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)

There is at least one immediate sense in which legal discourse is perspectival: it qualifies acts and facts in the world on the basis of rules. Legal concepts are for the most part constituted by rules, both in the sense that rules define these concepts’ semantic content and that, in order to engage with legal practice, we must act according to those rules, not necessarily complying with them but at least having them in mind. This is the distinctive perspective of (...) law: however, it would be misleading to think that this is the only perspective we can have in legal discourse. That of rule-constituted legal concepts is the fundamental perspective -- the inevitable presupposition of most legal assertions -- but other perspectives are possible on top of this fundamental background: perspectives on law, stemming from the basic perspective of law. -/- In this paper, I will try to argue that some different perspectives regarding law can be accounted for by analyzing different kinds of concepts that emerge in connection with legal institutions. My argument will consist of three steps as follows. First, I will explain how legal concepts are constituted by rules, referring in this regard to John Searle’s analysis of institutional concepts as it emerges in his Making the Social World, of 2010, and amending this analysis according to some criticisms that in 1986 Neil MacCormick had raised against Searle with specific reference to the legal domain. -/- Second, I will show that there are some kinds of concepts relevant for an institution which are not captured by Searle’s analysis in terms of constitutive rules, even if this is amended according to MacCormick’s criticisms. This I will do by considering the game of chess as a simple system of rule-constituted concepts (concepts such as 'checkmate,' 'bishop,' 'king'). I will consider four examples of perfectly legitimate assertions regarding a match of chess -- these being (1) ‘I won’; (2) 'you made a good attack'; (3) 'you are cheating'; (4) 'you made good use of the first-move advantage,' and I will show that, while the first three assertions can be analyzed in terms of concepts (those of 'victory,' 'attack,' and 'cheating') which are not constituted by the rules of chess but are rather common to several different competitive games, being typical of the broader practice of competitive game-playing of which chess is an instance, the fourth assertion includes a concept (that of 'first-move advantage') which is peculiar to chess, just like a rule-constituted element, but is not constituted by the rules of chess. This analysis will lead to a new categorization of institutional concepts. Apart from rule-constituted institutional concepts, which are the only ones recognized by Searle, in order to account for cases (1), (2), and (3) I will distinguish between three kinds of meta-institutional concepts, namely, goal-oriented, mode-oriented, and value-oriented meta-institutional concepts, and then I will introduce the category of para-institutional concepts to account for case (4). -/- Finally -- and this is the third step of my argument -- I will explain how these different kinds of institutional concepts appear when we adopt different perspectives on the institutional frameworks we deal with. This will lead us to a categorization of possible perspectives regarding law that corresponds to the previous one regarding concepts. There is first a structural perspective regarding the instantiation of institutional elements which clearly involves rule-constituted institutional concepts -- as when we say 'I am making a will.' There is then a teleological perspective regarding the goal of our institutional acts which calls into question goal-oriented meta-institutional concepts -- as when we say 'I wrote that will in order for you to have a distinctive right to my property.' Then, we can adopt a strategical perspective regarding some peculiar ways in which institutional acts can be performed, and this has often to do with mode-oriented meta-institutional concepts -- as when we say 'the Labour Party is making parliamentary obstructionism so that the Government will fall before the enactment of the labour reform,' or 'workers start today a work-to-rule action.' Clearly, we can also adopt an evaluative perspective over institutional facts or acts, and here typically value oriented meta-institutional concepts emerge -- as when we say 'that rule is clearly unjust' or 'that contract is unfair.' Finally, we can limit ourselves to a descriptive perspective on phenomena which are peculiar to a given institutional setting, and here para-institutional concepts are often useful -- as when we say 'the Italian electoral system before 1990 led to a sort of reform paralysis' or 'a strict use of the criterion requiring proof beyond any reasonable doubt can be expected to entail a low conviction rate.'. (shrink)

Presumption is a complex concept in law, affecting the dialogue setting. However, it is not clear how presumptions work in everyday argumentation, in which the concept of “plausible argumentation” seems to encompass all kinds of inferences. By analyzing the legal notion of presumption, it appears that this type of reasoning combines argument schemes with reasoning from ignorance. Presumptive reasoning can be considered a particular form of reasoning, which needs positive or negative evidence to carry a probative weight on the (...) conclusion. For this reason, presumptions shift the burden of providing evidence or explanations onto the interlocutor. The latter can provide new information or fail to do so: whereas in the first case the new information rebuts the presumption, in the second case, the absence of information that the interlocutor could reasonably provide strengthen the conclusion of the presumptive reasoning. In both cases the result of the presumption is to strengthen the conclusion of the reasoning from lack of evidence. As shown in the legal cases, the effect of presumption is to shift the burden of proof to the interlocutor; however, the shift a presumption effects is only the shift of the evidential burden, or the burden of completing the incomplete knowledge from which the conclusion was drawn. The burden of persuasion remains on the proponent of the presumption. On the contrary, reasoning from definition in law is a conclusive proof, and shifts to the other party the burden to prove the contrary. This crucial difference can be applied to everyday argumentation: natural arguments can be divided into dialectical and presumptive arguments, leading to conclusions materially different in strength. -/- . (shrink)

Proof by refutation of a geometry theorem that is not universally true produces a Gröbner basis whose elements, called side polynomials, may be used to give inequations that can be added to the hypotheses to give a valid theorem. We show that (in a certain sense) all possible subsidiary conditions are implied by those obtained from the basis; that what we call the kind of truth of the theorem may be derived from the basis; and that the side polynomials (...) may be classified in a useful way. We analyse the relationship between side polynomials and kinds of truth, and we give a unified algorithmic treatment of side polynomials, with examples generated by an implementation. (shrink)

ABSTRACT This part of the series has a dual purpose. In the first place we will discuss two kinds of theories of proof. The first kind will be called a theory of linear proof. The second has been called a theory of suppositional proof. The term "natural deduction" has often and correctly been used to refer to the second kind of theory, but I shall not do so here because many of the theories so-called are not (...) of the second kind--they must be thought of either as disguised linear theories or theories of a third kind (see postscript below). The second purpose of this part is 25 to develop some of the main ideas needed in constructing a comprehensive theory of proof. The reason for choosing the linear and suppositional theories for this purpose is because the linear theory includes only rules of a very simple nature, and the suppositional theory can be seen as the result of making the linear theory more comprehensive. CORRECTION: At the time these articles were written the word ‘proof’ especially in the phrase ‘proof from hypotheses’ was widely used to refer to what were earlier and are now called deductions. I ask your forgiveness. I have forgiven Church and Henkin who misled me. (shrink)

I argue that what determines whether a science is ‘formal’ or ‘empirical’ is not the ontological status of its objects of study, but, rather, its methodology. Since all sciences aim at generalizations, and generalizations concern types, if types are abstract (non-spatiotemporal) objects, then all sciences are concerned to discover the nature of certain abstract objects. What distinguishes empirical from formal sciences is how they study such things. If the types of a science have observable instances (‘tokens’), then the nature of (...) the types may be determined empirically. If the types have either abstract tokens, or no tokens at all, their nature must be determined by non-empirical methods involving intuition, reasoning and proof. I conclude that the status of (theoretical) linguistics depends on the methodologies of syntax, semantics, phonology, morphology and orthography (and any other subdiscipline that is concerned with the study of the structure of language). (shrink)

In this chapter we introduce concepts for analyzing proofs, and for analyzing undergraduate and beginning graduate mathematics students’ proving abilities. We discuss how coordination of these two analyses can be used to improve students’ ability to construct proofs. -/- For this purpose, we need a richer framework for keeping track of students’ progress than the everyday one used by mathematicians. We need to know more than that a particular student can, or cannot, prove theorems by induction or contradiction or can, (...) or cannot, prove certain theorems in beginning set theory or analysis. It is more useful to describe a student’s work in terms of a finer-grained framework that includes various smaller abilities that contribute to proving and that can be learned in differing ways and at differing periods of a student’s development. (shrink)

1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for improvement (...) of mathematical education. The present article presupposes the previous one. Herein we develop our ideas of the purposes of a theory of proof and the criterion of success to be applied to such theories. In addition we speculate at length concerning the specific kinds of uses to which a successful theory of proof may be put vis-a-vis improvement of various aspects of mathematical education. The final article will deal with the construction of such a theory. The 1st is the 1971. Discourse Grammars and the Structure of Mathematical Reasoning I: Mathematical Reasoning and Stratification of Language, Journal of Structural Learning 3, #1, 55–74. https://www.academia.edu/s/fb081b1886?source=link . (shrink)

This paper explains a way of understanding Kant's proof of God's existence in the Critique of Practical Reason that has hitherto gone unnoticed and argues that this interpretation possesses several advantages over its rivals. By first looking at examples where Kant indicates the role that faith plays in moral life and then reconstructing the proof of the second Critique with this in view, I argue that, for Kant, we must adopt a certain conception of the highest good, and (...) so also must choose to believe in the kind of God that can make it possible, because this is essentially a way of actively striving for virtue. One advantage of this interpretation, I argue, is that it is able to make sense of the strong link Kant draws between morality and religion. (shrink)

This chapter discusses Kant's 1763 "possibility proof" for the existence of God. I first provide a reconstruction of the proof in its two stages, and then revisit my earlier argument according to which the being the proof delivers threatens to be a Spinozistic-panentheistic God—a being whose properties include the entire spatio-temporal universe—rather than the traditional, ontologically distinct God of biblical monotheism. I go on to evaluate some recent alternative readings that have sought to avoid this result by (...) arguing that the relevant facts about real modality can be ultimately grounded in God’s powers or thoughts – or that Kant just leaves the grounding relations mysterious. I argue that the textual and philosophical costs of each of these alternative readings are formidable. The chapter concludes with a discussion of the fate of the proof in the critical period. Some commentators think that it disappears altogether, or that it is downgraded such that it produces a mere regulative idea of God as the most real being. I suggest that the proof survives but that the mode of assent it licenses towards its conclusion changes from knowledge to a certain kind of Belief (Glaube). (shrink)

This chapter discusses Kant's 1763 "possibility proof" for the existence of God. I first provide a reconstruction of the proof in its two stages, and then revisit my earlier argument according to which the being the proof delivers threatens to be a Spinozistic-panentheistic God—a being whose properties include the entire spatio-temporal universe—rather than the traditional, ontologically distinct God of biblical monotheism. I go on to evaluate some recent alternative readings that have sought to avoid this result by (...) arguing that the relevant facts about real modality can be ultimately grounded in God’s powers or thoughts – or that Kant just leaves the grounding relations mysterious. I argue that the textual and philosophical costs of each of these alternative readings are formidable. The chapter concludes with a discussion of the fate of the proof in the critical period. Some commentators think that it disappears altogether, or that it is downgraded such that it produces a mere regulative idea of God as the most real being. I suggest that the proof survives but that the mode of assent it licenses towards its conclusion changes from knowledge to a certain kind of Belief (Glaube). (shrink)

Most human actions are complex, but some of them are basic. Which are these? In this paper, I address this question by invoking slips, a common kind of mistake. The proposal is this: an action is basic if and only if it is not possible to slip in performing it. The argument discusses some well-established results from the psychology of language production in the context of a philosophical theory of action. In the end, the proposed criterion is applied to discuss (...) some well-known theories of basic actions. (shrink)

An adequate semantics for generic sentences must stake out positions across a range of contested territory in philosophy and linguistics. For this reason the study of generic sentences is a venue for investigating different frameworks for understanding human rationality as manifested in linguistic phenomena such as quantification, classification of individuals under kinds, defeasible reasoning, and intensionality. Despite the wide variety of semantic theories developed for generic sentences, to date these theories have been almost universally model-theoretic and representational. This essay (...) outlines a range of proof-theoretic analyses for characterizing generics. Particular attention is given to an expressivist proof-theory that can be traced to 1) work on logical syntax that Carnap undertook prior to his turn toward truth-conditional model theory in the late 1930s, and 2) research on sequent calculi and natural deduction systems that originate in work from Gentzen and Prawitz.11 This essay offers a more precise exposition of some of the material discussed in the first two chapters of my dissertation (Stovall Citation2015a). These ideas developed in the context of a working group on non-monotonic logic run by Robert Brandom, and they were subsequently clarified through the work of Nissim Francez (particularly Francez Citation2015). I am indebted to many people for feedback and criticism on this essay, though I am sure none among them would agree with everything I say and do here. I would particularly like to thank Brandom, Francez, Ulf Hlobil, Daniel Kaplan, Jared Millson, Bernhard Nickel, Jaroslav Peregrin, Jeffry Pelletier, Thomas Ricketts, Mark Risjord, Shawn Standefer, and two reviewers for this journal. Work on this essay was supported by the joint Lead-Agency research grant between the Austrian Science Foundation (FWF) and the Czech Science Foundation (GAČR), Inferentialism and Collective Intentionality, GF17-33808L. It was substantially revised prior to its final submission. (shrink)

Mümkün varlıkları aracı kılmadan Vâcibü’l-Vücûd’un varlığını ispatlama çabalarının bir sonucu olan sıddıkîn burhanı ilk defa Müslüman filozoflar tarafından dillendirildi. İbn Sînâ (ö. 428/1037) da Fârâbî’nin etkisiyle yeni bir burhan açıkladı ve buna sıddıkîn adını verdi. Molla Sadrâ (ö. 1050/1641) varlığın asaleti ilkesini mutasavvıflardan, teşkîk ilkesini de Sühreverdî’den iktibas ederek yeni bir sıddıkîn burhanı dillendirdi. Bu burhanın, varlığın asaleti, basîtliği/yalınlığı, teşkîkî ve ma’lûlün illete ihtiyacı olmak üzere bazı öncülleri vardır. O, bu öncülleri açıkladıktan sonra teselsüle ihtiyaç duymadan Vâcibü’l-Vücûd’un varlığını ispatlar. Onun (...) burhanı diğer sıddıkîn burhanlarına nispetle bazı üstün özelliklere sahiptir. Öncelikle bu burhan varlığın asaleti ilkesi üzerine bina edildiğinden dayanağı varlık kavramı değil, varlığın nesnel hakikatidir. İkincisi bu burhan Vâcibü’l-Vücûd’un zâtını ispatlamakla birlikte Vâcibü’l-Vücûd’un birliğini ve kemâlî sıfatlarını ispatlar. Üçüncüsü bu burhana göre mümkün varlıklar hiçbir aracı olmadan Vâcibü’l-Vücûd’a bağımlı olduklarından burhanın açıklanmasında teselsül ve kısır döngüden yararlanma ihtiyacı yoktur. Molla Sadrâ’nın teselsül ve kısır döngüden de yararlanarak Vâcibü’l-Vücûd’un varlığını ispatladığı burhanlar da vardır. Molla Sadrâ bu burhanıyla hem Vâcibü’l-Vücûd’un varlığını ve hem de onun kemâlî sıfatlarını ispatladığını iddia eder. Bu çalışmada bu iddia incelecek ve ispat-ı vacip meselesinde Molla Sadrâ’nın ne gibi yenilikler getirdiği ele alınacaktır. ABSTRACT A result of the attempts to prove the existence of The Necessary Existence without the mediation of possible beings, proof of the truthful was first expressed by Muslim philosophers called it sıddıkin. Mullā Ṣadrā’s “proof” that he explains has certain premises such as the fundamental of existence, indivisibility of the existence, existential gradation, effect’s need for cause. After explanining these premises, Mullā Ṣadrā then proves the Necessary Existence without needing succession. Mullā Ṣadrā’s proof of the truthful has certain superior features tan the proofs of truthful expressed before him. First of all, as this proof is built upon the principle of the fundamental of existence, its foundation is the external truth of existence, not the concept of existence itself. Secondly, this proof proves the unity and perfection attributes of The Necessary Existence as well as proving the existence of the Necessary Existence. Thirdly, according to this proof, as all possible existences are dependent on The Necessary Existence without any mediation, there is no need to benefit from succession and vicious circle in explaining the proof. However, Mullā Ṣadrā proves the Necessary Existence by benefitting from succession and vicious circle in other proofs. Mullā Ṣadrā asserts that this proof demonstrates the presence of The Necessary Existence and its perfection attributions. This study examines this assertion and addresses what kind of innovations was brought by Mullā Ṣadrā in terms of proving The Necessary Existence. (shrink)

After introductory reminder of and comments on Gödel’s ontological proof, we discuss the collapse of modalities, which is provable in Gödel’s ontological system GO. We argue that Gödel’s texts confirm modal collapse as intended consequence of his ontological system. Further, we aim to show that modal collapse properly fits into Gödel’s philosophical views, especially into his ontology of separation and union of force and fact, as well as into his cosmological theory of the nonobjectivity of the lapse of time. (...) As a result, modal collapse should not be conceived in Gödel so much as a deficit, but rather as a kind of the rise of modalities to the “perfect” being. We further show that, in accordance with Gödel’s ontology, the concepts of modality and time should be derived in terms of the “fundamental philosophical concept” of cause. To give an example of how a formalization of such causative Gödelian ontology and ontological proof might look, we propose the transformation of GO into a kind of causally re-interpreted justification logic. (shrink)

At first sight the Theory of Computation i) relies on a kind of mathematics based on the notion of potential infinity; ii) its theoretical organization is irreducible to an axiomatic one; rather it is organized in order to solve a problem: “What is a computation?”; iii) it makes essential use of doubly negated propositions of non-classical logic, in particular in the word expressions of the Church-Turing’s thesis; iv) its arguments include ad absurdum proofs. Under such aspects, it is like many (...) other scientific theories, in particular the first theories of both mechanical machines and heat machines. A more accurate examination of Theory of Computation shows a difference from the above mentioned theories in its essentially including an odd notion, “thesis”, to which no theorem corresponds. On the other hand, arguments of each of the other theories conclude a doubly negative predicate which then, by applying the inverse translation of the ‘negative one’, is translated into the corresponding affirmative predicate. By also taking into account three criticisms to the current Theory of Computation a rational re-formulation of it is sketched out; to Turing-Church thesis of the usual theory corresponds a similar proposition, yet connecting physical total computation functions with constructive mathematical total computation functions. -/- . (shrink)

For Aristotle, the shape of a physical body is perceptible per se (DA II.6, 418a8-9). As I read his position, shape is thus a causal power, as a physical body can affect our sense organs simply in virtue of possessing it. But this invites a challenge. If shape is an intrinsically powerful property, and indeed an intrinsically perceptible one, then why are the objects of geometrical reasoning, as such, inert and imperceptible? I here address Aristotle’s answer to that problem, focusing (...) on the version of it that he presents in De caelo III.8. I argue that if we grant that Aristotle conceived of the shape of a sensible body as some kind of causal power, then the satisfactory resolution of that challenge pushes us to interpret him as having conceived of it as being, more specifically, an impure power—that is, as a property that is not only intrinsically powerful but also, in some way, intrinsically non-powerful as well. This is a notable result not only insofar as it illuminates Aristotle’s conception of shape but also insofar as it contributes to our knowledge of Aristotle’s theory of dunameis and his ontology more broadly. (shrink)

You can be convinced that something is true but still desire to see it for yourself. A trusted critic makes some observations about a movie, now you want to watch it with them in mind. A proof demonstrates the validity of a formula, but you are not satisfied until you see how the formula works. In these cases, we place special value on knowing by what Sosa (2021) calls “firsthand insight” a truth that we might already know in some (...) other way such as by testimony, the balance of evidence, or proof. This phenomenon raises two questions. First, what is the nature of firsthand insight? Second, what value motivates us to pursue firsthand insight when other kinds of knowledge are readily available? In the two central parts of this paper, I develop answers to these questions. I argue that firsthand insight that a proposition is true is knowledge based on experience of what makes that proposition true, and I argue that desires for firsthand insight are motivated by concerns with alienation. In a concluding section, I briefly illustrate how the resulting view of the nature and value of firsthand insight might bear on broader topics in the theory of value. (shrink)

I argue for a kind of logical pluralism on the basis of a difficulty with defining the meaning of negation in the framework of Dummett's and Prawitz' proof-theoretic semantics.

Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due (...) to Gauss and Eisenstein, and a sophisticated proof using algebraic number theory, due to Hilbert. Philosophers have yet to look carefully at such explanatory disagreements in mathematics. I do so here. According to the view I defend, there are two important explanatory virtues—depth and transparency—which different proofs (and other potential explanations) possess to different degrees. Although not mutually exclusive in principle, the packages of features associated with the two stand in some tension with one another, so that very deep explanations are rarely transparent, and vice versa. After developing the theory of depth and transparency and applying it to the case of quadratic reciprocity, I draw some morals about the nature of mathematical explanation. (shrink)

In recent years, there has been a growing interest in truthmaker semantics as a framework for understanding a range of phenomena in philosophy and linguistics. Despite this interest, there has been limited study of the various logics that arise from the semantics. This paper aims to address this gap by exploring numerous ‘truthmaker logics’ and proving their compactness and decidability. This is in continuation with the inquiry of Fine and Jago (2019), who proved compactness and decidability for a particular kind (...) of truthmaker logic. The key results going into this are (1) ‘standard translations’ into first-order logic; (2) a truthmaker analogue of the finite model property; and (3) a proof showing that truthmaker consequence on semilattices coincides with truthmaker consequence on complete lattices. Finally, the connection with modal logic is examined. Specifically, it is illustrated how endowing truthmaker semantics with classical negation results in modal information logics. (shrink)

Sometimes we love and hate the same thing at the same time. Margaret Cavendish (1623-1673)—the maverick early modern materialist—appeals to this type of passionate conflict to argue that the mind is a material thing. When our passions conflict, the mind or reason conflicts with itself. From this Cavendish infers that the mind has parts and, therefore, is material. Cavendish says this argument is among the best proofs of the mind’s materiality. And yet, the existing scholarship on Cavendish lacks the kind (...) of detailed reconstruction required to evaluate this argument’s merits. In this paper, I provide just such a reconstruction. I also show that Cavendish’s argument is an effective intervention in her dispute with René Descartes and Henry More about the (im)materiality of the mind. (shrink)

Kant’s third question (“What may I hope?”) is underdiscussed in comparison to the other two, even though he himself took it to be the question that united his efforts in theoretical and practical philosophy. This is largely his own fault: in his discussion of the question he moves quickly from talking about rational hope to discussing the kind of Belief or faith (Glaube) that grounds it. Moreover, the canonical statements of his own moral proof do not seem to give (...) hope any essential role to play. In this chapter I first consider the ways in which pre-Kantian authors muddied the distinction between what we would call “hope” and “expectation.” I then look at how Kant’s views about hope evolve to the point where, by the time of the “End of All Things” essay of 1794, he seems to endorse a kind of hopeful pessimism about our this-worldly situation, at least. I then examine a version of Kant’s moral proof that succeeds in locating a role for hope that is distinct from that of Belief, expectation, optimism, and so on. Finally, I turn to some contemporary work in two very different arenas – Anthropocene scholarship and Christian eschatology – in order to look at how the concepts of hope and optimism are deployed in those contexts. We will see that although some of the recent discourses about the “Good Anthropocene” slip beyond hope into full-blown optimism, most authors working on ecological and environmental topics are careful to keep the attitudes distinct. By contrast, there is a tendency among contemporary theologians to follow earlier Christian authors in slipping beyond mere hope to optimistic faith, and even to full-blown certainty. (shrink)

Tichý’s Transparent Intensional Logic (TIL) is an overarching logical framework apt for the analysis of all sorts of discourse, whether colloquial, scientific, mathematical or logical. The theory is a procedural (as opposed to denotational) one, according to which the meaning of an expression is an abstract, extra-linguistic procedure detailing what operations to apply to what procedural constituents to arrive at the product (if any) of the procedure that is the object denoted by the expression. Such procedures are rigorously defined as (...) TIL constructions. Though TIL analytical potential is very large, deduction in TIL has been rather neglected. Tichý defined a sequent calculus for pre-1988 TIL, that is TIL based on the simple theory of types. Since then no other attempt to define a proof calculus for TIL has been presented. The goal of this paper is to propose a generalization and adjustment of Tichý’s calculus to TIL 2010. First, I briefly recapitulate the rules of simple-typed calculus as presented by Tichý. Then, I propose the adjustments of the calculus so that it be applicable to hyperintensions within the ramified hierarchy of types. TIL operates with a single procedural semantics for all kinds of logical-semantic context, be it extensional, intensional or hyperintensional. I show that operating in a hyperintensional context is far from being technically trivial. Yet, it is feasible. To this end, we introduce a substitution method that operates on hyperintensions. It makes use of a four-place substitution function (called Sub) defined over hyperintensions. (shrink)

Hume appeals to different kinds of certainties and necessities in the Treatise. He contrasts the certainty that arises from intuition and demonstrative reasoning with the certainty that arises from causal reasoning. He denies that the causal maxim is absolutely or metaphysically necessary, but he nonetheless takes the causal maxim and ‘proofs’ to be necessary. The focus of this paper is the certainty and necessity involved in Hume’s concept of knowledge. I defend the view that intuitive certainty, in particular, is (...) certainty of the invariability or necessity of relations between ideas. Against David Owen and Helen Beebee, I argue that the certainty involved in intuition depends on the activity of the mind. I argue, further, that understanding this activity helps us understand more clearly one of Hume’s most important theses, namely that experience is the source of a distinct kind of certainty and of necessity. (shrink)

The nature of Kant’s criticism of his pre-Critical ‘possibility proof’ for the existence of God, implicit in the account of the Transcendental Ideal in the Critique of Pure Reason, is still under dispute. Two issues are at stake: the error in the proof and diagnosis of the reason for committing it. I offer a new way to connect these issues. In contrast with accounts that locate the motivation for the error in reason’s interest in an unconditioned causal ground (...) of all contingent existence, I argue that it lies in reason’s interest in another kind of unconditioned ground, collective unity. Unlike the conception of the former, that of the latter directly explains the problematic ontological assumption of the possibility proof, the existence of intelligible objects as the ground of possibility. I argue that such Platonic entities are assumed because they are amenable to the kind of unity prescribed by reason. However, since the interest in collective unity has a legitimate regulative use when applied to the systematic unity of nature, the conception of God entailed by the possibility proof is retained as a regulative idea of reason. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation needs (...) philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. A comparison to Mach’s doctrine is used to be revealed the fundamental and philosophical reductionism of Husserl’s phenomenology leading to a kind of Pythagoreanism in the final analysis. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. Thus the problem which of the two mathematics is more relevant to our being is discussed. An information interpretation of the Schrödinger equation is involved to illustrate the above problem. (shrink)

Over almost a half-century, evidence law scholars and philosophers have contended with what have come to be called the “Proof Paradoxes.” In brief, the following sort of paradox arises: Factfinders in criminal and civil trials are charged with reaching a verdict if the evidence presented meets a particular standard of proof—beyond a reasonable doubt, in criminal cases, and preponderance of the evidence, in civil trials. It seems that purely statistical evidence can suffice for just such a level of (...) certainty in a variety of cases where our intuition is that it would nonetheless be wrong to convict the defendant, or find in favor of the plaintiff, on merely statistical evidence. So, we either have to convict with statistical evidence, in spite of an intuition that this is unsettling, or else explain what (dispositive) deficiency statistical evidence has. -/- Most scholars have tried to justify the resistance to relying on merely statistical evidence: by relying on epistemic deficiencies in this kind of evidence; by relying on court practice; and also by reference to the psychological literature. In fact, I argue, the epistemic deficiencies philosophers and legal scholars allege are suspect. And, I argue, while scholars often discuss unfairness to civil defendants, they ignore a long history of relying on statistical evidence in a variety of civil matters, including employment discrimination, toxic torts, and market share liability cases. Were the dominant arguments in the literature to prevail, it would extremely difficult for plaintiffs to recover in a variety of cases. -/- The various considerations I advance lead to the conclusion that when it comes to naked statistical evidence, philosophers and legal scholars who argue for its insufficiency have been caught with their pants down. (shrink)

This paper defends the Principle of Sufficient Reason, taking Baumgarten as its guide. The primary aim is not to vindicate the principle, but rather to explore the kinds of resources Baumgarten originally thought sufficient to justify the PSR against its early opponents. The paper also considers Baumgarten’s possible responses to Kant’s pre-Critical objections to the proof of the PSR. The paper finds that Baumgarten possesses reasonable responses to all these objections. While the paper notes that in the absence (...) of a response to Kant’s Critical discussion of the PSR, this result does not vindicate the principle, it shows how this discussion provides a deeper understanding of what, according to Baumgarten, the PSR really assumes and intends, and prepares the way for a more responsible discussion of Kant’s critical objections to Baumgarten’s supposed proof. (shrink)

St. Thomas’s Third Way to prove the existence of God, “Of Possibility and Necessity” (ST 1, q.2, art. 3, response) is one of the most controverted passages in the entire Thomistic corpus. The central point of dispute is that if there were only possible beings, each at some time would cease to exist and, therefore, at some point in time nothing would exist, and because something cannot come from nothing, in such an eventuality, nothing would exist now—a reductio ad absurdum (...) conclusion. Therefore, at least one necessary being must exist. Generations of critics and defenders have contended over St. Thomas’s proof. This article argues that the principle of pros hen analogy is implicit in the Third Way and that once identified explains the ontological dependency of possible beings, as secondary analogates, on the first necessary being, as primary analogate. Thus, without the necessary being as primary analogate, possible beings simply could not exist. The fact that they do exist is evidence for the existence of the necessary being. St. Thomas makes synthesizes the principle of pros hen analogy, as found in Aristotle’s Metaphysics, with the Neoplatonic principle of participation. Aristotle develops pros hen analogy in contradistinction to univocal and equivocal predication as well as to genus in Metaphysics 4.2, 11.3, 12.3-5. Since Scotus and re-enforced by modern analytic logic, philosophers have almost universally regarded any kind of analogical predication as a sub-category of equivocal predication and, thus, implicitly occlude the possibility of considering pros hen analogy in their readings of the Third Way. Distinction of per se and per accidens infinite regress and of radical and natural contingency are also central to understanding the Third Way. While resolving apparent problems in the Third Way, the article also seeks to rehabilitate the doctrine of pros hen analogy as a basic principle in Thomistic and, indeed, Aristotelian metaphysics. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted (...) rather a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

FROM THE HISTORY OF PHYSICS TO THE DISCOVERY OF THE FOUNDATIONS OF PHYSICS By Antonino Drago, formerly at Naples University “Federico II”, Italy – drago@unina,.it (Size : 391.800 bytes 75,400 words) The book summarizes a half a century author’s work on the foundations of physics. For the forst time is established a level of discourse on theoretical physics which at the same time is philosophical in nature (kinds of infinity, kinds of organization) and formal (kinds of mathematics, (...) kinds of logic). This double side of the two dichotomies assures a deep comprehension of theoretical physics by avoiding both a purely philosophical analysis and a purely formal analysis, each manifestly insufficient for representing all the aspects of theoretical physics. Among the many formulations of a physical theory, e.g. Mechanics, also Mach(1) recognized technical differences only, Instead my suggestion is to consider their differences as revealing the characteristic features of their foundations. No more radical differences may exist than those concerning both their kinds of Mathematics and their kinds of Logic. As a fact, after the 20th Century within each of these sciences there exist two antagonist foundations, within Mathematics either the classical one or the constructive one(2); within Mathematical Logic either the classical logic or the intuitionist one(3). Let us take Mechanics as an instance. Being the choices of the Newton’s formulation respectively the actual infinity of the differential equations relying on the infinitesimals and the classical logic, a formulation based on the alternative choices is Lazare Carnot’s,(4) whose mathematics is no more than algebraic-trigonometric and the logic is the intuitionist one, because this formulation makes use of doubly negated propositions, whose corresponding affirmative propositions are idealistic or false; i.e. in these cases the law of double negation fails, as in intuitionist logic occurs. By considering these two dichotomies as the foundations of the physical theories, each couple of choices upon them fashions one out four models of scientific theory, which are baptized through the authors of their most representative theories: Newtonian, Carnotian, Lagrangian, Descartesian. In correspondence four versions of the principle of inertia are recognized, as suggested by respectively: Descartes. Lazare Carnot, Enriques and Cavalieri.(5) All that suggests that the four models of scientific theory may be graphically represented as a compass orientating our minds amid the so numerous physical theories. By taking these dichotomies as interpretative categories, a new interpretative history of Physics including both classical and modern physics results according to a quadrilinear development. The birth of modern physics is characterized by the two theories - Einstein’s paper on special relativity and Einstein’s first paper on quanta - whose choices are the alternative ones to those of the previously dominant physical theory, Newtonian mechanics: in the latter paper Einstein i) declares the dichotomy on the kinds of mathematics (“Introduction”) and then he chooses the discrete mathematics; ii) by using doubly negated propositions he organizes his theory in an alternative way to the deductive-axiomatic one.(6) Moreover, a new history of Philosophy of knowledge results. Kant’s first two a priori transcendental categories represent the physical interpretation of the two choices out of the four pairs of choices on the two dichotomies, i.e. the choices of the dominant theory of mechanics, Newton’s. Hegel’s dialectic was a misleading attempt of anticipating the subsequent intuitionist logic. The book starts by a comparison of different formulations of thermodynamics in order to recognize the first dichotomy on the kind of organization. In chapter 2 the dichotomy on the kind of infinity is recognized through a comparison of Newrton’s mechanics and Lazare Carnot’s. A quickly history of the other classical physical theories is illustrated in chapter 3; it results a foundational conflict between the last two theories, and hence a conflict between their opposite couples of choices. The two main theories of modern physics, special realtivity and quantum mechanics confirm the foundational role played by the two dichotomies which gives reason for the radical change in the history of theoretical physics. Indeed, the opposition of the two main pairs of choices gives reason of the crisis in theoretical physics in the early 1900s. As a global result, the book represents the first interpretation of the entire history of Physics, both classical and modern; This fact proves that the four models of scientific theories can works as a compass (that of the front cover) suggesting a direction among the many physical theories. This new history of physics leads to re-visit both Koyré’s and Kuhn’s historiographies. Their interpretative categories are interpreted and explained through the two dichotomies so that it is possible to suggest à la Koyré categories based on the alternative choices theories to Newton’s as the suitable categories for interpreting the alternative theories to Newton’s mechanics. All that suggests a new interpretation of the crucial step in the history of Western philosophy of knowledge, i.e. the passage from Leibniz to Kant: Leibniz’s suggestion of the two labyrinths of human minds may be seen as a close anticipation of the two above dichotomies. Kant applied them in order to construct the well-known four cosmological proofs, which however he misinterpreted as leading to contradictions, instead to tow different methods of investigation corresponding to the two different kinds of logic.(7) Bibliography 1. Mach E. (1883), Die Mechanik, Leipzig: Brockhaus, Chap. IV, Sect. III. 2. Bishop E. (1967), Constructive Analysis, New York: Mc Graw-Hill. 3. Heyting A. (1962), Intuitionism. An Introduction, Amsterdam: North-Holland. 4. L. Carnot (1783), Essai on the Machines en général, Defay, Dijion (Enlish translation: Springer, Berlin, 2020). Drago A. (2004), “A new appraisal of old formulations of mechanics”, Am. J. Phys., 72(3), pp. 407-9. 5. Vella M.R. (2007), “Le quattro versioni del principio di inerzia”, in M. Leone et al. (eds.), L’eredità di Fermi, Majorana e altri Temi. Napoli: ESI, pp. 147-151. 6. Drago A. (2014), “The emergence of two options from Einstein°s first paper on Quanta”, in Pisano R., Capecchi D., Lukesova A. (eds.), Physics, Astronomy and Engineering. Critical Problems in the History of Science and Society, Scientia Socialis P., Siauliai, 2013, pp. 227-234. 7. This and all in the above points are illustrated by the book Drago A. (2017), Dalla Storia della Fisica ai Fondamenti della Scienza, Roma: Aracne. (shrink)

Epistemic conservatism maintains that some beliefs are immediately justified simply because they are believed. The intuitive implausibility of this claim sets the burden of proof against it. Some epistemic conservatives have sought to lessen this burden by limiting its scope, but I show that they cannot remove it entirely. The only hope for epistemic conservativism is to appeal to its theoretical fruit. However, such a defense is undercut by the introduction of phenomenal conservatism, which accomplishes the same work from (...) a more intuitive starting point. Thus, if one opts for conservatism, better to choose the phenomenal kind. (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)

It is a fact that there is ethical criticism about art. Art critics, the general public and even artists point out moral flaws in artworks while evaluating them. Philosophers, however, have maintained a hot debate on the meaning of such criticism. This debate can be understood as a disagreement about the kind of relation between the artistic value of artworks and their alleged moral value. While some claim that moral value can contribute to artistic value (moralism), others claim that there (...) cannot be such a contribution (autonomism). Since at least some works of architecture are artworks, that debate also concerns architecture. A moderate moralist view claims that some works of architecture have moral flaws/merits that bear on their artistic evaluation. In an apparently promising version, the contention is that some moral flaws/merits are aesthetically relevant. In this paper I argue against such contention and defend an autonomist view. Following some taxonomy remarks I distinguish the views in the debate and present two points in favour of autonomism: its simplicity and not having the burden of proof. Then I discuss Carroll’s merited response argument for moralism and I argue that in its best interpretation either it begs the question against autonomism or it is compatible with it. I conclude with some possible objections that may help further investigations on the subject. (shrink)

The paper presents and discusses the “which-is-which content of handedness,” the meaning of left as left and right as right, as a possible candidate for the idea of a genuine embodied cognitive content. After showing that the Ozma barrier, the non-transferability of the meaning of left and right, provides a kind of proof of the non-descriptive, indexical nature of the which-is-which content of handedness, arguments are presented which suggest that the classical representationalist account of cognition faces a perplexing problem (...) of underdetermination of reference of left and right in the which-is-which sense. By way of contrast, no such problems occur in a framework were embodied contents are not mediated by some extra body model which carries the representational power, but are instead directly represented. (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)

Religious experience is one of the fundamental problems of the philosophy of religion. Although it has entered the literature as a proof of God; discussions focus on its nature. The basic approaches to the nature of religious experience are: religious experience as a feeling, religious experience as a perception, religious experience as a comment. The main reason that makes the nature of religious experience controversial is that it consists of two concepts that have a wide range of meaning, such (...) as religion and experience. The meanings that individuals and traditions attach to these two concepts determine the understanding of religious experience. The beginning of religious experience as a term corresponds to the periods of Protestantism. With the emphasis of Enlightenment on the mind, the meanings attributed to religious experience have been reduced and narrowed. In the literature, religious experience is unclear, cannot be transferred to others, instant and extraordinary experiences. The preliminary acceptance of this article is that the meanings attributed to the term religious experience are narrowed and it is wrong to use the term in the same sense for different traditions. This article assumes that the reader knows the current discussion of the problem. Rather than reacting to the concerns of current debate, it takes a more proactive and pre-opener approach. Rather than reacting to the concerns of the current debate, it takes a more proactive approach to the subject. This paper will present a different reading of religious experience than the literature as a problem of the Philosophy of Religion. In this context, the concept of God, universe and human being in al-Ghazali will be firstly revealed as the ontological background of religious experience; then a description of the concept of religious experience will be proposed on this ontological basis. If you mean an experience related to religion, which is within religious boundaries with religious experience; Islam for a Muslim, that all experiences that cater to all aspects of human existence and religious boundaries cannot be the person to enter into any human experience that is experienced throughout the religious life. Certainly, here we can talk about the experiences that religion has ordered and forbidden, or in other words, experiences that religion regards as positive or negative. If an experience related to God is meant for religious experience, here are two cases: when the truth comes to the essence and attributes of God, the human experience does not reach there and in this sense, a religious experience is not possible. If the acts of God are mentioned; all the experiences that people live in are religious in this sense, because everything outside of their own is a deed of God, and whatever happens in the world of being, takes place within God's deeds. Here, too, whether or not people are aware of it, can be mentioned in other words, from conscious and unconscious religious experiences, which is the deciding factor. Faith, then, can be regarded as the first step of the conscious religious experience. If you are referring to experiences that seem to be unusual for those who are religious and have no religious experience, it is an extraordinary experience to go on a journey itself, compared to not going on a journey. That is to say, the faith itself, which is to ascend to a journey to perfection, is an extraordinary experience compared to those who are not on this path, that is, those who do not have it. For instance for children, the experiences of the elders are extraordinary, and therefore being ordinary and extraordinary is a relative concept. It is necessary to acknowledge the differences in conscious religious experiences mentioned above in the meaning of intense and deep living in themselves. There is a deeper and more intense experience that expresses progress in a journey that leads to God in the sense of the strengthening of faith. This is the kind of experience that most people have not experienced in this sense that the task of the person who is experienced in his own journey is not to stick to them and continue on their way. So living out of order for a Muslim is seen as a barrier that must be encountered and which should not be lingered on, while experiencing something extraordinary has a distinctive place for religious experience in current debates. The issue is not that they cannot be explained but they are not deliberately explained due to the fear of misunderstanding. This can be regarded as a method of education that older adults use to train minors. As a result, if we would define a religious experience according to al-Ghazali, we can say that religion is a journey made towards God, and religious experience is the experience of traveling to God. Traveling to him means to get close to Him, but this approach is not in spatial means but in perfection means. So, religious experience is the journey to perfection of the man himself. Man's perfection is to have the attributes of God who have absolute perfection. These attributes are present in man's own essence. What a person must do, is to place an effort to make these virtual adjectives real. This journey is basically an existential necessity as it provides the happiness that is essential to human existence. In this journey, which can be understood as becoming a human being who was born as a human being. It should also be added that it is not possible to be absolutely perfect and to reach the reality of God himself in this endless journey of perfection. Therefore, the absolute perfection belongs to God, and it is necessary to understand the concept of perfect human being as a person who has traveled in the journey to perfection. (shrink)

I propose and articulate a novel theory of desire, called the Revised Reward Theory. As the name suggests, the theory is based—and expands—on Arpaly and Schroeder’s (2014) Reward Theory of Desire. The initial Reward Theory identifies desires with states of the reward learning system such that for an organism to desire some P is for its reward system to treat P as a reward upon receipt. The Revised Reward Theory identifies desires with a different state of the same system, such (...) that for an organism to desire some P is for its reward system to expect or predict that P will be rewarding (roughly) prior to receipt. The difference amounts to equating desires with what we ultimately find rewarding or satisfying versus those that underlie our motivations to obtain that which we take ourselves to desire. I argue that the structure of the reward system is incompatible with the original Reward Theory but compatible with the Revised Reward Theory. I demonstrate that this difference has important philosophical implications. I focus on moral responsibility and demonstrate Arpaly and Schroeder’s argument, that addiction can mitigate moral responsibility, turns on this precise difference. Arpaly, Schroeder, and I all ascribe to a meta-theory called ‘natural kindism’ which identifies mental kinds with neurocognitive kinds. This discussion, in addition to defending a theory of desire, is intended to act as a proof of concept for natural kindism as offering a powerful framework for relating empirical results to philosophical issues. (shrink)

Frege's puzzle about propositional attitude reports is considered. Proposed solution: Every utterance comes from the world model of the speaker, and sometimes it may contain references to (speaker's models of) other world models. More generally, every sentence comes from some kind of world model. It may be the world model of a (real or imagined) person, the world model represented in a novel, movie, scientific book, virtual reality, etc. In principle, even smaller informational units (stories, poems, newspaper articles, jokes, mathematical (...) proofs, video-clips, dreams, halucinations, etc.) may introduce their own “partial world models” – as small additions to “bigger” world models (regarded as background knowledge). Sometimes, sentences contain references to other world models. Trying to understand such sentences, we should identify and keep separated the world models involved. (shrink)

The purpose of this paper is to introduce a bi-intuitionistic sequent calculus and to give proofs of admissibility for its structural rules. The calculus I will present, called SC2Int, is a sequent calculus for the bi-intuitionistic logic 2Int, which Wansing presents in [2016a]. There he also gives a natural deduction system for this logic, N2Int, to which SC2Int is equivalent in terms of what is derivable. What is important is that these calculi represent a kind of bilateralist reasoning, since they (...) do not only internalize processes of verifcation or provability but also the dual processes in terms of falsifcation or what is called dual provability. In [Wansing, 2017] a normal form theorem for N2Int is stated, here, I want to prove a cut-elimination theorem for SC2Int, i.e., if successful, this would extend the results existing so far. (shrink)

Education can transform our cognitive world. Recent use of enactivist and enactivist-friendly work to propose understanding transformational learning in terms of affective reframing is a promising first step to understanding how we can have or inculcate transformational learning in different ways without relying on meta-cognition. Building on this work, I argue that to fully capture the kind of perspectival changes that occur in transformational learning we need to further distinguish between ways of reorienting one’s perspective, and I specify why different (...) ways are differently valuable. I propose that recent approaches to Confucian ritual provide a clue to what is missing in characterisations of perspective transformation and the resultant transformed perspective. I argue that focussing on ritualised interpersonal interactions provides a further clue as to what’s missing from a mere appeal to the ritual-based inculcation of new perspectives, namely the kind of lightness and flexibility that some ritualised interactions encourage participants to have, and the deepening of perspective associated with that lightness. I argue that a case study of a project implementing a highly ritualised philosophical practice with prisoners in Scotland shows how these constraints, seemingly paradoxically, function so as to actually deepen the perspectival spaces of those agents. This case study provides a proof of concept for the proposal that certain forms of ritual engagement can reliably bring about the kind of transformation of perspective that is the target phenomenon of transformative learning theory. (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)

The categoricity problem for a system of logic reveals an asymmetry between the model-theoretic and the proof-theoretic resources of that logic. In particular, it reveals prima facie that the proof-theoretic instruments are insufficient for matching the envisaged model-theory, when the latter is already available. Among the proposed solutions for solving this problem, some make use of new proof-theoretic instruments, some others introduce new model-theoretic constrains on the proof-systems, while others try to use instruments from both sides. (...) On the proof-theoretical side, two main approaches for solving the categoricity problem for propositional classical logic consist in the enforcement of the formal systems of this logic by introducing rules of inference of a new kind. A multiple-conclusions logic allows rules of inference with more than one conclusion, while a bilateralist system contains rules of inference formulated in terms of assertion and rejection. Both these approaches reveal interesting formal features of logical reasoning. This paper analyses some of the advantages and limitations of these two approaches as solutions for a full formalization of logic, i.e., for a categorical formalization. (shrink)

Let mathematical justification be the kind of justification obtained when a mathematician provides a proof of a theorem. Are Gettier cases possible for this kind of justification? At first sight we might think not: The standard for mathematical justification is proof and, since proof is bound at the hip with truth, there is no possibility of having an epistemically lucky justification of a true mathematical proposition. In this paper, I argue that Gettier cases are possible (and indeed (...) actual) in mathematical reasoning. By analysing these cases, I suggest that the Gettier phenomenon indicates some upshots for actual mathematical practice. (shrink)

In artificial intelligence (AI), responses generated by machine-learning models (most often large language models) may be unfactual information presented as a fact. For example, a chatbot might state that the Mona Lisa was painted in 1815. Such phenomenon is called AI hallucinations, seeking inspiration from human psychology, with a great difference of AI ones being connected to unjustified beliefs (that is, AI “beliefs”) rather than perceptual failures). -/- AI hallucinations may have their source in the data itself, that is, the (...) source content, or in the training procedure, i.e. the way the knowledge was encoded in the model’s parameters, so that errors in encoding and decoding textual and non-textual representations can cause hallucinations. In this paper, we will observe how such errors come to life and how they might be mitigated. For this purpose, we will analyze the usability of justification logics, to behave as a proof checker for validating the correctness of large language models’ (LLM) responses. Justification logic was developed by S. Artemov, and later on mostly by Artemov and M. Fitting, deriving its main idea from the logic of proofs (LP): knowledge and belief modalities are seen as justification terms, i.e. t:X stands for t is a (proper) justification for X. Justification logic originated from attempts to create semantics for intuitionistic logic where proofs were the most proper justifications, but in further development, justification logic could be applied to different kinds of justifications). With the recent attempts to mitigate incorrect LLM responses, we will analyze various guardrails that are currently used for LLM responses, and see how the logic of justification may provide its benefits as an AI safety layer against false data. (shrink)

This book researches the thought of Jin Yuelin’s epistemology with some notions and methods of contemporary epistemology as the frame of reference. There are two kinds of academical significance in this book, one is that author has accurately comprehended the specific content, inadequacies and contradictions in Jin’ s epistemology, recognized the methods by which Jin Yuelin built his theory of knowledge. The other is that author has known about the differences in research objects and methods between Jin’s theory and (...) contemporary epistemology, and showed the position of Jin’s epistemology in the whole theory of knowledge through the comparative study. On the one hand, the book focuses on the core problem of Jin Yuelin’ epistemology that is how objective knowledge is produced. On the other hand, it is made up of seven chapters in accordance with the structure of Jin’s Theory of Knowledge. The first chapter introduces and comparatively analyzes the comprehensions about the concepts of “knowledge” and “epistemology” between Jin Yuelin and contemporary epistemologists. This chapter supplies the means and methods for following chapters. The second chapter describes Jin’s standpoint and criticism to idealism starting mode, analyzes the objective starting mode that belongs to Jin’s theory and reveals his negative attitude to skepticism. This chapter shows the essential characteristics of the Jin Yuelin’s epistemology. The given is the content of sensation, which is the most basic part of cognitive activity. Moreover Jin Yuelin regards sensation as foundation of knowledge, so the research on theory of the given is separated from the whole study of cognitive activity and treated as the third chapter, which presents Jin’s theory of the given and analyzes the problems of Jin’s theory, then introduces some kinds of theory of the given and theory of perception in the contemporary epistemology, finally comparatively investigates theories of the given between Jin Yuelin and contemporary epistemologists. From the perspective of cognitive activity, the fourth chapter describes the perceptual activity, the activity of knowing, the activity of thinking, means and outlines of reception in Jin’s epistemology, then exposes its contradictions and inadequacies; Induction is the important research object of the Western epistemologists, similarly Jin Yuelin paid more attention to induction and regards the principle of induction as outline of reception. In fact, his standpoint about the principle of induction is vital and creative, so the study of induction separately belongs to the fifth chapter. This chapter presents the Jin’s comprehension about the principle of induction and some answers to the problem of induction in contemporary epistemology, then comparatively analyzes two kinds of the thought about induction. The sixth chapter successively introduces being, nature and fact which all are objects of cognitive activity, then analyzes the problems within them. From the perspective of cognitive results, the last chapter presents the Jin’s standpoint about verification and demonstration of proposition, definition and criteria of truth, then simply describes the point views of contemporary epistemologists about verification and truth of proposition, finally comparatively investigates two kinds of thought. From the vertical, the thesis analyzes the fundamental sections of objective knowledge one by one, such as the given, experience, idea, proposition and truth. From the horizontal, the book focuses on the three main parts of knowledge event, for example, cognitive activity, objects of knowledge and the true proposition treated as knowledge. In a word, the whole book is coherent and organic unity. Through the comparative study, it can be concluded that it is reasonable for Jin Yuelin to enjoy a high academic status, because he is the first philosopher who specializes in the study of epistemology. At the same times, he improves transmission of logic, metaphysics and epistemology from the Western to China. So, his hard work enriches and expands the realm of Chinese philosophy. With the development of the study of epistemology, descriptive content of it, such as, perceptual activity and rational activity, will be regarded as the objects of psychology and cognitive science. Meanwhile, normative content will be retained. For example, analysis of conditions of knowledge, justification for belief claims, comprehension about the proofs of justification, as well as reactions to challenges of skepticism. The latter will continue to be objects of epistemology, of course, they must establish close relationships with psychology and cognitive science. According to this prospect, we should split Jin Yuelin’s theory of knowledge, of which the descriptive content would be allocated to psychology and cognitive science. On the contrary, the normative content would be kept as important resource for deeply studying epistemology. -/- Key words: Knowledge; Contemporary epistemology; Compare; The given; Idea; The principle of induction; Fact. (shrink)

The problem of underdetermination is thought to hold important lessons for philosophy of science. Yet, as Kyle Stanford has recently argued, typical treatments of it offer only restatements of familiar philosophical problems. Following suggestions in Duhem and Sklar, Stanford calls for a New Induction from the history of science. It will provide proof, he thinks, of “the kind of underdetermination that the history of science reveals to be a distinctive and genuine threat to even our best scientific theories” (Stanford (...) 2001, p. S12). This paper examines Stanford’s New Induction and argues that it – like the other forms of underdetermination that he criticizes – merely recapitulates familiar philosophical conundra. (shrink)

Carnap’s result about classical proof-theories not ruling out non-normal valuations of propositional logic formulae has seen renewed philosophical interest in recent years. In this note I contribute some considerations which may be helpful in its philosophical assessment. I suggest a vantage point from which to see the way in which classical proof-theories do, at least to a considerable extent, encode the meanings of the connectives (not by determining a range of admissible valuations, but in their own way), and (...) I demonstrate a kind of converse to Carnap’s result. (shrink)

Gillian Russell has recently proposed counterexamples to such elementary argument forms as Conjunction Introduction and Identity. These purported counterexamples involve expressions that are sensitive to linguistic context—for example, a sentence which is true when it appears alone but false when embedded in a larger sentence. If they are genuine counterexamples, it looks as though logical nihilism—the view that there are no valid argument forms—might be true. In this paper, I argue that the purported counterexamples are not genuine, on the grounds (...) that they equivocate. Having defused the threat of logical nihilism, I argue that the kind of linguistic context sensitivity at work in Russell’s purported counterexamples, if taken seriously, far from leading to logical nihilism, reveals new, previously undreamt-of valid forms. By way of proof of concept I present a simple logic, Solo-Only Propositional Logic, designed to capture some of them. Along the way, some interesting subtleties about the fallacy of equivocation are revealed. (shrink)