C. Stephen Layman contends that an argument supporting theism over naturalism can be constructed based on three defensible, non–question-begging premises about the moral order. Previous critics of Layman’s argument have challenged the truth of these premises. We stipulate them arguendo but go on to show that there is a deeper problem: a fourth premise introduced to complete the argument—the “completion premise,” as we call it—is true only if we assume that God exists or we concede that there is no afterlife. (...) We close with suggestions for how Layman’s argument must be strengthened to meet with dialectical success. (shrink)

Cancel culture is a form of societal self-defense that becomes prominent particularly during periods of substantial moral upheaval. It can lead to the polarization of incompatible viewpoints if it is indiscriminately demonized. In this brief editorial letter, I consider framing cancel culture as an essentially contested concept (ECC), according to the theory of Walter B. Gallie, with the aim of establishing a groundwork for a more productive discourse on it. In particular, I propose that intermediate agreements and principles of reasonableness (...) can help refocus the debate on cancel culture towards democratic discourse, without blanket justification for every instance. In this context, asserting that cancel culture is an ECC does not dismiss the potential of achieving consensus on its shared core meaning or societal role. Like other similar ECCs, such as democracy or rule of law, it highlights the importance of contestations in shaping our collective understanding of the concept. (shrink)

Following Post program, we will propose a linguistic and empirical interpretation of Gödel’s incompleteness theorem and related ones on unsolvability by Church and Turing. All these theorems use the diagonal argument by Cantor in order to find limitations in finitary systems, as human language, which can make “infinite use of finite means”. The linguistic version of the incompleteness theorem says that every Turing complete language is Gödel incomplete. We conclude that the incompleteness and unsolvability theorems find limitations in our finitary (...) tool, which is our complete language. (shrink)

What is the best way to make sustained societal progress over time? Non-ideal theory done on its own faces the problem of second best, but ideal theory seems unable to cope with disagreement about how to make progress. If ideal theory gives up its claims to completeness, then we can use the method of incompletely theorized agreements to make progress over time.

Luck egalitarianism makes a fundamental distinction between inequalities for which agents are responsible and inequalities stemming from luck. I give several reasons to find luck egalitarianism a compelling view of distributive justice. I then argue that it is an incomplete theory of equality. Luck egalitarianism lacks the normative resources to achieve its ends. It is unable to specify the prior conditions under which persons are situated equivalently such that their choices can bear this tremendous weight. This means that luck egalitarians (...) need to become pluralists who understand equality not merely in terms of choice, luck, and responsibility. After developing my critical argument that luck egalitarianism is incomplete, I sketch a strategy for rehabilitating and filling out the theory. (shrink)

The Mamanuas of Basey, Samar have been in an itinerant state since the 1950s. Their indigenous experience can be capped in the term ‘diaspora,’ which pictures their plight as dispersive habituation, moving from town to town away from their homeland. In a recent study which this paper hinges upon, the concept of diaspora can no longer work and is argued to imperatively function as a vanishing mediator so that indigeneity must come to mean as a constant identity of becoming. Following (...) from such a theoretical lens, this paper delves again into the concept of ‘diaspora’ in the Mamanuan indigenous experience to argue further that its act of mediating functions as performative indigeneity. To do this, the paper runs in three parts: first, it plots the Mamanuan diaspora experience; second, it briefly reiterates the core argument of diaspora as vanishing mediator; and finally, it theorizes on a concept of what Judith Butler calls ‘performative indigeneity’ that takes its form from the mediation of an indigenous diaspora experience. (shrink)

It is often argued that while biases routinely influence the generation of scientific theories, a subsequent rational evaluation of such theories will ensure that biases do not affect which theories are ultimately accepted. Against this line of thought, this paper shows that the existence of certain kinds of biases at the generation-stage implies the existence of biases at the evaluation-stage. The key argumentative move is to recognize that a scientist who comes up with a new theory about some phenomena has (...) thereby gained an unusual type of evidence, viz. information about the space of theories that could be true of the phenomena. It follows that if there is bias in the generation of scientific theories in a given domain, then the rational evaluation of theories with reference to the total evidence in that domain will also be biased. (shrink)

The determinism-free will debate is perhaps as old as philosophy itself and has been engaged in from a great variety of points of view including those of scientific, theological, and logical character. This chapter focuses on two arguments from logic. First, there is an argument in support of determinism that dates back to Aristotle, if not farther. It rests on acceptance of the Law of Excluded Middle, according to which every proposition is either true or false, no matter whether (...) the proposition is about the past, present or future. In particular, the argument goes, whatever one does or does not do in the future is determined in the present by the truth or falsity of the corresponding proposition. The second argument coming from logic is much more modern and appeals to Gödel's incompleteness theorems to make the case against determinism and in favour of free will, insofar as that applies to the mathematical potentialities of human beings. The claim more precisely is that as a consequence of the incompleteness theorems, those potentialities cannot be exactly circumscribed by the output of any computing machine even allowing unlimited time and space for its work. The chapter concludes with some new considerations that may be in favour of a partial mechanist account of the mathematical mind. (shrink)

The starting point of this paper is the thought that the phenomenal appearances that accompany mental states are somehow only there, or only real, from the standpoint of the subject of those mental states. The world differs across subjects in terms of which appearances obtain. Not only are subjects standpoints across which the world varies, subjects are standpoints that we can ‘adopt’ in our own theorizing about the world (or stand back from). The picture that is suggested by these claims (...) has an appeal but is at the same time obscure and stands in need of regimentation. This paper explores and motivates a metaphysical account of what it is for subjects to be standpoints, what it is to adopt standpoints in our representations and, most importantly, how these notions might help us better understand the subjective character of conscious mental states. Some well-known observations by Thomas Nagel serve as starting points and the paper concludes by revisiting Nagel’s argument for the inevitable incompleteness of objective accounts of mental states, which will be reframed in terms of the central commitments of the proposed framework. (shrink)

The revisionist critique of conventional just war theory has undoubtedly scored some important victories. Walzer’s elegantly unified defense of combatant legal equality and noncombatant immunity has been seriously undermined. This critical success has not, however, been matched by positive arguments, which when applied to the messy reality of war would deprive states and soldiers of the permission to fight wars that are plausibly thought to be justified. The appeal to law that is sought to resolve this objection by casting (...) it as a practical concern, a pragmatic worry about implementation, which while germane to debates over the laws of war, need not undermine our convictions in the fundamental principles the revisionists advocate. This response is inadequate. Revisionists have not shown that soldiers should obey the laws of war, in practice, when they conflict with their other moral reasons – our worries about application remain intact. Moreover, a theory of war that offers only an account of the laws of war, and a set of fundamental principles developed in abstraction from feasibility constraints, is radically incomplete. We need to know how to apply those fundamental principles, and whether, when applied, they lead to defensible conclusions. Only two options seem to remain. Perhaps the revisionists’ arguments for their chosen fundamental principles are sufficiently compelling that we should stick with them, and accept their troubling conclusions – in other words, accept pacifism. Alternatively, we need to revise our fundamental principles, so that when applied they yield conclusions that we can more confidently endorse. -/- Though it does not save the revisionist view from the responsibility dilemma and cognate objections, the appeal to law does raise an important, and previously inadequately theorized, question – or, rather, resurrects a neglected topic, discussed in depth by historical just war theorists such as Grotius and Vattel. There are good grounds for distinguishing the laws of war from the morality of war, and for adjusting the former to accommodate predictable noncompliance, that should not impact on our account of the latter. Nonetheless, I have argued that there are some profound moral insights underlying both combatant legal equality and noncombatant immunity: specifically, we cannot infer from a combatant’s side having not satisfied jus ad bellum that he may not justifiably use lethal force; and other things equal, it is more wrongful to harm a nonliable noncombatant than to harm a nonliable combatant. (shrink)

Defeasible argumentation has been applied successfully in several real-world domains in which it is necessary to handle incomplete and contradictory information. In recent years, there have been interesting attempts to carry out argumentation processes supported by massive repositories developing argumentative reasoning applications. One of such efforts builds arguments by retrieving information from relational databases using the DBI-DeLP framework; this article presents eDBI-DeLP, which extends the original DBI-DeLP framework by providing two novel aspects which refine the interaction between DeLP programs (...) and relational databases. First, we expand the expressiveness of dbi-delp programs by providing ways of controlling how the information in databases is recovered; this is done by introducing filters that enable an improved fine-grained control on the argumentation processes which become useful in applications, providing the semantics and the implementation of such filters. Second, we introduce an argument comparison criterion which can be adjusted at the level of literals to model particular features such as credibility and topic expertise, among others. These new tools can be particularly useful in environments such as medical diagnosis expert systems, decision support systems, or recommender systems based on argumentation, where datasets are often provided in the form of relational databases. (shrink)

A growing body of recent work in informal logic investigates the process of argumentation. Among other things, this work focuses on the ways in which individuals attempt to understand written or verbalised arguments in light of the fact that these are often presented in forms that are incomplete and unmarked. One of its aims is to develop general procedures for natural language argument recognition and reconstruction. Our aim here is to draw on this growing body of knowledge in informal (...) logic in order to take preliminary steps towards developing an architecture for computer systems that are able to recognise and reconstruct natural language arguments. This architecture aims to structure research of an applied and computational nature that strives to implement linguistic systems of various sorts, and to analyse problems in a way that both yields manageable and relatively independent components and also highlights how implementations can interact with existing resources from natural language processing. (shrink)

According to indexical contextualism, the perspectival element of taste predicates and epistemic modals is part of the content expressed. According to nonindexicalism, the perspectival element must be conceived as a parameter in the circumstance of evaluation, which engenders “thin” or perspective-neutral semantic contents. Echoing Evans, thin contents have frequently been criticized. It is doubtful whether such coarse-grained quasi-propositions can do any meaningful work as objects of propositional attitudes. In this paper, I assess recent responses by Recanati, Kölbel, Lasersohn and MacFarlane (...) to the “incompleteness worry”. None of them manages to convince. Particular attention is devoted to an argument by John MacFarlane, which states that if perspectives must be part of the content, so must worlds, which would make intuitively contingent propositions necessary. I demonstrate that this attempt to defend thin content views such as nonindexical contextualism and relativism conflates two distinct notions of necessity, and that radical indexicalist accounts of semantics, such as Schaffer’s necessitarianism, are in fact quite plausible. (shrink)

The ambiguity theory of ‘knows’ is the view that ‘knows’ and its cognates have more than one propositional sense – i.e. more than one sense that can properly be used in ‘knows that’ etc. constructions. Given that most of us are ‘intuitive invariantists’ – i.e. most of us initially have the intuition that ‘knows’ is univocal – defenders of the ambiguity theory need to offer an explanation for the semantic blindness present if ‘knows’ is in fact ambiguous. This paper is (...) an attempt to offer such an explanation. Section 1 contains a general argument for the ubiquity of semantic blindness for ambiguous words; the upshot being that semantic blindness for the ambiguity of ‘knows’ is thus unsurprising. Section 2 offers more specific arguments for why ‘knows’ is the type of ambiguous word that we’re very unlikely to quickly recognize is ambiguous. (shrink)

Arguments of stability, intended in a wide sense, including the discussion of the conditions of the onset of instability and of stability changes, play a central role in the main theorizations of morphogenesis in 20th century theoretical biology. The aim of this essay is to shed light on concepts and images mobilized in the construction of arguments of stability in theorizing morphogenesis, since they are pivotal in establishing meaningful relationships between mathematical models and empirical morphologies.

This paper proposes the feasibility of a second-order approach in cosmology. It is intended to encourage cosmologists to rethink standard ideas in their field, leading to a broader concept of self-organization and of science itself. It is argued, from a cognitive epistemology perspective, that a first-order approach is inadequate for cosmology; study of the universe as a whole must include study of the scientific observer and the process of theorizing. Otherwise, concepts of self-organization at the cosmological scale remain constrained by (...) unacknowledged assumptions and biases. Examples of limiting notions are discussed in the context of alternatives. To include the role of the theorist does not mean reducing science to subjective or sociological terms. On the contrary, second-order science would provide a more complete portrait of nature. The work of cosmologist Lee Smolin is discussed as a candidate example of second-order cosmology. (shrink)

The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity in set (...) theory. Thus, the pair of arithmetic and set are to be similar to Euclidean and non-Euclidean geometries distinguishably only by the Fifth postulate now, i.e. after replacing it and its negation correspondingly by the axiom of finiteness (induction) versus that of finiteness being idempotent negations to each other. Indeed, the axiom of choice, as far as it is equivalent to the well-ordering “theorem”, transforms any set in a well-ordering either necessarily finite according to the axiom of induction or also optionally infinite according to the axiom of infinity. So, the Gödel incompleteness statement relies on the logical contradiction of the axiom of induction and the axiom of infinity in the final analysis. Nonetheless, both can be considered as two idempotent versions of the same axiom (analogically to the Fifth postulate) and then unified after logicism and its inherent intensionality since the opposition of finiteness and infinity can be only extensional (i.e., relevant to the elements of any set rather than to the set by itself or its characteristic property being a proposition). So, the pathway for interpreting the Gödel incompleteness statement as an axiom and the originating from that assumption for “Hilbert mathematics” accepting its negation is pioneered. A much wider context relevant to realizing the Gödel incompleteness statement as a metamathematical axiom is consistently built step by step. The horizon of Hilbert mathematics is the proper subject in the third part of the paper, and a reinterpretation of Gödel’s papers (1930; 1931) as an apology of logicism as the only consistent foundations of mathematics is the topic of the next second part. (shrink)

Evolutionary Debunking Arguments are defined as arguments that appeal to the evolutionary genealogy of our beliefs to undermine their justification. Recently, Helen De Cruz and her co-authors supported the view that EDAs are self-defeating: if EDAs claim that human arguments are not justified, because the evolutionary origin of the beliefs which figure in such arguments undermines those beliefs, and EDAs themselves are human arguments, then EDAs are not justified, and we should not accept their conclusions (...) about the fact that human arguments are unjustified. De Cruz's objection to EDAs is similar to the objection raised by Reuben Hersh against the claim that, since by Gödel's second incompleteness theorem the purpose of mathematical logic to give a secure foundation for mathematics cannot be achieved, mathematics cannot be said to be absolutely certain. The response given by Carlo Cellucci to Hersh's objection shows that the claim that by Gödel's results mathematics cannot be said to be absolutely certain is not self-defeating, and can be adopted to show that EDAs are not self-defeating as well in a twofold sense: an argument analogous to Cellucci's one may be developed to face De Cruz's objection, and such argument may be further refined incorporating Cellucci's response itself in it, to make it stronger. This paper aims at showing that the accusation of being self-defeating moved against EDAs is inadequate by elaborating an argument which can be considered an EDA and which can also be shown not to be self-defeating. (shrink)

Some theorists—including Elizabeth Anderson, Gerald Gaus, and Amartya Sen—endorse versions of 'public reason' as the appropriate way to justify political decisions while rejecting 'ideal theory'. This chapter proposes that these ideas are not easily separated. The idea of public reason expresses a form of mutual 'civic' respect for citizens. Public reason justifications for political proposals are addressed to citizens who would find acceptable those justifications, and consequently would comply freely with those proposals should they become law. Hence public reasoning involves (...) 'local ideal theorizing': the justification of political proposals includes their consideration and evaluation under conditions of compliance with them by the citizens to whom those justifications are addressed. Local ideal theorizing, moreover, can lead to 'full ideal theorizing', wherein citizens outline and evaluate an amended version of their society’s 'basic structure'. This argument is illustrated by some recent empirical work on inequality within the United States. (shrink)

In his 1918 logical atomism lectures, Russell argued that there are no molecular facts. But he posed a problem for anyone wanting to avoid molecular facts: we need truth-makers for generalizations of molecular formulas, but such truth-makers seem to be both unavoidable and to have an abominably molecular character. Call this the problem of generalized molecular formulas. I clarify the problem here by distinguishing two kinds of generalized molecular formula: incompletely generalized molecular formulas and completely generalized molecular formulas. I (...) next argue that, if empty worlds are logically possible, then the model-theoretic and truth-functional considerations that are usually given address the problem posed by the first kind of formula, but not the problem posed by the second kind. I then show that Russell’s commitments in 1918 provide an answer to the problem of completely generalized molecular formulas: some truth-makers will be non-atomic facts that have no constituents. This shows that the neo-logical atomist goal of defending the principle of atomicity—the principle that only atomic facts are truth-makers—is not realizable. (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)

In support of a lean and humble anthropology I discuss six key articles that provide indirect arguments for humility. In summary, these articles teach us that the terms of a discussion may be flawed and cannot be resolved by agreeing shared meanings (Gallie); we must accept limits on what we can know (Nagel); depictions, visual representations are potentially confusing, forms of translation across media types are ubiquitous; (Wolf); portraits are exemplary performances of the self, even the most casual depictions (...) are of the act of posing; (Berger); varying meanings may be associated with a single item, which may convey different things to different people in different places and at different times (Miller and Woodward); and that accounts of a social group and its ideas must encompass vagueness and inconsistency rather than present a misleading coherence and consistency (Favret-Saada). Together these provide reasons for developing a humble anthropology, one that recognizes its incompleteness and revisability. Keywords: Humility, sparsity, meaning, vagueness. (shrink)

Almost all philosophers interested in parthood and composition think that a composite object is a further thing, numerically distinct from the objects that compose it. Call this the orthodox view. I argue that the orthodox view is false, and that a composite object is identical to the objects that compose it (collectively). This view is known as composition as identity. -/- I argue that, despite its unpopularity, there are many reasons to favour com- position as identity over the orthodox view. (...) First, defenders of the orthodox view have not offered complete theories of composition. For instance, they have not given adequate accounts of heterogeneous properties like being black and white in composite objects. Nor have they given satisfactory explanations for the necessary connections that hold between composite objects and their proper parts. -/- Second, there appears to be no good way for defenders of the orthodox view to remedy this. Any account of the heterogeneous properties of composite objects which is compatible with the orthodox view faces serious problems, as does any account of the necessary connections between an object and its proper parts. Composition as identity, on the other hand, is compatible with intuitive responses to both of these challenges. -/- Third, there are a number of strong arguments in favour of composition as identity. For example, composition as identity fits our evidence about the way the world is better than the orthodox view does. It also allows us to easily maintain that composition sometimes occurs and sometimes does not—i.e., it allows us to easily maintain that composition is restricted. The orthodox view does not. The theories of composition put forward by most philosophers are at best incomplete or in need of improvement. At worst, they are false and composition as identity is true. (shrink)

Ignited by Einstein and Bohr a century ago, the philosophical struggle about Reality is yet unfinished, with no signs of a swift resolution. Despite vast technological progress fueled by the iconic Einstein/Podolsky/Rosen paper (EPR) [1] [2] [3], the intricate link between ontic and epistemic aspects of Quantum Theory (QT) has greatly hindered our grip on Reality and further progress in physical theory. Fallacies concealed by tortuous logical negations made EPR comprehension much harder than it could have been had Einstein written (...) it himself in German. EPR is plagued with preconceptions about what a physical property is, the 'Uncertainty Principle', and the Principle of Locality. Numerous interpretations of QT vis à vis Reality exist and are keenly disputed [4] [5] [6] [7] [8] [9] [10] [11]. This is the first of a series of articles arguing for a novel physical interpretation I call ‘The Ontic Probability Interpretation’ (TOPI). A gradual explanation of TOPI is given intertwined with a meticulous logico-philosophical scrutiny of EPR, with Part I focusing on the meaning of Einstein’s ‘incompleteness’ claim for QT: a conceptual confusion, a preconception about Reality, and a flawed dichotomy are shown to be severe obstacles for the EPR argument to succeed. Part II completes the analysis, proving EPR claim of ‘incompleteness’ for QT is fallacious [12]. Part III further develops TOPI, while scrutinizing the mythical ‘Schrödinger’s Cat’, as well as the ‘Basis’ and ‘Measurement’ pseudo-problems [13]. Part IV introduces QR/TOPI: a new theory that solves the century-old problem of integrating Special Relativity with Quantum Theory [14]. (shrink)

After identifying in Part I [1] a conceptual confusion (TCC), a Reality preconception (TRP1), and a fallacious dichotomy (TFD), the famous EPR/EPRB [2] [3] [4] [5] [6] argument for correlated ‘particles’ is now studied in the light of the Ontic Probability Interpretation of Quantum Theory (QT/TOPI). Another Reality preconception (TRP2) is found, showing that EPR used and ignored QT predictions in a single paralogism. Employing TFD and TRP2, EPR unveiled a contradiction veiled in its premises. By removing nonlocality from QT’s (...) Ontology [1] by fiat, EPR preordained its incompleteness. The Petitio Principii fallacy was at work from the outset. Einstein surmised the proper solution to his incompleteness/nonlocality dilemma in 1949 [7], but never abandoned his philosophical stance [8]. It is concluded that there are no definitions of Reality: we have to accept that Reality may not conform to our prejudices and, if an otherwise successful theory predicts what we do not believe in, no gedankenexperiment will help because our biases may slither through. Only actual experiments could assist in solving Einstein’s dilemma, as has been proven in the last 50 years. Notwithstanding, EPR is one of the most influential papers in history and has immensely sparked both conceptual and technological progress. Part III of this series further develops QT/TOPI, while scrutinizing the mythical ‘Schrödinger’s Cat’, as well as the ‘Basis’ and ‘Measurement’ pseudo-problems [9]. Part IV introduces QR/TOPI: a new theory that solves the century-old problem of integrating Special Relativity with Quantum Theory [10]. (shrink)

Despite the vast literature on Rawls's work, few have discussed his arguments for the value of democracy. When his arguments have been discussed, they have received staunch criticism. Some critics have charged that Rawls's arguments are not deeply democratic. Others have gone further, claiming that Rawls's arguments denigrate democracy. These criticisms are unsurprising, since Rawls's arguments, as arguments that the principle of equal basic liberty needs to include democratic liberties, are incomplete. In contrast to (...) his trenchant remarks about core civil liberties, Rawls does not say much about the inclusion of political liberties of a democratic sort – such as the right to vote – among the basic liberties. -/- In this paper, I complete some of Rawls's arguments and show that he has grounds for including political liberties, particularly those of a democratic nature, in the principle of equal basic liberty. In doing so, I make some beginning steps toward illustrating the genuinely democratic nature of Rawls's arguments. Rawls believes that a few different arguments can be given for democratic institutions and that these arguments work together to support the value of democracy. In this paper, I focus on Rawls's arguments relating to self-respect. I focus on this set of arguments because they are among the strongest of Rawls's arguments for equal political liberty and its fair value. (shrink)

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

Quantum theory offers mathematical descriptions of measurable phenomena with great facility and accuracy, but it provides absolutely no understanding of why any particular quantum outcome is observed. It is the province of genuine explanations to tell us how things actually work—that is, why such descriptions hold and why such predictions are true. Quantum theory is long on the what, both mathematically and observationally, but almost completely silent on the how and the why. What is even more interesting is that, in (...) some sense, this state of affairs seems to be a necessary consequence of the empirical adequacy of quantum descriptions. One of the most noteworthy achievements of quantum theory is the accurate prediction of phenomena that, on pain of experimental contradiction, have no physical explanation. It is the purpose of this essay to make clear why quantum mechanics and quantum field theory are complete physical descriptions that describe the metaphysical incompleteness of the physical world, then to press the negative implications of this fact for naturalistic metaphysics. (shrink)

Few have discussed Rawls's arguments for the value of democracy. This is because his arguments, as arguments that the principle of equal basic liberty should include democratic liberties, are incomplete. Rawls says little about the inclusion of political liberties of a democratic sort – such as the right to vote – among the basic liberties. And, at times, what he does say is unconvincing. My aim is to complete and, where they fail, to reconceive Rawls's arguments (...) and to show that a principle requiring equal political liberty and its fair value is an appropriate component of his theory of justice. (shrink)

Conceptual engineering concerns the assessment and improvement of our concepts. But how can proposals to engineer concepts be implemented in the real world? This is known as the implementation challenge to conceptual engineering. In this paper, I am concerned with the meta-philosophical implications of the implementation challenge. Specifically, must we overcome the implementation challenge prior to undertaking conceptual engineering? Some critics have recently answered this question affirmatively. I intend to show that they are mistaken. I argue as follows. First, successful (...) implementation is not an integral part of conceptual engineering. Second, the idea that the value of conceptual engineering relies on successful implementation is in tension with widespread assumptions about normative theorizing. (shrink)

Storrs McCall continues the tradition of Lucas and Penrose in an attempt to refute mechanism by appealing to Gödel’s incompleteness theorem. That is, McCall argues that Gödel’s theorem “reveals a sharp dividing line between human and machine thinking”. According to McCall, “[h]uman beings are familiar with the distinction between truth and theoremhood, but Turing machines cannot look beyond their own output”. However, although McCall’s argumentation is slightly more sophisticated than the earlier Gödelian anti-mechanist arguments, in the end it fails (...) badly, as it is at odds with the logical facts. (shrink)

The cis-regulatory hypothesis is one of the most important claims of evolutionary developmental biology. In this paper I examine the theoretical argument for cis-regulatory evolution and its role within evolutionary theorizing. I show that, although the argument has some weaknesses, it acts as a useful example for the importance of current scientific debates for science education.

The formalist philosophy of mathematics (in its purest, most extreme version) is widely regarded as a “discredited position”. This pure and extreme version of formalism is called by some authors “game formalism”, because it is alleged to represent mathematics as a meaningless game with strings of symbols. Nevertheless, I would like to draw attention to some arguments in favour of game formalism as an appropriate philosophy of real mathematics. For the most part, these arguments have not yet been (...) used or were neglected in past discussions. (shrink)

In The Rationality of Induction, David Stove presents an argument against scepticism about inductive inference—where, for Stove, inductive inference is inference from the observed to the unobserved. Let U be a finite collection of n particulars such that each member of U either has property F-ness or does not. If s is a natural number less than n, define an s-fold sample of U as s observations of distinct members of U each either having F-ness or not having F-ness. Let (...) pU denote the proportion of members of U that are Fs and, if S is an s-fold sample of U, let pS denote the proportion of members of S that are Fs. Call S representative if and only if |pS – pU|<0.01. Stove‘s argument against inductive scepticism is built on the following statistical fact: -/- As s gets larger the proportion of all possible s-fold samples of U that are representative gets closer to 1 (regardless of the size of U or of the value of pU). -/- In this essay I subject Stove‘s argument to thorough scrutiny. I show that the argument – as it stands – is incomplete, and I illuminate the issues involved in trying to fill the gaps. Along the way I demonstrate that one of the commonest objects to Stove‘s argument misses the point. -/- . (shrink)

In this paper Lucas suggests that many of his critics have not read carefully neither his exposition nor Penrose’s one, so they seek to refute arguments they never proposed. Therefore he offers a brief history of the Gödelian argument put forward by Gödel, Penrose and Lucas itself: Gödel argued indeed that either mathematics is incompletable – that is axioms can never be comprised in a finite rule and so human mind surpasses the power of any finite machine – or (...) there exist absolutely unsolvable diophantine problems, and he suggest that the second disjunct is untenable; on the other side, Penrose proposed an argument similar to Lucas’ one but making use of Turing’s theorem. Finally Lucas exposes again his argument and considers some of the most important objections to it. (shrink)

Certain selected issues around the Gödelian anti-mechanist arguments which have received less attention are discussed.

Analytic philosophers have, since the pioneering work of B.K. Matilal, emphasized the contributions of Nyāya philosophers to what contemporary philosophy considers epistemology. More recently, scholarly work demonstrates the relevance of their ideas to argumentation theory, an interdisciplinary area of study drawing on epistemology as well as logic, rhetoric, and linguistics. This paper shows how early Nyāya theorizing about argumentation, from Vātsyāyana to Jayanta Bhaṭṭa, can fruitfully be juxtaposed with the pragma-dialectic approach to argumentation pioneered by Frans van Eemeren. I illustrate (...) the implications of this analysis with a case study from Jayanta Bhaṭṭa’s satirical play, Much Ado about Religion (Āgamaḍambara). (shrink)

The Mozi contains at least three distinct arguments against offensive warfare. The "moral argument" claims that offensive warfare is morally wrong. The "economic argument" calculates that the foreseeable costs of a military campaign inevitably outweigh its possible benefits. The "religious argument" warns that military aggression harms the interests of Heaven. This paper discusses these three lines of argumentation, with extensive reference to the original text in translation. The paper explores what the arguments entail, to whom they may have (...) been addressed, and how persuasive they are from a modern academic perspective. It shows not only how Mozi and his followers theorized about offensive warfare, but also how their arguments were used in practice, at least according to anecdotes in the latter part of the received Mozi. The ultimate goal of this paper is to show how the Mohists actively adapted their argumentative strategies so as to find the best words to end wars. (shrink)

In Zettel, Wittgenstein considered a modified version of Cantor’s diagonal argument. According to Wittgenstein, Cantor’s number, different with other numbers, is defined based on a countable set. If Cantor’s number belongs to the countable set, the definition of Cantor’s number become incomplete. Therefore, Cantor’s number is not a number at all in this context. We can see some examples in the form of recursive functions. The definition "f(a)=f(a)" can not decide anything about the value of f(a). The definiton is incomplete. (...) The definition of "f(a)=1+f(a)" can not decide anything about the value of f(a) too. The definiton is incomplete.<br><br>According to Wittgenstein, the contradiction, in Cantor's proof, originates from the hidden presumption that the definition of Cantor’s number is complete. The contradiction shows that the definition of Cantor’s number is incomplete. <br><br>According to Wittgenstein’s analysis, Cantor’s diagonal argument is invalid. But different with Intuitionistic analysis, Wittgenstein did not reject other parts of classical mathematics. Wittgenstein did not reject definitions using self-reference, but showed that this kind of definitions is incomplete.<br><br>Based on Thomson’s diagonal lemma, there is a close relation between a majority of paradoxes and Cantor’s diagonal argument. Therefore, Wittgenstein’s analysis on Cantor’s diagonal argument can be applied to provide a unified solution to paradoxes. (shrink)

Our objectives in this paper are, first, to identify several puzzling aspects of the “Trilemma Argument” of Section 6 against the Sense Datum Theory; second, to resolve these puzzles by reconstructing the Trilemma Argument; third to point to a distinction Sellars makes between two versions of the Sense Datum Theory, the “nominalist” version and the “realist” version; fourth, to reconstruct Sellars’s arguments against both; and, finally, to find in an earlier paper, “Is There a Synthetic A Priori?” that his (...) argument against the second version, assumed but not actually given in EPM, is against property realism and depends on taking language expressing propositional perception as fundamental and language expressing non-propositional perception as incomplete and derivative from the former. (shrink)

Philosophical arguments usually are and nearly always should be abductive. Across many areas, philosophers are starting to recognize that often the best we can do in theorizing some phenomena is put forward our best overall account of it, warts and all. This is especially true in esoteric areas like logic, aesthetics, mathematics, and morality where the data to be explained is often based in our stubborn intuitions. -/- While this methodological shift is welcome, it's not without problems. Abductive (...) class='Hi'>arguments involve significant theoretical resources which themselves can be part of what's being disputed. This means that we will sometimes find otherwise good arguments which suggest their own grounds are problematic. In particular, sometimes revising our beliefs on the basis of such an argument can undermine the very justification we used in that argument. -/- This feature, which I'll call self-effacingness, occurs most dramatically in arguments against our standing views on the esoteric subject matters mentioned above: logic, mathematics, aesthetics, and morality. This is because these subject matters all play a role in how we reason abductively. This isn't an idle fact; we can resist some challenges to our standing beliefs about these subject matters exactly because the challenges are self-effacing. The self-effacing character of certain arguments is thus both a benefit and limitation of the abductive turn and deserves serious attention. I aim to give it the attention it deserves. (shrink)

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are predicates (...) in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (shrink)

We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

The theorizing about the doctrine of the Trinity by contemporary analytic philosophers of religion has recently been imbued with an air of enthusiastic excitement and self-confidence. My intuition is that there’s room for saying something more in support to the embarrassment and puzzlement traditionally related to the predication of God’s onefoldness and threefoldness. My purpose is to deliver a general argument for (weak) trinitarian skepticism. My view is that the argument provides substantive reasons in support to the common sense intuition (...) that either God’s onefoldness and threefoldness aren’t actually compatible or God’s onefoldness and threefoldness aren’t robustly construed. (shrink)

In the 1951 Gibbs lecture, Gödel asserted his famous dichotomy, where the notion of informal proof is at work. G. Priest developed an argument, grounded on the notion of naïve proof, to the effect that Gödel’s first incompleteness theorem suggests the presence of dialetheias. In this paper, we adopt a plausible ideal notion of naïve proof, in agreement with Gödel’s conception, superseding the criticisms against the usual notion of naïve proof used by real working mathematicians. We explore the connection between (...) Gödel’s theorem and naïve proof so understood, both from a classical and a dialetheic perspective. (shrink)

Some arguments against the assumption that ordinary people may share common knowledge are sound. The apparent cost of such arguments is the rejection of scientific theories that appeal to common knowledge. My proposal is to accept the arguments without rejecting the theories. On my proposal, common knowledge is shared by ideally rational people, who are not just mathematically simple versions of ordinary people. They are qualitatively different from us, and theorizing about them does not lead to predictions (...) about our behavior. Nevertheless, models of action that assume common knowledge have a role to play in our understanding of collective rationality. (shrink)

Frank Jackson’s knowledge argument (KA) aims to prove, by means of a thought experiment concerning the hypothetical scientist Mary, that conscious experiences have non-physical properties, called qualia. Mary has complete scientific knowledge of colours and colour vision without having had any colour experience. The central intuition in the KA is that, by seeing colours, Mary will learn what it is like to have colour experiences. Therefore, her scientific knowledge is incomplete, and conscious experiences have qualia. In this paper I consider (...) an objection to the KA raised by Daniel Dennett. He maintains that the KA is vitiated by Jackson’s account of Mary’s scientific knowledge. While endorsing this criticism, I will defend the plausibility and relevance of the type of strategy involved in the KA by offering an account of Mary’s scientific knowledge. This account involves formulating a reasonable and not immediately false version of the physicalist thesis with regard to colour experiences. Whether this version of the KA is successful against this type of physicalism is not investigated here. (shrink)

The aim of this paper is threefold. Firstly, §1 and §2 introduce the novel concept logical akrasia by analogy to epistemic akrasia. If successful, the initial sections will draw attention to an interesting akratic phenomenon which has not received much attention in the literature on akrasia (although it has been discussed by logicians in different terms). Secondly, §3 and §4 present a dilemma related to logical akrasia. From a case involving the consistency of Peano Arithmetic and Gödel’s Second Incompleteness Theorem (...) it’s shown that either we must be agnostic about the consistency of Peano Arithmetic or akratic in our arithmetical theorizing. If successful, these sections will underscore the pertinence and persistence of akrasia in arithmetic (by appeal to Gödel’s seminal work). Thirdly, §5 concludes by suggesting a way of translating the dilemma of arithmetical akrasia into a case of regular epistemic akrasia; and further how one might try to escape the dilemma when it’s framed this way. (shrink)

A satisfactory theory of linguistic communication must explain how it is that, through the interpersonal exchange of auditory, visual, and tactile stimuli, the communicative preconditions for the acquisition of testimonial knowledge regularly come to be satisfied. Without an account of knowledge-yielding communication this success condition for linguistic theorizing is left opaque, and we are left with an incomplete understanding of testimony, and communication more generally, as a source of knowledge. This paper argues that knowledge-yielding communication should be modelled on knowledge (...) itself. It is argued that knowledge-yielding communication occurs iff interlocutors coordinate on truth values in a non-lucky and non-deviant way. This account is able to do significant explanatory work: it sheds light on the nature of referential communication, and it allows us to capture, in an informative way, the sense in which interlocutors must entertain similar propositions in order to communicate successfully. (shrink)

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such as (...) Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (shrink)