Researchers often pursue proof of concept research, but criteria for evaluating such research remain poorly specified. This article proposes a general framework for proof of concept research that k...

“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)

Introduction to the Scientific Proof of the Natural Moral Law This paper proves that Aquinas has a means of demonstrating and deriving both moral goodness and the natural moral law from human nature alone. Aquinas scientifically proves the existence of the natural moral law as the natural rule of human operations from human nature alone. The distinction between moral goodness and transcendental goodness is affirmed. This provides the intellectual tools to refute the G.E. Moore (Principles of Ethics) attack against (...) the natural law as committing a "naturalistic fallacy". This article proves that instead Moore commits the fallacy of equivocation between moral goodness and transcendental goodness in his very assertion of a "naturalistic fallacy" by the proponents of the natural moral law. In the process the new deontological/kantian theory of natural law as articulated by John Finnis, Robert George, and Germain Grisez is false historically and philosophically. Ethical naturalism is affirmed as a result. (shrink)

Machine intelligence already helps medical staff with a number of tasks. Ethical decision-making, however, has not been handed over to computers. In this proof-of-concept study, we show how an algorithm based on Beauchamp and Childress’ prima-facie principles could be employed to advise on a range of moral dilemma situations that occur in medical institutions. We explain why we chose fuzzy cognitive maps to set up the advisory system and how we utilized machine learning to train it. We report on (...) the difficult task of operationalizing the principles of beneficence, non-maleficence and patient autonomy, and describe how we selected suitable input parameters that we extracted from a training dataset of clinical cases. The first performance results are promising, but an algorithmic approach to ethics also comes with several weaknesses and limitations. Should one really entrust the sensitive domain of clinical ethics to machine intelligence? (shrink)

The problem of resurrection, one of the most important issues in the philosophy and theology. Some of Muslim philosophers and the vast majority of theologians always discussed about this topic. Some of Muslim philosophers accepted this problem and prove it, but, in quality of occurrence of them, they have differ believe from each other. However, some of Muslim theologians except those who believe in transmogrification, they consider the resurrection to be one of the principle of religion, beside monotheism and (...) prophecy. Moreover, they proved the principle of resurrection through reasons, and explanations them elaborates through the Holy Quran and Prophetic saying (Traditions- Hadith). Avicenna and Suhrawardi have been proving resurrection. Of course, for prove of this problem, they adopted of different manner from Muslim Theologians. Both of philosophers according to codify of ordinary psychological system, have proved and explanation this issue. Thus, for understand of Avicenna and Suhrawardi’s eschatology. First of all, we must understand of their psychological system. Furthermore, in this paper, we will discuss about survival of the soul according to immaterial soul and perfecting of soul as two premises for prove of resurrection. (shrink)

The latest draft (posted 05/14/22) of this short, concise work of proof, theory, and metatheory provides summary meta-proofs and verification of the work and results presented in the Theory and Metatheory of Atemporal Primacy and Riemann, Metatheory, and Proof. In this version, several new and revised definitions of terms were added to subsection SS.1; and many corrected equations, theorems, metatheorems, proofs, and explanations are included in the main text. The body of the text is approximately 18 pages, with (...) 3 sections; 1, an Introduction (with a 108 page listing of key terms & definitions), sect. 2, the Results, sect. 3, Discussion (commentary & predictions), and sect. 4, Works Cited. As much as possible, the style is intended for readability and understanding by very bright children (with some interest & knowledge of maths, etc.) and very interested nonprofessionals. The results of this project also enable upgrades of number theory, set theory, proof theory, metamathematics, the foundations of science, and quantum mechanics theory (etc.). (shrink)

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

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)

Edward Feser defends the ‘Neo-Platonic proof ’ for the existence of the God of classical theism. After articulating the argument and a number of preliminaries, I first argue that premise three of Feser’s argument—the causal principle that every composite object requires a sustaining efficient cause to combine its parts—is both unjustified and dialectically ill-situated. I then argue that the Neo-Platonic proof fails to deliver the mindedness of the absolutely simple being and instead militates against its mindedness. Finally, (...) I uncover two tensions between Trinitarianism and the Neo-Platonic proof. (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)

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)

This paper examines the role of reason in Shepherd's account of acquiring knowledge of the external world via first principles. Reason is important, but does not have a foundational role. Certain principles enable us to draw the required inferences for acquiring knowledge of the external world. These principles are basic, foundational and, more importantly, self‐evident and thus justified in other ways than by demonstration. Justificatory demonstrations of these principles are neither required, nor possible. By drawing on textual and contextual evidence, (...) I will show that Shepherd should have said that we know the first principles of any science, in general, and that “everything which begins to exist must have a cause”, in particular, via intuition, not via reason. Reasoning about such principles can help their self‐evidence shine through in certain cases; their justification, and our being justified in believing them, does not come from this reasoning, however. (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)

Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a (...) wider audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

The concept of burden of proof is used in a wide range of discourses, from philosophy to law, science, skepticism, and even in everyday reasoning. This paper provides an analysis of the proper deployment of burden of proof, focusing in particular on skeptical discussions of pseudoscience and the paranormal, where burden of proof assignments are most poignant and relatively clear-cut. We argue that burden of proof is often misapplied or used as a mere rhetorical gambit, with (...) little appreciation of the underlying principles. The paper elaborates on an important distinction between evidential and prudential varieties of burdens of proof, which is cashed out in terms of Bayesian probabilities and error management theory. Finally, we explore the relationship between burden of proof and several (alleged) informal logical fallacies. This allows us to get a firmer grip on the concept and its applications in different domains, and also to clear up some confusions with regard to when exactly some fallacies (ad hominem, ad ignorantiam, and petitio principii) may or may not occur. (shrink)

Is life a simple result of a conjunction of physico-chemical processes? Can be reduced to a mere juxtaposition of spatially determined events? What epistemology or world-view allows us to comprehend it? Aristotle built a novel philosophical system in which nature is a dynamical totality which is in constant movement. Life is a manifestation of it, and is formed and governed by the psyche. Psyche is the organizational principle of the different biological levels: nutritive, perceptive and intelective. Driesch's crucial experiment (...) provided empirical proof of the principle of life, which he called entelechy. Entelechy is an intensive manifoldness and cannot be comprehended by the usual extensive parameters. The entelechian's own ambiance is duration. This allows the reintroduction of the concept of teleology in the sphere of the living, understood not as a final cause, but as an order born from desire and leading to action. (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)

Despite recent controversies surrounding the principle that knowledge entails truth (KT), this paper aims to prove that the principle is true. It offers a proof of (KT) in the following sense. It advances a deductively valid argument for (KT), whose premises are, by most lights, obviously true. Moreover, each premise is buttressed by at least two supporting arguments. And finally, all premises and supporting arguments can be rationally accepted by people who don’t already accept (KT).

The work provides comprehensively definitive, unconditional proofs of Riemann's hypothesis, Goldbach's conjecture, the 'twin primes' conjecture, the Collatz conjecture, the Newcomb-Benford theorem, and the Quine-Putnam Indispensability thesis. The proofs validate holonomic metamathematics, meta-ontology, new number theory, new proof theory, new philosophy of logic, and unconditional disproof of the P/NP problem. The proofs, metatheory, and definitions are also confirmed and verified with graphic proof of intrinsic enabling and sustaining principles of reality.

It is a striking fact from reverse mathematics that almost all theorems of countable and countably representable mathematics are equivalent to just five subsystems of second order arithmetic. The standard view is that the significance of these equivalences lies in the set existence principles that are necessary and sufficient to prove those theorems. In this article I analyse the role of set existence principles in reverse mathematics, and argue that they are best understood as closure conditions on the powerset of (...) the natural numbers. (shrink)

The standard of proof applied in civil trials is the preponderance of evidence, often said to be met when a proposition is shown to be more than 50% likely to be true. A number of theorists have argued that this 50%+ standard is too weak – there are circumstances in which a court should find that the defendant is not liable, even though the evidence presented makes it more than 50% likely that the plaintiff’s claim is true. In this (...) paper, I will recapitulate the familiar arguments for this thesis, before defending a more radical one: The 50%+ standard is also too strong – there are circumstances in which a court should find that a defendant is liable, even though the evidence presented makes it less than 50% likely that the plaintiff’s claim is true. I will argue that the latter thesis follows naturally from the former once we accept that the parties in a civil trial are to be treated equally. I will conclude by sketching an alternative interpretation of the civil standard of proof. (shrink)

This work in metaphysics adheres to the critical demands of Immanuel Kant for what Kant would call a science of metaphysics, in that it consits strictly of a priori principles that, while from pure reason, can help make sense of our phenomenal world (Kant's criterion for objective validity). The work has an Appendix quoting Kant's most relevant remarks with regard to a science, and offers parallel quotes from David Hume's "Treatise of Human Nature". The work advances the explanation of a (...) causal process that accounts for the origination of the universals: space, time, mass (or substance), and mind (or consciousness), and it necessitates the existence of God as Absolute Being and Absolute Mind. Hegel's 'Science of Logic' is quoted wherein Hegel makes an analogous claim. The causal process is defined with both a definite beginning and a definite end and agreement can be found with the statement found in the book of Revelation, final chapter: "I am the Alpha and the Omega, the first and the last, the beginning and the end." The statement suggests a movement that is not in conflict with the science, and seems to reflect Hegel's own thoughts. The science does not conflict with, but it further finds agreement with the science of big bang cosmology, but it goes further in necessitating a 'singularity' at the beginning of time. The causal process defined has a Formative Phase and a Creative Phase, with the former preceding the big bang and the latter following after the big bang. (shrink)

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

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)

The paper briefly surveys the sentential proof-theoretic semantics for fragment of English. Then, appealing to a version of Frege’s context-principle (specified to fit type-logical grammar), a method is presented for deriving proof-theoretic meanings for sub-sentential phrases, down to lexical units (words). The sentential meaning is decomposed according to the function-argument structure as determined by the type-logical grammar. In doing so, the paper presents a novel proof-theoretic interpretation of simple type, replacing Montague’s model-theoretic type interpretation (in arbitrary (...) Henkin models). The domains of derivations are collections of derivations in the associated “dedicated” natural-deduction proof-system, and functions therein (with no appeal to models, truth-values and elements of a domain). The compositionality of the semantics is analyzed. (shrink)

We review the definition of the Full Bayesian Significance Test (FBST), and summarize its main statistical and epistemological characteristics. We review also the Abstract Belief Calculus (ABC) of Darwiche and Ginsberg, and use it to analyze the FBST’s value of evidence. This analysis helps us understand the FBST properties and interpretation. The definition of value of evidence against a sharp hypothesis, in the FBST setup, was motivated by applications of Bayesian statistical reasoning to legal matters where the sharp hypotheses were (...) defendants statements, to be judged according to the Onus Probandi juridical principle. (shrink)

One of the main motivations for having a compositional semantics is the account of the productivity of natural languages. Formal languages are often part of the account of productivity, i.e., of how beings with finite capaci- ties are able to produce and understand a potentially infinite number of sen- tences, by offering a model of this process. This account of productivity con- sists in the generation of proofs in a formal system, that is taken to represent the way speakers grasp (...) the meaning of an indefinite number of sentences. The informational basis is restricted to what is represented in the lexicon. This constraint is considered as a requirement for the account of productivity, or at least of an important feature of productivity, namely, that we can grasp auto- matically the meaning of a huge number of complex expressions, far beyond what can be memorized. However, empirical results in psycholinguistics, and especially particular patterns of ERP, show that the brain integrates informa- tion of different sources very fast, without any felt effort on the part of the speaker. This shows that formal procedures do not explain productivity. How- ever, formal models are still useful in the account of how we get at the seman- tic value of a complex expression, once we have the meanings of its parts, even if there is no formal explanation of how we get at those meanings. A practice-oriented view of modeling gives an adequate interpretation of this re- sult: formal compositional semantics may be a useful model for some ex- planatory purposes concerning natural languages, without being a good model for dealing with other explananda. (shrink)

This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, (...) we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate. (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. (...) Much of Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

The work provides comprehensively definitive, unconditional proofs of Riemann's hypothesis, Goldbach's conjecture, the 'twin primes' conjecture, the Collatz conjecture, the Newcomb-Benford theorem, and the Quine-Putnam Indispensability thesis. The proofs validate holonomic metamathematics, meta-ontology, new number theory, new proof theory, new philosophy of logic, and unconditional disproof of the P/NP problem. The proofs, metatheory, and definitions are also confirmed and verified with graphic proof of intrinsic enabling and sustaining principles of reality.

I have read many recent discussions of the limits of computation and the universe as computer, hoping to find some comments on the amazing work of polymath physicist and decision theorist David Wolpert but have not found a single citation and so I present this very brief summary. Wolpert proved some stunning impossibility or incompleteness theorems (1992 to 2008-see arxiv.org) on the limits to inference (computation) that are so general they are independent of the device doing the computation, and even (...) independent of the laws of physics, so they apply across computers, physics, and human behavior. They make use of Cantor's diagonalization, the liar paradox and worldlines to provide what may be the ultimate theorem in Turing Machine Theory, and seemingly provide insights into impossibility,incompleteness, the limits of computation,and the universe as computer, in all possible universes and all beings or mechanisms, generating, among other things,a non-quantum mechanical uncertainty principle and a proof of monotheism. (shrink)

As the 19th century drew to a close, logicians formalized an ideal notion of proof. They were driven by nothing other than an abiding interest in truth, and their proofs were as ethereal as the mind of God. Yet within decades these mathematical abstractions were realized by the hand of man, in the digital stored-program computer. How it came to be recognized that proofs and programs are the same thing is a story that spans a century, a chase with (...) as many twists and turns as a thriller. At the end of the story is a new principle for designing programming languages that will guide computers into the 21st century. -/- For my money, Gentzen’s natural deduction and Church’s lambda calculus are on a par with Einstein’s relativity and Dirac’s quantum physics for elegance and insight. And the maths are a lot simpler. I want to show you the essence of these ideas. I’ll need a few symbols, but not too many, and I’ll explain as I go along. -/- To simplify, I’ll present the story as we understand it now, with some asides to fill in the history. First, I’ll introduce Gentzen’s natural deduction, a formalism for proofs. Next, I’ll introduce Church’s lambda calculus, a formalism for programs. Then I’ll explain why proofs and programs are really the same thing, and how simplifying a proof corresponds to executing a program. Finally, I’ll conclude with a look at how these principles are being applied to design a new generation of programming languages, particularly mobile code for the Internet. (shrink)

What Bar-On and Simmons call 'Conceptual Deflationism' is the thesis that truth is a 'thin' concept in the sense that it is not suited to play any explanatory role in our scientific theorizing. One obvious place it might play such a role is in semantics, so disquotationalists have been widely concerned to argued that 'compositional principles', such as -/- (C) A conjunction is true iff its conjuncts are true -/- are ultimately quite trivial and, more generally, that semantic theorists have (...) misconceived the relation between truth, meaning, and logic. This paper argues, to the contrary, that even such simple compositional principles as (C) have substantial content that cannot be captured by deflationist 'proofs' of them. The key thought is that (C) is supposed, among other things, to affirm the truth-functionality of conjunction and that disquotationalists cannot, ultimately, make sense of truth-functionality. -/- This paper is something of a companion to "The Logical Strength of Compositional Principles". (shrink)

I have read many recent discussions of the limits of computation and the universe as computer, hoping to find some comments on the amazing work of polymath physicist and decision theorist David Wolpert but have not found a single citation and so I present this very brief summary. Wolpert proved some stunning impossibility or incompleteness theorems (1992 to 2008-see arxiv dot org) on the limits to inference (computation) that are so general they are independent of the device doing the computation, (...) and even independent of the laws of physics, so they apply across computers, physics, and human behavior. They make use of Cantor's diagonalization, the liar paradox and worldlines to provide what may be the ultimate theorem in Turing Machine Theory, and seemingly provide insights into impossibility, incompleteness, the limits of computation, and the universe as computer, in all possible universes and all beings or mechanisms, generating, among other things, a non- quantum mechanical uncertainty principle and a proof of monotheism. There are obvious connections to the classic work of Chaitin, Solomonoff, Komolgarov and Wittgenstein and to the notion that no program (and thus no device) can generate a sequence (or device) with greater complexity than it possesses. One might say this body of work implies atheism since there cannot be any entity more complex than the physical universe and from the Wittgensteinian viewpoint, ‘more complex’ is meaningless (has no conditions of satisfaction, i.e., truth-maker or test). Even a ‘God’ (i.e., a ‘device’with limitless time/space and energy) cannot determine whether a given ‘number’ is ‘random’, nor find a certain way to show that a given ‘formula’, ‘theorem’ or ‘sentence’ or ‘device’ (all these being complex language games) is part of a particular ‘system’. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 2nd ed (2019) and Suicidal Utopian Delusions in the 21st Century 4th ed (2019) . (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)

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

Tsui and Weymark (Economic Theory, 1997) have shown that the only continuous social welfare orderings on the whole Euclidean space which satisfy the weak Pareto principle and are invariant to individual-specific similarity transformations of utilities are strongly dictatorial. Their proof relies on functional equation arguments which are quite complex. This note provides a simpler proof of their theorem.

Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...) foundations of mathematics and in relation to philosophical motivations leading to the development of intuitionistic logic. This sets the stage for a brief description of the relevant part of Dummett’s program to recast debates in metaphysics, and in particular disputes about realism and anti-realism, as closely intertwined with issues in philosophical logic, with the acceptance of classical logic for a domain reflecting a commitment to realism for that domain. Then I review extant results about what is provable and what is not when one adds epsilon to intuitionistic logic, largely due to Bell and DeVidi, and I give several new proofs of intermediate logics from intuitionistic logic+ε without identity. With all this in hand, I turn to a discussion of the philosophical significance of choice operators. Among the conclusions I defend are that these results provide a finer-grained basis for Dummett’s contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions; that Dummett’s framework is improved by these results as they show that questions of realism and anti-realism are not an “all or nothing” matter, but that there are plausibly metaphysical stances between the poles of anti-realism and realism, because different sorts of ontological assumptions yield intermediate rather than classical logic; and that these intermediate positions between classical and intuitionistic logic link up in interesting ways with our intuitions about issues of objectivity and reality, and do so usefully by linking to questions around intriguing everyday concepts such as “is smart,” which I suggest involve a number of distinct dimensions which might themselves be objective, but because of their multivalent structure are themselves intermediate between being objective and not. Finally, I discuss the implications of these results for ongoing debates about the status of arbitrary and ideal objects in the foundations of logic, showing among other things that much of the discussion is flawed because it does not recognize the degree to which the claims being made depend on the presumption that one is working with a very strong logic. (shrink)

Robert Koons claims that my previous critique of his “new” cosmological argument is vitiated by confusion about the nature of defeasible argumentation.In response, I claim that Koons misrepresents—and perhaps misunderstands—the nature of my objections to his “new” cosmological argument. The main claims which I defend are: (1) that the move from a non-defeasible to a defeasible causal principle makes absolutely no difference to the success of the cosmological argument in which it is contained; and (2) that, since it is (...) perfectly well understood that non-theists have many reasons for rejecting the defeasible causal principle, it is pointless to claim that the move to a defeasible principle brings about a shift in the “burden of proof”. (Since some people may have forgotten—or may choose to ignore—the fact that non-theists do have reasons for rejecting the defeasible causal principle, I also provide a discussion of a modest sample of these reasons.). (shrink)

This Article aims to demonstrate that the WTO jurisprudence on science-related trade disputes has become imbued with a specific vision of science that has prevented any possible application of the precautionary principle. This situation is due both to the WTO’s specific dispute settlement procedures and to the substantive nature of precautionary measures. Indeed, such measures’ foundation on “insufficient scientific evidence” dramatically undermines the probative value of science in WTO adjudication and creates a seeming contradiction: The system requires defendants to (...) provide legal evidence of the absence of sufficient scientific evidence. The reasoning of the Panel on the EC–Biotech case was riddled with this apparent paradox. For the first time, the US–Continued Suspension case has opened a gateway to address this fundamental issue. (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)

It is widely assumed among contemporary philosophers that Descartes’ version of ontological proof, among other weaknesses, makes an impossible and unjustified move from the mental world of concepts to the real world of things. Contrary to this opinion I will try to show that Descartes’ famous principle of clear and distinct perception suffices to find an adequate inferential connection between the contents of the human mind and extra-mental reality. In a clear and distinct way we cognitively grasp the (...) concept of supremely perfect being as the concept that we do not construct by an arbitrary definition of the word ”God’. (shrink)

In debates about animal sentience, the precautionary principle is often invoked. The idea is that when the evidence of sentience is inconclusive, we should “give the animal the benefit of the doubt” or “err on the side of caution” in formulating animal protection legislation. Yet there remains confusion as to whether it is appropriate to apply the precautionary principle in this context, and, if so, what “applying the precautionary principle” means in practice regarding the burden of (...) class='Hi'>proof for animal sentience. Here I construct a version of the precautionary principle tailored to the question of animal sentience together with a practical framework for implementing it. I explain and defend the key features of this framework, argue that it is well-aligned with current practice in animal welfare science, and consider and reject a number of influential counterarguments to the use of precautionary reasoning in this area. (shrink)

We investigate the theory IΔ 0 + Ω 1 and strengthen [Bu86. Theorem 8.6] to the following: if NP ≠ co-NP. then Σ-completeness for witness comparison formulas is not provable in bounded arithmetic. i.e. $I\delta_0 + \Omega_1 + \nvdash \forall b \forall c (\exists a(\operatorname{Prf}(a.c) \wedge \forall = \leq a \neg \operatorname{Prf} (z.b))\\ \rightarrow \operatorname{Prov} (\ulcorner \exists a(\operatorname{Prf}(a. \bar{c}) \wedge \forall z \leq a \neg \operatorname{Prf}(z.\bar{b})) \urcorner)).$ Next we study a "small reflection principle" in bounded arithmetic. We prove that (...) for all sentences φ $I\Delta_0 + \Omega_1 \vdash \forall x \operatorname{Prov}(\ulcorner \forall y \leq \bar{x} (\operatorname{Prf} (y. \overline{\ulcorner \varphi \urcorner}) \rightarrow \varphi)\urcorner).$ The proof hinges on the use of definable cuts and partial satisfaction predicates akin to those introduced by Pudlak in [Pu86]. Finally, we give some applications of the small reflection principle, showing that the principle can sometimes be invoked in order to circumvent the use of provable Σ-completeness for witness comparison formulas. (shrink)

I present and discuss three previously unpublished manuscripts written by Bertrand Russell in 1903, not included with similar manuscripts in Volume 4 of his Collected Papers. One is a one-page list of basic principles for his “functional theory” of May 1903, in which Russell partly anticipated the later Lambda Calculus. The next, catalogued under the title “Proof That No Function Takes All Values”, largely explores the status of Cantor’s proof that there is no greatest cardinal number in the (...) variation of the functional theory holding that only some but not all complexes can be analyzed into function and argument. The final manuscript, “Meaning and Denotation”, examines how his pre-1905 dis­tinction between meaning and denotation is to be understood with respect to functions and their arguments. In them, Russell seems to endorse an extensional view of functions not endorsed in other works prior to the 1920s. All three manuscripts illustrate the close connection between his work on the logical paradoxes and his work on the theory of meaning. (shrink)

Table of Contents: Chapter 1: Wolff and the Refinement of the Mathematical Method / Chapter 2: Wolff’s Emendation of Ontology / Chapter 3: Soul, World, and God: Wolff’s Metaphysics / Chapter 4: The Abuse of Philosophy: Pietism and the Metaphysics of Freedom / Chapter 5: Women and the Wolffian Philosophy / Chapter 6: Reason beyond Proof: Debating the Use and Limits of the PSR / Chapter 7: The Paradoxes of Sensation from Wolff to Amo / Chapter 8: The Fate (...) of the Soul: G. F. Meier on Immortality / Chapter 9: Moses Mendelssohn and Spinoza’s Ghost . (shrink)

We defend hylomorphism against Maegan Fairchild’s purported proof of its inconsistency. We provide a deduction of a contradiction from SH+, which is the combination of “simple hylomorphism” and an innocuous premise. We show that the deduction, reminiscent of Russell’s Paradox, is proof-theoretically valid in classical higher-order logic and invokes an impredicatively defined property. We provide a proof that SH+ is nevertheless consistent in a free higher-order logic. It is shown that the unrestricted comprehension principle of property (...) abstraction on which the purported proof of inconsistency relies is analogous to naïve unrestricted set-theoretic comprehension. We conclude that logic imposes a restriction on property comprehension, a restriction that is satisfied by the ramified theory of types. By extension, our observations constitute defenses of theories that are structurally similar to SH+, such as the theory of singular propositions, against similar purported disproofs. (shrink)

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

This chapter investigates the precise ways in which Antonio Gramsci engaged with ancient philosophy. A brief examination of the longest discussion in the Prison Notebooks of any ancient philosopher or text, Plato’s Republic (Q8, §22), raises many questions about Gramsci’s approach to ancient philosophy. These questions motivate an investigation into Gramsci’s surprisingly minimal discussion of ancient philosophy and philosophers, which is best explained in the light of his theoretical commitments to his distinctive species of historical materialism. Rather than responding to (...) specific critical insights advanced about politics or human nature by ancient philosophers, such as Plato and Aristotle, Gramsci is shown to appropriate ancient philosophy into a broad-spectrum project of the history of philosophy, which interrogates the specific conditions under which historical epochs and the philosophical ideas that characterise them emerge. Tracking the conditions and characteristic ideas is revealed to be the project of the ‘specialist philosopher’, who must grasp both general methodological principles and particular historical examples. Gramsci’s treatment of ancient philosophy reveals more about his universal theories of history, and his engagement with the ideas of his contemporaries (including Benedetto Croce), than a special concern with ancient philosophy itself. (shrink)

Growing technological advances in intelligent artifacts and bitter experiences of the past have emphasized the need to use and operate ethics in this field. Accordingly, it is vital to discuss the ethical integrity of having intelligent artifacts. Concerning the method of gathering materials, the current study uses library and documentary research followed by attribution style. Moreover, descriptive analysis is employed in order to analyze data. Explaining and criticizing the opposing views in this field and reviewing the related literature, it is (...) concluded that the proof of the ethical integrity of the intelligent artifacts is possible due to the specific features of these artifacts and their own moral system. (shrink)