as πρᾶγμα, ἐπιστήμη, δύναμις, each of which has its own meaning in Plato. In the first part of Gorgias Plato presents the principles previously occurring in other dialogues in a certain order, thus constructing the structure of the conversation with Gorgias. The notions are not novum in Plato but the fact that he clearly wants to systematise them and present a certain concept of art is a new and significant aspect. This tendency is of paramount importance for the discussion because Gorgias’ answers are evaluated by Plato from the perspective of this clearly set concept consisting of not only established notions but also certain principles. The discussion between Socrates and Gorgias introduces a theme which is crucial for the dialogue: the relation between art and good, i.e. the technical and ethical spheres. The issue is introduced by Gorgias, who mentions that rhetoric may be used for evil purposes. On this basis Socrates proves that if rhetoricians can use rhetoric for evil purposes, they have no knowledge concerning the subject of their art – justice, because one who knows what is just, always acts justly. Thus the relation between the technical and ethical spheres transpires to be the main point of contention. The question is whether a technician following the principles of the art he practices may act against good. This paradoxical statement based on the well-known Socrates’ principle "nemo sua sponte peccat" acquires philosophical foundations in the dialogue. In its remaining two parts Plato presents a justification, placing the principle within the framework of a certain concept of art, as a result of which not only rhetoric but also many other skills are criticised. The notions on which the conversation with Gorgias focuses are more precisely defined in the subsequent parts of the dialogue. Additionally, Plato presents twice the conditions which art should fulfill. They oblige the “technicians” to know the nature and purpose of the art and to know the causes of undertaken activities and to be able to justify them. These conditions determine the relation between the two spheres – technical and ethical. According to Plato, art may not act against good because it should be the objective of its activities. Certain concepts of good and knowledge outlined in the dialogue are the guarantees of “technicality”. Good, which should be respected by every art, is understood objectively and is contrasted with subjective pleasure. Knowledge, which should be the basis of art, opposes experience, which uses observation and recollection. Additionally, the definition of knowledge, significance of order in the world assuming the form of “geometrical equality”, significance of mathematics becoming the ideal of exactness indicate that Plato’s concept of knowledge is formed in Gorgias. These conclusions render it impossible that the results of any activity deserving the name of art should oppose good. And this is Plato’s main reproach of Gorgias’ concept, who wrote about false speeches possessing the power of conviction because they were written according to the principles proof of art or who defined tragedy as “a deceit, where he who cheats is more just than he who does not and the cheated is wiser than he who was not cheated”. Such determination of the relation between the technical and ethical sphere resulted from Gorgias’ concept of the world and fundamental philosophical principles. The whole concept of art described by Plato in the dialogue opposes the view presented by Gorgias. According to Plato, every technical activity has a defined object (ἔργον), is based on knowledge (ἐπιστήμη) and is always aimed at the good of human soul or body. The danger revealed and presented in the dialogue by Plato exists in the very concept of art presented by Gorgias, i.e. in its empirical foundations and the resulting understanding of the relation between art and good. Gorgias’ concept of art based on empirical cognition, which concerns the world of phenomena and rejects the possibility of perfect knowledge, leads, according to Plato, to a dangerous falsification of the relation between art and good. Plato proves that this weakness of Gorgias’ concept is revealed when confronted with these representatives of “the magnificent art” who are not protected against radicalism by the adherence to the moral tradition. The comparison of two, completely contrasting concepts of art based on different philosophical understanding of knowledge and good is decisive for the criticism of rhetoric in Gorgias. The concept presented by Plato criticises contemporary rhetoric and sophistry but determines the direction of research of the real art of rhetoric. (shrink)

This chapter discusses the reception of Avicenna’s well-known “flying man” thought experiment in twelfth- and thirteenth-century Latin philosophy. The central claim is that the argumentative role of the thought experiment changed radically in the latter half of the thirteenth century. The earlier authors—Dominicus Gundissalinus, William of Auvergne, Peter of Spain, and John of la Rochelle—understood it as an ontological proof for the existence and/or the nature of the soul. By contrast, Matthew of Aquasparta and Vital du Four used the flying (...) man as an argument for the soul’s ability to be directly aware of itself. A detailed analysis of the views of these authors shows interesting philosophical differences between them and reveals how one of the crucial premises of the original thought experiment—namely that the flying man is unaware of his body—loses its importance due to the changes in the argumentative role that is assigned to it. The most radical example of a new way of understanding bodily self-awareness is Peter Olivi’s so-called ‘man before the creation.’. (shrink)

It is now widely expected that climate change will be serious enough that a very large number of people will be displaced from their homes because of events relating to or resulting from climate change. Such events may include rising sea levels (and resulting increased salination of ground water), stronger hurricanes and tropical storms, drought, floods, increased and more intense wildfires, and other extreme or (previously) unusual weather events. Although estimates vary widely, it seems very likely that many millions of (...) people—perhaps hundreds of millions if sufficient precautions are not taken—will be forced from their homes by these events related to climate change. In the public imagination, much of the attention has been on ‘climate refugees’, where this is taken to mean people who have crossed borders. However, there is good reason to believe that a very large percentage—probably a significant majority—of displacement resulting from climate change will be, or could be, internal. In this chapter I argue that there are likely to be a large number of cases where internal displacement related to climate change is of international concern, and where, therefore, states have significant moral reasons to provide assistance, either directly to those displaced, or else to the state in which the displacement has taken place. My claim is that internal displacement arising from climate change is of international concern and so grounds a duty of aid by states able to provide it, when this displacement threatens the basic human rights of those displaced, and when the local or domestic government cannot or will not take the necessary steps to meet the needs and protect the rights of those who are displaced. (The uploaded version of this paper is an uncorrected proof. Please cite and refer to the published version.). (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)