“Proof of concept” is a phrase frequently used in descriptions of research sought in program announcements, in experimental studies, and in the marketing of new technologies. It is often coupled with either a short definition or none at all, its meaning assumed to be fully understood. This is problematic. As a phrase with potential implications for research and technology, its assumed meaning requires some analysis to avoid it becoming a descriptive category that refers to all things scientifically exciting. I provide (...) a short analysis of proof of concept research and offer an example of it within synthetic biology. I suggest that not only are there activities that circumscribe new epistemological categories but there are also associated normative ethical categories or principles linked to the research. I examine these and provide an outline for an alternative ethical account to describe these activities that I refer to as “extended agency ethics”. This view is used to explain how the type of research described as proof of concept also provides an attendant proof of principle that is the result of decision-making that extends across practitioners, their tools, techniques, and the problem solving activities of other research groups. (shrink)

This paper articulates and defends a conception of logical form as semantic form revealed by a compositional meaning theory. On this conception, the logical form of a sentence is determined by the semantic types of its primitive terms and their mode of combination as it relates to determining under what conditions it is true. We develop this idea in the framework of truth-theoretic semantics. We argue that the semantic form of a declarative sentence in a language L is revealed (...) by a (canonical) proof of its T- sentence in an interpretive truth theory for L. We give a precise characterization of sameness of logical form between any two declarative sentences in any two languages in terms of the notion of corresponding proofs in interpretive truth theories for the languages. We illustrate the utility of this approach with a number of examples. We then extend the characterization to non-declaratives in a generalization of truth-theoretic semantics that appeals to fulfillment conditions, of which truth conditions are one variety. On this approach, logical forms are not reified, and the notion of sameness of logical form is treated as conceptually basic. We discuss the relation of this conception of logical form to the project of identifying logical constants, reviewing two approaches, one of which takes topic neutrality as central, the other recursion. We argue that the project of identifying logical constants for the purposes of classifying together valid arguments is largely independent of that identifying logical form of sentences, and urge an ecumenical approach to extending talk of logical constants beyond where it is currently well-grounded. (shrink)

Rigorous proof is supposed to guarantee that the premises invoked imply the conclusion reached, and the problem of rigor may be described as that of bringing together the perspectives of formal logic and mathematical practice on how this is to be achieved. This problem has recently raised a lot of discussion among philosophers of mathematics. We survey some possible solutions and argue that failure to understand its terms properly has led to misunderstandings in the literature.

The focus of this paper are Dummett's meaning-theoretical arguments against classical logic based on consideration about the meaning of negation. Using Dummettian principles, I shall outline three such arguments, of increasing strength, and show that they are unsuccessful by giving responses to each argument on behalf of the classical logician. What is crucial is that in responding to these arguments a classicist need not challenge any of the basic assumptions of Dummett's outlook on the theory of meaning. In particular, (...) I shall grant Dummett his general bias towards verificationism, encapsulated in the slogan 'meaning is use'. The second general assumption I see no need to question is Dummett's particular breed of molecularism. Some of Dummett's assumptions will have to be given up, if classical logic is to be vindicated in his meaning-theoretical framework. A major result of this paper will be that the meaning of negation cannot be defined by rules of inference in the Dummettian framework. (shrink)

Robert Brandom’s expressivism argues that not all semantic content may be made fully explicit. This view connects in interesting ways with recent movements in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously - as more than a mere “heuristic aid” to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a semiotic natural kind? The paper will argue that such a natural kind (...) does exist in Charles Peirce’s conception of iconic signs, but that fully understood, logical diagrams involve a structured array of normative reasoning practices, as well as just a “picture on a page”. (shrink)

This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two (...) arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics. (shrink)

This chapter argues that Davidson's truth-theoretic semantics was not intended to replace the traditional pursuit of providing a compositional meaning theory but rather to achieve the same aim indirectly by placing conditions on a truth theory that would enable someone who understood it to understand its object language. The chapter argues that by placing constraints on the axioms of a Tarski-style truth theory, namely, that they interpret the terms for which they give satisfaction conditions, and specifying a suitable canonical proof (...) procedure that issues in T-sentence that remove all the metalanguage semantic terms from the right hand side and draw intuitively only on the content of the axioms, we can use the theory to interpret object language sentences. It further argues that if we ask what body of knowledge one must be in possession of to interpret the language, it turns out to be a set of propositions about the truth theory but not the axioms of the truth theory itself. This shows how to avoid the problem of the semantic paradoxes and the problem of vagueness. (shrink)

Contemporary public discourse is saturated with speech that vilifies and incites hatred or violence against vulnerable groups. The term “hate speech” has emerged in legal circles and in ordinary language to refer to these communicative acts. But legal theorists and philosophers disagree over how to define this term. This paper makes the case for, and subsequently develops, the first corpus-based analysis of the ordinary meaning of “hate speech.” We begin by demonstrating that key interpretive and moral disputes surrounding hate speech (...) laws—in particular, surrounding their compatibility with the rule of law, democracy, and free speech—depend crucially on the ordinary meaning of “hate speech.” Next, we argue, drawing on recent developments in legal philosophy, that corpus linguistics constitutes a distinctively promising tool for ascertaining the ordinary meaning of “hate speech.” Finally, we offer a proof of concept, by outlining, and analyzing the interpretive and moral implications of, the first such study. (shrink)

Introduction to mathematical logic. Part 2.Textbook for students in mathematical logic and foundations of mathematics. Platonism, Intuition, Formalism. Axiomatic set theory. Around the Continuum Problem. Axiom of Determinacy. Large Cardinal Axioms. Ackermann's Set Theory. First order arithmetic. Hilbert's 10th problem. Incompleteness theorems. Consequences. Connected results: double incompleteness theorem, unsolvability of reasoning, theorem on the size of proofs, diophantine incompleteness, Loeb's theorem, consistent universal statements are provable, Berry's paradox, incompleteness and Chaitin's theorem. Around Ramsey's theorem.

It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the same conclusion would have to be identified. In this paper it will be shown that the question, which reductions we accept in our system, is not only important if we see them as generating a theory of proof identity but is also (...) decisive for the more general question whether a proof has meaningful content. There are certain reductions which would not only force us to identify proofs of different arbitrary formulas but which would render derivations in a system allowing them meaningless. To exclude such cases, a minimal criterion is proposed which reductions have to fulfill to be acceptable. (shrink)

The standard of proof in criminal trials in many liberal democracies is proof beyond a reasonable doubt, the BARD standard. It is customary to describe it, when putting a number on it, as requiring that the fact finder be at least 90% certain, after considering the evidence, that the defendant is guilty. Strikingly, no good reason has yet been offered in defense of using that standard. A number of non-consequentialist justifications that aim to support an even higher standard have been (...) offered; all are morally unsound. Meanwhile, consequentialist arguments plausibly support a substantially lower standard — in some cases so low as to undermine the idea that punishment is what is at stake. In this paper, I offer a new retributive justification that supports excluding the instrumental benefits of punishment from the balance that sets the standard. The resulting balance supports a standard arguably in the ballpark of the customary understanding of BARD: a standard requiring that the fact finder have a high, though not maximally high, degree of confidence that the defendant is guilty. (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)

Kurt Gödel wrote (1964, p. 272), after he had read Husserl, that the notion of objectivity raises a question: “the question of the objective existence of the objects of mathematical intuition (which, incidentally, is an exact replica of the question of the objective existence of the outer world)”. This “exact replica” brings to mind the close analogy Husserl saw between our intuition of essences in Wesensschau and of physical objects in perception. What is it like to experience a mathematical (...) proving process? What is the ontological status of a mathematical proof? Can computer assisted provers output a proof? Taking a naturalized world account, I will assess the relationship between mathematics, the physical world and consciousness by introducing a significant conceptual distinction between proving and proof. I will propose that proving is a phenomenological conscious experience. This experience involves a combination of what Kurt Gödel called intuition, and what Husserl called intentionality. In contrast, proof is a function of that process — the mathematical phenomenon — that objectively self-presents a property in the world, and that results from a spatiotemporal unity being subject to the exact laws of nature. In this essay, I apply phenomenology to mathematical proving as a performance of consciousness, that is, a lived experience expressed and formalized in language, in which there is the possibility of formulating intersubjectively shareable meanings. (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 they 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)

Andrew Wiles' analytic proof of Fermat's Last Theorem FLT, which appeals to geometrical properties of real and complex numbers, leaves two questions unanswered: (i) What technique might Fermat have used that led him to, even if only briefly, believe he had `a truly marvellous demonstration' of FLT? (ii) Why is x^n+y^n=z^n solvable only for n<3? In this inter-disciplinary perspective, we offer insight into, and answers to, both queries; yielding a pre-formal proof of why FLT can be treated as a (...) true arithmetical proposition (one which, moreover, might not be provable formally in the first-order Peano Arithmetic PA), where we admit only elementary (i.e., number-theoretic) reasoning, without appeal to analytic properties of real and complex numbers. We cogently argue, further, that any formal proof of FLT needs---as is implicitly suggested by Wiles' proof---to appeal essentially to formal geometrical properties of formal arithmetical propositions. (shrink)

Looking at every sense this article proves through deduction; that your mind needs a source to dream. Dreams are old experienced essences of platonic forms. You can only experience new forms essences when you are awake because of initial experiences. If dreams are old, experienced essences (what this article proves) therefore you know you are awake when you initially sense new experienced essences.

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical (...) statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim. (shrink)

Plato is commonly considered a metaphysical dualist conceiving of a world of Forms separate from the world of particulars in which we live. This paper explores the motivation for postulating that second world as opposed to making do with the one we have. The main objective is to demonstrate that and how everything, Forms and all, can instead fit into the same world. The approach is exploratory, as there can be no proof in the standard sense. The debate between explaining (...) Plato’s ontology with a single world and requiring a two-world model to make sense of the same thing is typically about scouring the Platonic corpus for evidence and turning to Aristotle for help where we need it. The aim here is to dig deeper than what either of them, or anyone else, has said or implied about the number or worlds, searching instead for any insight that might be gained from the way Forms are supposed to exist versus what we ourselves might understand by existence. Although the paper is, at its most basic level, about the existence of the Forms, the intention is not to prove that they exist, nor to evaluate the proofs and objections already on record, but to consider how they might exist and what follows if they do. Dialogue toward consensus on why we think the Forms exist, and why we think they do not, could perhaps provide a smoother “second sailing” in waters where we have been unable to agree whether they do and where they would if they did. (shrink)

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

How is the burden of proof to be distributed among individuals who are involved in resolving a particular issue? Under what conditions should the burden of proof be distributed unevenly? We distinguish attitudinal from dialectical burdens and argue that these questions should be answered differently, depending on which is in play. One has an attitudinal burden with respect to some proposition when one is required to possess sufficient evidence for it. One has a dialectical burden with respect to some (...) proposition when one is required to provide supporting arguments for it as part of a deliberative process. We show that the attitudinal burden with respect to certain propositions is unevenly distributed in some deliberative contexts, but in all of these contexts, establishing the degree of support for the proposition is merely a means to some other deliberative end, such as action guidance, or persuasion. By contrast, uneven distributions of the dialectical burden regularly further the aims of deliberation, even in contexts where the quest for truth is the sole deliberative aim, rather than merely a means to some different deliberative end. We argue that our distinction between these two burdens resolves puzzles about unevenness that have been raised in the literature. (shrink)

In August 2002, three Indian computer scientists published a paper, ‘PRIMES is in P’, online. It presents a ‘deterministic algorithm’ which determines in ‘polynomial time’ if a given number is a prime number. The story was quickly picked up by the general press, and by this means spread through the scientific community of complexity theorists, where it was hailed as a major theoretical breakthrough. This is although scientists regarded the media reports as vulgar popularizations. When the paper was published in (...) a peer-reviewed journal only two years later, the three scientists had already received wide recognition for their accomplishment. Current sociological theory challenges the ability to clearly distinguish on independent epistemic grounds between distorted and non-distorted scientific knowledge. It views the demarcation lines between such forms of presentation as contextual and unstable. In my paper, I challenge this view. By systematically surveying the popular press coverage of the ‘PRIMES is in P’ affair, I argue--against the prevailing new orthodoxy--that distorted simplifications of scientific knowledge are distinguishable from non-distorted simplifications on independent epistemic grounds. I argue that in the ‘PRIMES is in P’ affair, the three scientists could ride on the wave of the general press-distorted coverage of their algorithm, while counting on their colleagues’ ability to distinguish genuine accounts from distorted ones. Thus, their scientific reputation was unharmed. This suggests that the possibility of the existence of independent epistemic standards must be incorporated into the new SSK model of popularization. (shrink)

I explore, from a proof-theoretic perspective, the hierarchy of classical and paraconsistent logics introduced by Barrio, Pailos and Szmuc in (Journal o f Philosophical Logic,49, 93-120, 2021). First, I provide sequent rules and axioms for all the logics in the hierarchy, for all inferential levels, and establish soundness and completeness results. Second, I show how to extend those systems with a corresponding hierarchy of validity predicates, each one of which is meant to capture “validity” at a different inferential level. Then, (...) I point out two potential philosophical implications of these results. (i) Since the logics in the hierarchy differ from one another on the rules, I argue that each such logic maintains its own distinct identity (contrary to arguments like the one given by Dicher and Paoli in 2019). (ii) Each validity predicate need not capture “validity” at more than one metainferential level. Hence, there are reasons to deny the thesis (put forward in Barrio, E., Rosenblatt, L. & Tajer, D. (Synthese, 2016)) that the validity predicate introduced in by Beall and Murzi in (Journal o f Philosophy,110(3), 143–165, 2013) has to express facts not only about what follows from what, but also about the metarules, etc. (shrink)

Janet Radcliffe Richards’ The Ethics of Transplants outlines a novel framework for moral inquiry in practical contexts and applies it to the topic of paid living kidney donation. In doing so, Radcliffe Richards makes two key claims: that opponents of organ markets bear the burden of proof, and that this burden has not yet been satisfied. This paper raises four related objections to Radcliffe Richards’ methodological framework, focusing largely on how Radcliffe Richards uses this framework in her discussion of kidney (...) sales. We conclude that Radcliffe Richards’ method of inquiry hinders our ability to answer the very question that it ought to help us resolve: What is there best reason to do, all things considered? (shrink)

We present an approach in which ancient Greek mathematical proofs by Hippocrates of Chios and Euclid are addressed as a form of (guided) intentional reasoning. Schematically, in a proof, we start with a sentence that works as a premise; this sentence is followed by another, the conclusion of what we might take to be an inferential step. That goes on until the last conclusion is reached. Guided by the text, we go through small inferential steps; in each one, we (...) go through an autonomous reasoning process linking the premise to the conclusion. The reasoning process is accompanied by a metareasoning process. Metareasoning gives rise to a feeling-knowing of correctness. In each step/cycle of the proof, we have a feeling-knowing of correctness. Overall, we reach a feeling of correctness for the whole proof. We suggest that this approach allows us to address the issues of how a proof functions, for us, as an enabler to ascertain the correctness of its argument and how we ascertain this correctness. (shrink)

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to (...) be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. -/- Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. -/- However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. -/- The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion. (shrink)

Kant's A-Edition objective deduction is naturally (and has traditionally been) divided into two arguments: an " argument from above" and one that proceeds " von unten auf." This would suggest a picture of Kant's procedure in the objective deduction as first descending and ascending the same ladder, the better, perhaps, to test its durability or to thoroughly convince the reader of its soundness. There are obvious obstacles to such a reading, however; and in this chapter I will argue that the (...) arguments from above and below constitute different, albeit importantly inter-related, proofs. Rather than drawing on the differences in their premises, however, I will highlight what I take to be the different concerns addressed and, correspondingly, the distinct conclusions reached by each. In particular, I will show that both arguments can be understood to address distinct specters, with the argument from above addressing an internal concern generated by Kant’s own transcendental idealism, and the argument from below seeking to dispel a more traditional, broadly Humean challenge to the understanding’s role in experience. These distinct concerns also imply that these arguments yield distinct conclusions, though I will show that they are in fact complementary. (shrink)

What explains change? Edward Feser argues in his ‘Aristotelian proof’ that the only adequate answer to these questions is ultimately in terms of an unchangeable, purely actual being. In this paper, I target the cogency of Feser’s reasoning to such an answer. In particular, I present novel paths of criticism—both undercutting and rebutting—against one of Feser’s central premises. I then argue that Feser’s inference that the unactualized actualizer lacks any potentialities contains a number of non-sequiturs.

Kant's A-Edition objective deduction is naturally (and has traditionally been) divided into two arguments: an " argument from above" and one that proceeds " von unten auf." This would suggest a picture of Kant's procedure in the objective deduction as first descending and ascending the same ladder, the better, perhaps, to test its durability or to thoroughly convince the reader of its soundness. There are obvious obstacles to such a reading, however; and in this chapter I will argue that the (...) arguments from above and below constitute different, albeit importantly inter-related, proofs. Rather than drawing on the differences in their premises, however, I will highlight what I take to be the different concerns addressed and, correspondingly, the distinct conclusions reached by each. In particular, I will show that both arguments can be understood to address distinct specters, with the argument from above addressing an internal concern generated by Kant’s own transcendental idealism, and the argument from below seeking to dispel a more traditional, broadly Humean challenge to the understanding’s role in experience. These distinct concerns also imply that these arguments yield distinct conclusions, though I will show that they are in fact complementary. (shrink)

Frank Snare had a puzzle. Noncognitivism implies No-Ought-From-Is but No- Ought-From-Is does not imply non-cognitivism. How then can we derive non-cognitivism from No-Ought-From-Is? Via an abductive argument. If we combine non-cognitivism with the conservativeness of logic (the idea that in a valid argument the conclusion is contained in the premises), this implies No-Ought-From-Is. Hence if No-Ought-From-Is is true, we can arrive at non-cognitivism via an inference to the best explanation. With prescriptivism we can make this argument more precise. I develop (...) an account of imperative consequence that underwrites Hare’s principle that you cannot derive imperatives from indicatives. Thus if moral judgments contain an imperative component, it will be impossible to derive moral conclusions from indicative or non-moral premises. Given this account of imperative consequence, we can explain No-Ought-From-Is without appealing to anything as nebulous as the conservativeness of logic. Hence if No-Ought-From-Is is true, we have an inference to the best explanation for prescriptivism. Both lines of argument face problems from Prior. Given Prior’s counterexamples, No-Ought-From-Is as originally conceived is false. The version that survives is No-Non-Vacuous-Ought-From-Is. But the best explanation of this does not include non-cognitivism. With prescriptivism it is worse. For the version of No-Ought-From-Is that prescriptivism ‘explains’ – that is, the version of No-Ought-From-Is that prescriptivism implies – would exclude Prior’s counter-examples to Autonomy as invalid. But they are not invalid. Thus Prior’s counter-examples to No-Ought-From- Is refute prescriptivism. Thus from 1960 onwards R. M.Hare was a dead philosopher walking. But if non-cognitivism cannot be derived from No-Ought-From-Is, this suggests that it is not what Hume was trying to prove. I argue that what Hume was trying to prove is that moral truths are not demonstrable. To be demonstrable, a proposition must be either self-evident or logically derivable from self-evident propositions. By Treatise 3.1.1.27, Hume had proved to his own satisfaction that no moral propositions are self-evident. That leaves open the possibility that they are logically derivable from self-evident but NON-moral propositions. The point of No-Ought-From-Is was to exclude this possibility. If you cannot logically derive moral conclusions from non-moral premises, you cannot demonstrate the truths of morality by deriving them from self-evident but NON-moral truths. I also discuss why Hume abandoned No-Ought-From-Is in the EPM. He had no need of it since he thought he had a proof that (with some exceptions) no nontrivial truths are demonstrable. Hence no non-trivial MORAL truths are demonstrable. No-Ought-From-Is drops out as unnecessary. (shrink)

Criminal courts make decisions that can remove the liberty and even life of those accused. Civil trials can cause the bankruptcy of companies employing thousands of people, asylum seekers being deported, or children being placed into state care. Selecting the right standards when deciding legal cases is of utmost importance in giving those affected a fair deal. This Element is an introduction to the philosophy of legal proof. It is organised around five questions. First, it introduces the standards of proof (...) and considers what justifies them. Second, it discusses whether we should use different standards in different cases. Third, it asks whether trials should end only in binary outcomes (e.g. guilty or not guilty) or rather use more fine-grained or precise verdicts. Fourth, it considers whether proof is simply about probability, concentrating on the famous 'Proof Paradox'. Finally, it examines who should be trusted with deciding trials, focusing on the jury system. (shrink)

John von Neumann's proof that quantum mechanics is logically incompatible with hidden varibales has been the object of extensive study both by physicists and by historians. The latter have concentrated mainly on the way the proof was interpreted, accepted and rejected between 1932, when it was published, and 1966, when J.S. Bell published the first explicit identification of the mistake it involved. What is proposed in this paper is an investigation into the origins of the proof rather than the (...) aftermath. In the first section, a brief overview of the his personal life and his proof is given to set the scene. There follows a discussion on the merits of using here the historical method employed elsewhere by Andrew Warwick. It will be argued that a study of the origins of von Neumann's proof shows how there is an interaction between the following factors: the broad issues within a specific culture, the learning process of the theoretical physicist concerned, and the conceptual techniques available. In our case, the ‘conceptual technology’ employed by von Neumann is identified as the method of axiomatisation. (shrink)

Faith is the highest truth that ensures the happiness and salvation of man in the world and in the Hereafter. But the essence of superstitious is invalid and wrong. The realization of this happiness and salvation is possible by having a true faith. Another consequence of the true faith is the ability to recognize that this belief is right. Believing in true faith, ensures rightness and makes possible to prove and disclose this truth. It is important to have true faith (...) and accurate affirmation. This certainty requires certain criteria for accuracy and precision. In addition, this situation involves advocating the faith and delivering it to other people. This is closely related to the recognition and proof of these truths. It also makes it necessary to explore the distinction between presumption and believing as well as knowledge and ignorance. It requires examination of the concepts of certainty, doubt, evidence, persuasion and proof and what they have implied in terms of faith. The examination of the proofs of faith in terms of persuasion and proof also increases the understanding of the certainty of a belief. (shrink)

Although traditionally neglected, mathematical diagrams have recently begun to attract attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and justification. Certain preliminary questions have, however, been mostly bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term “mathematical diagram” is used in diverse ways. I propose a working definition that carves out the phenomena that are of most importance for (...) a taxonomy of diagrams in the context of a practice-based philosophy of mathematics, privileging examples from contemporary mathematics. In doing so, I move away from vague, ordinary notions. I define mathematical diagrams as forming notational systems and as being geometric/topological representations or two-dimensional representations. I also examine the relationship between mathematical diagrams and spatiotemporal intuition. By proposing an explication of diagrams, I explain certain controversies in the existing literature. Moreover, I shed light on why mathematical diagrams are so effective in certain instances, and, at other times, dangerously misleading. (shrink)

This paper discusses critically what simulation models of the evolution ofcooperation can possibly prove by examining Axelrod’s “Evolution of Cooperation” and the modeling tradition it has inspired. Hardly any of the many simulation models of the evolution of cooperation in this tradition have been applicable empirically. Axelrod’s role model suggested a research design that seemingly allowed to draw general conclusions from simulation models even if the mechanisms that drive the simulation could not be identified empirically. But this research design (...) was fundamentally flawed, because it is not possible to draw general empirical conclusions from theoretical simulations. At best such simulations can claim to prove logical possibilities, i.e. they prove that certain phenomena are possible as the consequence of the modeling assumptions built into the simulation, but not that they are possible or can be expected to occur in reality I suggest several requirements under which proofs of logical possibilities can nevertheless be considered useful. Sadly, most Axelrod-style simulations do not meet these requirements. I contrast this with Schelling’s neighborhood segregation model, thecore mechanism of which can be retraced empirically. (shrink)

Semantics plays a role in grammar in at least three guises. (A) Linguists seek to account for speakers‘ knowledge of what linguistic expressions mean. This goal is typically achieved by assigning a model theoretic interpretation in a compositional fashion. For example, *No whale flies* is true if and only if the intersection of the sets of whales and fliers is empty in the model. (B) Linguists seek to account for the ability of speakers to make various inferences based on (...) semantic knowledge. For example, *No whale flies* entails *No blue whale flies* and *No whale flies high*. (C) The wellformedness of a variety of syntactic constructions depends on morpho-syntactic features with a semantic flavor. For example, *Under no circumstances would a whale fly* is grammatical, whereas *Under some circumstances would a whale fly* is not, corresponding to the downward vs. upward monotonic features of the preposed phrases. It is usually assumed that once a compositional model theoretic interpretation is assigned to all expressions, its fruits can be freely enjoyed by inferencing and syntax. What place might proof theory have in this picture? (shrink)

The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by the (...) ‘proportional syllogism’, or argument from frequencies, such as ‘nearly all aeroplane flights arrive safely, so my flight is very likely to arrive safely’. Such arguments raise the ‘problem of the reference class’, arising from the fact that an individual case may be a member of many different classes in which frequencies differ. For example, if 15 per cent of swans are black and 60 per cent of fauna in the zoo is black, what should I think about the likelihood of a swan in the zoo being black? The nature of the problem is explained, and legal cases where it arises are given. It is explained how recent work in data mining on the relevance of features for prediction provides a solution to the reference class problem. (shrink)

This is a defense of John Stuart Mill’s proof of the principle of utility in the fourth chapter of his Utilitarianism. The proof is notorious as a fallacious attempt by a prominent philosopher, who ought not to have made the elementary mistakes he is supposed to have made. This book shows that he did not. The aim is not to glorify utilitarianism, in a full sweep, as the best normative ethical theory, or even to vindicate, on a more specific level, (...) Mill’s universalistic ethical hedonism as the best form of utilitarianism. The book is concerned only with Mill’s utilitarianism, and primarily with his proof of the principle of utility. The purpose is to show that Mill proceeds intelligibly and systematically in pursuing a well-defined project in the fourth chapter of Utilitarianism, and that he successfully defends what he sets out to establish in his proof of the principle of utility. (shrink)

Berkeley in his Introduction to the Principles of Human knowledge uses geometrical examples to illustrate a way of generating “universal ideas,” which allegedly account for the existence of general terms. In doing proofs we might, for example, selectively attend to the triangular shape of a diagram. Presumably what we prove using just that property applies to all triangles.I contend, rather, that given Berkeley’s view of extension, no Euclidean triangles exist to attend to. Rather proof, as Berkeley would normally assume, (...) requires idealizing diagrams; treating them as if they obeyed Euclidean constraints. This convention solves the problem of representative generalization. View HTML Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.Berkeley and Proof in GeometryVolume 51, Issue 3RICHARD J. BROOK DOI: https://doi.org/10.1017/S0012217312000686Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. Berkeley and Proof in GeometryVolume 51, Issue 3RICHARD J. BROOK DOI: https://doi.org/10.1017/S0012217312000686Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. Berkeley and Proof in GeometryVolume 51, Issue 3RICHARD J. BROOK DOI: https://doi.org/10.1017/S0012217312000686Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

Mill’s Principle of Utility: Origins, Proof, and Implications (Leiden: Brill, 2022) is a scholarly monograph on John Stuart Mill’s utilitarianism with a particular emphasis on his proof of the principle of utility. Originally published as Mill’s Principle of Utility: A Defense of John Stuart Mill’s Notorious Proof (Amsterdam: Editions Rodopi, 1994), the present volume is a revised and enlarged edition with additional material, tighter arguments, crisper discussions, and updated references. The initiative is still principally an analysis, interpretation, and defense of (...) the controversial proof, which has yet to attract a scholarly consensus on how it works and whether it succeeds. Well over a century and a half after Mill’s contribution, the subject matter continues to figure prominently in classroom discussions, where the principle and its proof are presented and debated in connection with the critical baggage of logical problems and conceptual confusions wrongly attributed to Mill from the beginning. The overarching aim of the book, now supplemented by a comprehensive historical background and salient philosophical implications, remains the vindication of Mill’s reasoning in pursuit of what he promises as a proof of the principle of utility. (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)

What It’s Like to Chill Out With Whom the Rest of the World Considers As The Most Ruthless Men: Ratko Mladic, Goran Hadzic and Radovan Karadzic (+) Confessions of a Female War Crimes Investigator By Jill Louise Starr NJ USA -/- Read My Entire Book Here (True Story) http://sites.google.com/site/thelawprojectscenternycoffices/what-it-s-like-to-chill-out-with-whom-the-rest-of-the-world-considers-as-the-most-ruthless-men-ratko-mla dic-goran-hadzic-and-radovan-karadzic-confessions-of-a-female-war-crimes-investigator -/- Retrospectively, it was all so simple, natural and matter of fact being on a boat restaurant in Belgrade, sitting with, laughing, drinking a two hundred bottle of wine and (...) chatting about war and peace while Ratko Mladic held my hand. Mladic, a man considered the world’s most ruthless war criminal since Adolf Hitler, still at large and currently having a five million dollar bounty on his head for genocide by the international community. Yet there I was with my two best friends at the time, a former Serbian diplomat, his wife, and Ratko Mladic just chilling. There was no security, nothing you’d ordinarily expect in such circumstances. Referring to himself merely as, Sharko; this is the story of it all came about. Diplomatic / International Relations Consultant & War Crimes Investigator - War - Peace - Preventive Diplomatic Strategies - International Law - Charitable Causes - International Business - International Political Economy - Human Rights - Politics - War Crimes Investigations - Anti-Terrorism - Law Projects Center Funded Projects (YCICC) Internationally LPCYU Home Website -/- Irrefutable Proof ICTY Is Corrupt Court/Irrefutable Proof the Hague Court Cannot Legitimately Prosecute Karadzic Case By Jill Starr I want to stress, in this particular meeting , there was no observer status at the ICC Preparatory Meetings at the United Nations in New York City in 2001. What I did, made a historical precedent. I was asked by, Darko Trifunovic 1st Secretary of the Bosnian MIssion, to take his place, in a CLOSED DOOR UNITED NATIONS MEETING. This means, ONLY HEADS OF AMBASSADORIAL MISSIONS WERE ALLOWED IN THE MEETING. There was no "Observer Status for say NGO's such as Amnesty International." I represented a Country as an American Citizen that day; the Repuklika Srpska. This never occurred before to my knowledge ever. It was an error. My former professor, Arnold Stark, walked me in, A former State Dept. man chosen to be the former Ambassador from the USA to Bonn/Germany (and he declined years back because of his wife at the time). He knew it was illegal. It said on these paper I picked up in the meeting, Anyone, Richard Holbrooke, sat across from me, discussing this meeting outside the meeting itself thereafter , "would be prosecuted to the fullest extent of int'l law." I heard the Ambassadors of the world ALL DISCUS TRADING MONEY FOR ICC AND ICTY COURT VERDICT AS WELL AS FUTURE JUDICIAL APPOINTMENTS -/- http://sites.google.com/site/thelawprojectscenternycoffices/home/irrefutable-proof-icty-is-corrupt-c ourt-irrefutable-proof-the-hague-court-cannot-legitimately-prosecute-karadzic-case -/- http://picasaweb.google.com/lpcyusa/IrrefutableProofICTYIsCorruptCourtIrrefutabl# (The Documentary Secret United Nations ICC Meeting Papers Scanned Images) OR http://community.jigsaw.com/t5/media/gallerypage/user-id/903610# -/- Rea dMore Here _> Read the entire story here My testimonial video on Youtube _> http://www.youtube.com/watch?v=dKe-5LORsGs -/- http://www.youtube.com/watch?v=dKe-5LORsGs (My YouTube VIDEO) -/- This legal technicality indicates the Hague must dismiss charges against Dr Karadzic and others awaiting trials in the Hague jail; like it or not. -/- Unfortunately for the Signatures Of the Rome Statute United Nations member states instituting the ICC & ICTY housed at the Hague, insofar as the, Radovan Karadzic, as with the other Hague cases awaiting trial there, I personally witnessed these United Nations member states having a substantial conversations, and, openly speaking about trading judicial appointments and verdicts for financial funding when I attended the 2001 ICC Preparatory Meetings at the UN in Manhattan making the iCTY and ICC morally incapable trying Radovan Karazdic and others. -/- I witnessed with my own eyes and ears when attending the 2001 Preparatory Meetings to establish an newly emergent International Criminal Court, the exact caliber of criminal corruption running so very deeply at the Hague, that it was a perfectly viable topic of legitimate conversation in those meetings I attended to debate trading verdicts AND judicial appointments, for monetary funding. -/- Jilly wrote:*The rep from Spain became distraught and when her country’s proposal was not taken to well by the chair of the meeting , then Spain argued in a particularly loud and noticably strongly vocal manner, “Spain (my country) strongly believes if we contribute most financial support to the Hague’s highest court, that ought to give us and other countries feeding it financially MORE direct power over its decisions.” -/- ((((((((((((((((((((((((( ((((((((((((((((((((((((( Instead of censoring the country representative from Spain for even bringing up this unjust, illegal and unfair judicial idea of bribery for international judicial verdicts and judicial appointments, all country representatives present in the meeting that day all treated the Spain proposition as a ”totally legitimate topic” discussed and debated it between each other for some time. I was quite shocked! The idea was “let’s discuss it.” "It’s a great topic to discuss." -/- Some countries agreed with Spain’s propositions while others did not. The point here is, bribery for judicial verdicts and judicial appointments was treated as a totally legitimate topic instead of an illegitimate topic which it is in the meeting that I attended in 2001 that day to establish the ground work for a newly emergent international criminal court.)))))))))))))))))))))))))))) -/- In particular., since “Spain” was so overtly unafraid in bringing up this topic of trading financial funding the ICC for influence over its future judicial appointments and verdicts in front of every other UN member state present that day at the UN, “Spain” must have already known by previous experience the topic of bribery was “socially acceptable” for conversation that day. They must have previously spoke about bribing the ICTY and ICC before in meetings; this is my take an international sociological honor student. -/- SPAIN’s diplomatic gesture of international justice insofar as, Serbia, in all of this is, disgusting morally!SPAIN HAS TAUGHT THE WORLD THE TRUE DEFINITION OF AN “INTERNATIONAL CRIMINAL COURT.” -/- I represented the state interests’ of the Former Yugoslavia, in Diplomat Darko Trifunovic’s absence in those meetings and I am proud to undertake this effort on Serbia’s behalf. http://picasaweb.google.com/lpcyusa (My Political Satire Blog) Diplomatic / International Relations Consultant & War Crimes Investigator - War - Peace - Preventive Diplomatic Strategies - International Law - Charitable Causes - International Business - International Political Economy - Human Rights - Politics - War Crimes Investigations - Anti-Terrorism - Law Projects Center Funded Projects (YCICC) Internationally http://sites.google.com/site/jillstarrsite -/- -/- . 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The 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)

Could it be right to convict and punish defendants using only statistical evidence? In this paper, I argue that it is not and explain why it would be wrong. This is difficult to do because there is a powerful argument for thinking that we should convict and punish defendants using statistical evidence. It looks as if the relevant cases are cases of decision under risk and it seems we know what we should do in such cases (i.e., maximize expected (...) value). Given some standard assumptions about the values at stake, the case for convicting and punishing using statistical evidence seems solid. In trying to show where this argument goes wrong, I shall argue (against Lockeans, reliabilists, and others) that beliefs supported only by statistical evidence are epistemically defective and (against Enoch, Fisher, and Spectre) that these epistemic considerations should matter to the law. To solve the puzzle about the role of statistical evidence in the law, we need to revise some commonly held assumptions about epistemic value and defend the relevance of epistemology to this practical question. (shrink)

What is the highest good actually good for in Kant’s third Critique? While there are well-worked out answers to this question in the literature that focus on the highest good’s practical importance, this paper argues that there is an important function for the highest good that has to do exclusively with contemplation. This important function becomes clear once one notices that coherent [konsequent] thinking, for Kant, was synonymous with "bündiges" thinking, and that both are connected with the highest good (...) in the third Critique’s moral proof for God’s existence. I show that the original meaning of "bündig," which is from the carpentry trade and has been forgotten, illuminates the stakes of the highest good in Kant’s system. For us, as proverbial carpenters of reason, coherence is essential for the intellectual activity of constructing a philosophical worldview in his transcendental idealism. I motivate the reading further by showing how this function can neatly reconstruct Kant’s proof for God’s existence in the third Critique. I conclude by sketching Kant’s reasons for why the project of creating a coherent worldview grounded in the highest good is worth the labor costs. (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)

Practical reasoning is a domain of concerns that deal with our most intimate views on what should be done, every day, in facing the world. Unlike theoretical reasoning which forms only beliefs, practical reasoning forms intensions and sets ground for actions. It deals mostly with the notion of reason, broadly understood as a term that acquires both rationality and motivation for our actions. Bernard Williams in “Internal and external reasons” introduced a strong and influential distinction, the distinction between internal (...) and external reasons. Williams explicitly argues in favour of internalism, excluding the existence of external reasons and placing the burden of proof on the externalists. In this paper I will reconsider his views drawing on John Skorupski’s insights on Williams in “Internal Reasons and the Scope of Blame” and Skorupski’s cognitive internalism. I will criticise both of their internalistic accounts and argue for an Aristotelian framing of their main arguments which I believe is a fairer deal in their contribution to the practical reasoning issues. (shrink)

There was a time in my school years when I have learned about Achilles and Tortoise “paradox” originated from Zeno. It was then clear that the ancient Greeks were arguing about this problem but contemporary science has clarified the issue. Yet to my surprise the problem is still debated over and over, despite the fact there exist mathematical proofs. I feel like reminding myself why this is not a paradox beyond reasonable doubt. This is a draft to a section of (...) a future publication. (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)

What is the role of the principle of sufficient reason in Baruch Spinoza’s ontological proof for God’s existence? Is this role identical within Spinoza’s early work on method, the Treatise on the Emendation of the Intellect, and his magnum opus, the Ethics? This paper argues affirmatively that the methodology employed within the Ethics is consonant with that method found within the Treatise, and this claim is substantiated through an engagement with the influential works of Don Garrett and Aaron Garrett. (...) It is also demonstrated through an original reconstruction of the Treatise itself. In this reconstruction, basic premises are identified which can validly prove Spinoza’s intended conclusion of substance monism. It is finally determined that what the Treatise and the Ethics share, specifically, is a methodology which begins with non-nominal definitions that denote the real, sufficient causes of their respective objects. However, at certain junctures, this methodology is expressed with greater consistency within the Treatise as opposed to within the Ethics. Evidence for this will be provided from the primary texts themselves and from the subsequent analyses of Don Garrett and Aaron Garret as well. (shrink)

Abstract: When do we meet the standard of proof in a criminal trial? Some have argued that it is when the guilt of the defendant is sufficiently probable on the evidence. Some have argued that it is a matter of normic support. While the first view provides us with a nice account of how we ought to manage risk, the second explains why we shouldn’t convict on the basis of naked statistical evidence alone. Unfortunately, this second view doesn’t help us (...) understand how we should manage risk (e.g., the risk of violating rights against wrongful conviction) and faces counterexamples of its own. I shall defend an alternative approach that builds on the strengths of these two accounts. On the approach defending here, it is objectively suitable to punish iff we know a defendant to be guilty. To determine what is consistent with procedural justice and to determine what we prospectively ought to do, we need to think about the risks we face of deviating from this objective ideal. (shrink)