One of Derek Parfit’s greatest legacies was the search for Theory X, a theory of population ethics that avoided all the implausible conclusions and paradoxes that have dogged the field since its inception: the Absurd Conclusion, the Repugnant Conclusion, the Non-Identity Problem, and the Mere Addition Paradox. In recent years, it has been argued that this search is doomed to failure and no satisfactory population axiology is possible. This chapter reviews Parfit’s life’s work in the field and argues (...) that he provided all the necessary components necessary for a Theory X. It then shows how these components can be combined together and applied to the global challenges Parfit argued matter most: preventing human extinction, managing catastrophic risks, and eradicating global poverty and suffering. Finally, it identifies a number of challenges facing his theory and suggests how these may be overcome. (shrink)

A remarkable feature of the philosophical work on conspiracy theory theory has been that most philosophers agree there is nothing inherently problematic about conspiracy theories (AKA the thesis of particularism). Recent work, however, has challenged this consensus view, arguing that there really is something epistemically wrong with conspiracy theorising (AKA generalism). Are particularism and generalism incompatible? By looking at just how much particularists and generalists might have to give away to make their theoretical viewpoints compatible, I will argue (...) that particularists can accept many of the concerns that motivate generalism because generalism can never be about ‘all’ conspiracy theories without being either ahistorical or apolitical. In the end generalist critiques are best seen as useful guidelines or considerations for the appraising of particular conspiracy theories. (shrink)

Conspiracy theories and conspiracy theorists have been accused of a great many sins, but are the conspiracy theories conspiracy theorists believe epistemically problematic? Well, according to some recent work, yes, they are. Yet a number of other philosophers like Brian L. Keeley, Charles Pigden, Kurtis Hagen, Lee Basham, and the like have argued ‘No!’ I will argue that there are features of certain conspiracy theories which license suspicion of such theories. I will also argue that these features only license a (...) limited suspicion of these conspiracy theories, and thus we need to be careful about generalising from such suspicions to a view of the warrant of conspiracy theories more generally. To understand why, we need to get to the bottom of what exactly makes us suspicious of certain conspiracy theories, and how being suspicious of a conspiracy theory does not always tell us anything about how likely the theory in question is to be false. (shrink)

In this paper I interrogate the notion of `debunking conspiracy theories’, arguing that the term `debunk’ carries with it pejorative implications, given that the verb `to debunk’ is commonly understood as `to show the wrongness of a thing or concept’. As such, the notion of `debunking conspiracy theories’ builds in the notion that such theories are not just wrong but ought to be shown as being wrong. I argue that we should avoid the term `debunk’ and focus on investigating conspiracy (...) theories. Looking at recent research work in epistemology on conspiracy theory, I argue that the best way to avoid talk of `debunking’ conspiracy theories is by working with a non-pejorative definition of `conspiracy theory’, and forming communities of inquiry which allow us to investigate the warrant of such theories without the prejudice associated with working with a pejorative definition. (shrink)

Judging the warrant of conspiracy theories can be difficult, and often we rely upon what the experts tell us when it comes to assessing whether particular conspiracy theories ought to be believed. However, whereas there are recognised experts in the sciences, I argue that only are is no such associated expertise when it comes to the things we call `conspiracy theories,' but that the conspiracy theorist has good reason to be suspicious of the role of expert endorsements when it comes (...) to conspiracy theories and their rivals. The kind of expertise, then, we might associate with conspiracy theories is largely improvised—in that it lacks institutional features—and, I argue, ideally the product of a community of inquiry. (shrink)

This reply to an ongoing debate between conspiracy theory researchers from different disciplines exposes the conceptual confusions that underlie some of the disagreements in conspiracy theory research. Reconciling these conceptual confusions is important because conspiracy theories are a multidisciplinary topic and a profound understanding of them requires integrative insights from different fields. Specifically, we distinguish research focussing on conspiracy *theories* (and theorizing) from research of conspiracy *belief* (and mindset, theorists) and explain how particularism with regards to conspiracy theories (...) does not mean we cannot define a problematic subclass of conspiracy beliefs, while avoiding the problems of generalism. We hope this reply helps conspiracy theory researchers recognize the differences between studying conspiracy theories and conspiracy beliefs and appreciate the possibilities for fruitful, integrative, and interdisciplinary research. (shrink)

An analysis of the recent efforts to define what counts as a "conspiracy theory", in which I argue that the philosophical and non-pejorative definition best captures the phenomenon researchers of conspiracy theory wish to interrogate.

An overview of the current epistemic literature concerning conspiracy theories, as well as indications for future research avenues on the topic.

This introduction to this special issue of Inquiry looks at recent work in the philosophy of conspiracy theory theory. Looking at two related worries expressed in the wider conspiracy theory theory (the academic study of conspiracy theories) – the Problem of Conspiracy Theories and the Problem of Conspiracy Theorists – this special issue argues that recent work in the philosophy of conspiracy theories is getting all the more closer to not just an epistemic understanding of what, (...) if anything, is wrong with belief in conspiracy theories, but also a framework for both investigating conspiracy theories and understanding how we should talk about the beliefs of conspiracy theorists. (shrink)

I’m to push back on Hill’s (2022) criticism in four ways. First: we need some context for the debate that occurred in the pages of the Social Epistemology Review and Reply Collective that so concerns Hill. Second: getting precise with our terminology (and not working with stereotypes) is the only theoretically fruitful way to approach the problem of conspiracy theories. Third: I address Hill’s claim there is no evidence George W. Bush or Tony Blair accused their critics, during the build-up (...) the invasion of Iraq in 2003ACE, as being “conspiracy theorists.” Fourth (and finally): I will gently suggest that Hill has succumbed to a stereotypical view of work in Philosophy on conspiracy theories. (shrink)

Research on conspiracy theories has proliferated since 2016, in part due to the US election of President Trump, the COVID-19 pandemic, and increasingly threatening environmental conditions. In the rush to publication given these concerning social consequences, researchers have increasingly treated as definitive a 2016 paper by Michael Wood (Political Psychology, 37(5), 695–705, 2016) that concludes that the phrase “conspiracy theory” has no negative effect upon people’s willingness to endorse a claim. We revisit Wood’s findings and its (re)uptake in the (...) recent literature. Is the label “conspiracy theory” a pejorative? If so, does it sway or affect people’s belief in specific claims of conspiracy (i.e. particular conspiracy theories), or is the effect one that concerns claims of conspiracy more generally (i.e. all conspiracy theories)? Through an examination of the conceptual and methodological scope of Wood’s work and the results of our similar quasi-experimental design, we argue that it is premature to suggest the label “conspiracy theory” has no impact on the believability of a claim, or that it has no rhetorical power. (shrink)

A reply to Patrick Stokes' 'Reluctance and Suspicion'—itself a reply to an early piece by myself replying to Stokes—in which I clarify what it is I intend when talking about how we should investigate conspiracy theories.

A response to Lee Basham's 'The Need for Accountable Witnesses: A Reply to Dentith'.

A reply to Gérald Bronner, Véronique Campion-Vincent, Sylvain Delouvée, Sebastian Dieguez, Nicolas Gauvrit, Anthony Lantian, and Pascal Wagner-Egger's piece, '“They” Respond: Comments on Basham et al.’s “Social Science’s Conspiracy-Theory Panic: Now They Want to Cure Everyone”.

Conspiracy theories are typically thought to be examples of irrational beliefs, and thus unlikely to be warranted. However, recent work in Philosophy has challenged the claim that belief in conspiracy theories is irrational, showing that in a range of cases, belief in conspiracy theories is warranted. However, it is still often said that conspiracy theories are unlikely relative to non-conspiratorial explanations which account for the same phenomena. However, such arguments turn out to rest upon how we define what gets counted (...) both as a ‘conspiracy’ and a ‘conspiracy theory’, and such arguments rest upon shaky assumptions. It turns out that it is not clear that conspiracy theories are prima facie unlikely, and so the claim that such theories do not typically appear in our accounts of the best explanations for particular kinds of events needs to be reevaluated. (shrink)

Belief in conspiracy theories is typically considered irrational, and as a consequence of this, conspiracy theorists––those who dare believe some conspiracy theory––have been charged with a variety of epistemic or psychological failings. Yet recent philosophical work has challenged the view that belief in conspiracy theories should be considered as typically irrational. By performing an intra-group analysis of those people we call “conspiracy theorists”, we find that the problematic traits commonly ascribed to the general group of conspiracy theorists turn out (...) to be merely a set of stereotypical behaviours and thought patterns associated with a purported subset of that group. If we understand that the supposed prob- lem of belief in conspiracy theories is centred on the beliefs of this purported sub- set––the conspiracists––then we can reconcile the recent philosophical contribu- tions to the wider academic debate on the rationality of belief in conspiracy theories. (shrink)

In the literature on conspiracy theories, the least contentious part of the academic discourse would appear to be what we mean by a “conspiracy”: a secretive plot between two or more people toward some end. Yet what, exactly, is the connection between something being a conspiracy and it being secret? Is it possible to conspire without also engaging in secretive behavior? To dissect the role of secrecy in con- spiracies – and thus contribute to the larger debate on the epistemology (...) of conspir- acy theories – we dene the concepts of “conspiracy,” “conspirator,” and “secret,” and argue that while conspirators might typically be thought to commit to keeping secrets once their conspiracy is underway, the idea that conspiracies are necessarily secretive to start with is not as obvious as previously thought. (shrink)

A reply to “Why ‘Healthy Conspiracy Theories’ Are (Oxy)morons” by Pascal Wagner-Egger, Gérald Bronner, Sylvain Delouvée, Sebastian Dieguez and Nicolas Gauvrit.

A reply to Patrick Stokes' “Between Generalism and Particularism About Conspiracy Theory".

Typical analyses of belief in conspiracy theories have it that identifying as a conspiracy theorist is irrational. However, given that we know conspiracies occur, and theories about said conspiracies can be warranted, should we really be scared of the locution 'I'm a conspiracy theorist...'?

Conspiracies are, by definition, a group activity; to conspire requires two or more people working together towards some end, typically in secret. Conspirators have intentions; this is borne out by the fact they want some end and are willing to engage in action to achieve. Of course, what these intentions are can be hard to fathom: historians have written a lot about the intentions of the assassins of Julius Caesar, for example; did they want to restore the Republic; was Marcus (...) Brutus lusting after power; was it an attempt to curb the ambitions of the plebeian class, who saw in Caesar someone not unlike themselves? If intentions can be hard to infer, who is a knowing conspirator and who is a dupe is almost as tricky to parse. Not all purported members of a conspiracy are conspirators, even if they aid and abet the conspiracy. Take, for example, the notorious lax engineer who the conspirators know will sign off on substandard building compliance measures, making it all the easier for them to plant their controlled demolitions. On some account of causal or even moral responsibility the lax engineer would then be responsible for the subsequent event, the one the conspirators desired. Yet it also seems clear that even if she is responsible in some sense for the culminating event of the conspiracy, it is clear that they did not conspire. Or, at least, we would like to think so, although should the authorities find out about the lax engineer’s involvement, they may well be considered part of the conspiracy, especially if the conspirators do their best to hide their own involvement or identities. (shrink)

In the first part of this article we briefly describe the design and development of a Consciousness Studies concentration at Goddard College, a student centered, progressive educational institution in the northeastern United States. We emphasize the tensions we experienced between different orientations in Consciousness Studies and especially the one related to the scientific and transpersonal ends of the spectrum of consciousness. In the second part, we relate the scientific‐transpersonal issue that we experienced at Goddard to the broader theory and (...) practice of Consciousness Studies. We also link the latter to the so‐called explanatory gap between third and first person forms of consciousness and the call for first person methods of exploring consciousness. Our conclusion is that the scientific approach has the edge and is at risk of assimilating other approaches to the detriment of Consciousness Studies. In our view, the future development of Consciousness Studies, both in theory and practice, requires several different approaches from the scientific to the transpersonal and privileging one is to narrow the field of possibilities and to risk falling prey to one‐sidedness. (shrink)

As humans, we use the power of thinking to make scientific discoveries, develop technologies, manage social interactions, and transmit knowledge to the next generations. With the ability to think, we can trace back and discover the origin of the universe, the natural world, and ourselves. The content of this book, Mindsponge Theory, is part of that discovery process. -/- Product Details -/- Publisher ‏ : ‎ Walter de Gruyter (December 6, 2022) Publication date ‏ : ‎ December 6, 2022 (...) Language ‏ : ‎ English Hardcover ‏ : ‎ 214 pages ISBN-10 ‏ : ‎ 8367405145 ISBN-13 ‏ : ‎ 978-8367405140 Dimensions ‏ : ‎ 6.3 x 0.71 x 9.29 inches -/- . (shrink)

This paper is part of a larger project to better understand the limitations of the economic theory of agency and incentives.1 The economic approach focuses on extrinsic incentives whereas a better understanding of human organization requires an understanding of intrinsic motivation and the complementary or substitutive relationships with extrinsic motivation. I will focus on different treatments of informational or “panoptic” questions regarding transparency or non-transparency in the management of firms or other human organizations. This context will give the questions (...) definiteness but the ideas might also be applied in a broader social context. As a conceptual framework, I will use the seminal work of Douglas McGregor. The economic approach to agency and incentives theory is based essentially on what McGregor called the “Theory X” worldview, and the alternative explored here is essentially what he called the “Theory Y” view of individuals in organizations. (shrink)

An introduction to sentential logic and first-order predicate logic with identity, logical systems that significantly influenced twentieth-century analytic philosophy. After working through the material in this book, a student should be able to understand most quantified expressions that arise in their philosophical reading. -/- This books treats symbolization, formal semantics, and proof theory for each language. The discussion of formal semantics is more direct than in many introductory texts. Although forall x does not contain proofs of soundness and completeness, (...) it lays the groundwork for understanding why these are things that need to be proven. -/- The book highlights the choices involved in developing sentential and predicate logic. Students should realize that these two are not the only possible formal languages. In translating to a formal language, we simplify and profit in clarity. The simplification comes at a cost, and different formal languages are suited to translating different parts of natural language. (shrink)

In the past twenty years, scholarly interest in John Dewey's later writings has surged. While later works such as Art as Experience (1934), Logic: The Theory of Inquiry (1938), and Freedom and Culture (1939) have received considerable attention, Knowing and the Known (1949), Dewey's late-in-life collaboration with Arthur F. Bentley, has been largely neglected. A common bias among Dewey scholars is that this work, instead of developing Dewey's Logic, departs from its spirit, reflects the overbearing influence of Bentley on (...) Dewey (who was at the time an octogenarian), and, therefore, merits little serious scholarly consideration. However, Dewey and Bentley engaged in an extended correspondence, collected in John Dewey and Arthur Bentley: A Philosophical Correspondence, 1932-1951 (1964), the result of which was no less than a watershed moment in Dewey's thinking on the experimental method of inquiry. The Logic was improved in ways that incorporated the insights of Charles Sanders Peirce's logic and developed Dewey's earlier work in a direction expressly intended by the aging pragmatist. Indeed, Dewey writes in correspondence with his co-author: "You [Bentley] shouldn't lean too heavily on the [1938] Logic; it wasn't a bad job at the time, but I could do better now [with Knowing and the Known]; largely through association with you and getting the courage to see my thing [logical theory] through without compromise" (Correspondence, 4:595, see also 184, 420, 481, 483-84). One of the few scholars of American pragmatism to acknowledge that Knowing and the Known was a watershed development in Dewey's thinking is Frank X. Ryan, author of an exciting new book, Seeing Together: Mind, Matter, and the Experimental Outlook of John Dewey and Arthur F. Bentley, that clearly and concisely presents the revolutionary method developed in Knowing and Known: the transactional approach. (shrink)

In the Appendix I of his "Remarks on the Foundations of Mathematics", Wittgenstein elaborates a different interpretation of Gödel’s First Incompleteness Theorem, which we have come to refer to as "Gödel’s Theorem" or "Incompleteness Theorem". This nomenclature arises from the recognition that the so-called "Second Incompleteness Theorem" is essentially a corollary of the primary theorem. Wittgenstein aims to reassess Gödel’s conclusion that there exist true formulas not demonstrable within formal systems capable of representing a sufficient amount of arithmetic theory. (...) Gödel’s initial reaction, as well as other commentators, was that Wittgenstein had not understood the proof. Nevertheless, recent commentators view worthy commentaries in wittgensteinian writings: some commentators, such as Juliet Floyd and Hilary Putnam, distinguish between mathematical proof and philosophical prose that surrounds the theorem, making it possible to understand Wittgenstein’s remarks. Ultimately, Wittgenstein’s observations serve as a lens through which Gödel’s theorem can be reconsidered within the realm of non-classical logics, such as paraconsistent logic. (shrink)

1. The Bundle Theory I shall discuss is a theory about the nature of substances or concrete particulars, like apples, chairs, atoms, stars and people. The point of the Bundle Theory is to avoid undesirable entities like substrata that allegedly constitute particulars. The version of the Bundle Theory I shall discuss takes particulars to be entirely constituted by the universals they instantiate.' Thus particulars are said to be just bundles of universals. Together with the claim that (...) it is necessary that particulars have constituents, the fundamental claim of the Bundle Theory is: (BT) Necessarily, for every particular x and every entity y, y constitutes x if and only ify is a universal and x instantiates y. 2 The standard and supposedly devastating objection to the Bundle Theory is that it entails or is committed to a false version of the Principle of Identity of Indiscernibles (Armstrong 1978: 91, Loux 1998: 107), namely: (Pll) Necessarily, for all particulars x and y and every universal z, if z is instantiated by x if and only if z is instantiated byy, then x is numerically identical with y. The most famous counterexample to the Identity of Indiscernibles is that put forward by Max Black, consisting of a world where there are only two iron spheres two miles apart from each other, having the same diameter, temperature, colour, shape, size, etc (Black 1952: 156). Let us from now on think of the properties of the spheres in this world as universals. The possibility of this world, which I shall hereafter refer to as 'Black's world', makes (Pll) false.' And according to common philosophical opinion this means that the Bundle Theory is false.. (shrink)

I explain Loophole Theory (LT) and show some applications of it. The basic element of LT is the truism that everything physical is physical. Any ontological domain that can be defined according to this template (everything X is X) is called a universe. LT allows causal relations between universes via the notion of interfaces. Interfaces are hypothetical domains that are not universes. The idea is that the one universe can be followed by another universe via an interface. Interfaces are (...) defined as being composed of, at least, parts of two universes. Some examples could be the mind/body interface, the physical/mathematical interface and the something/nothing interface. (shrink)

ABSTRACT: The Reflexive Theory of Perception (RTP) claims that perception of an object or property X by an organism Z consists in Z being caused by X to acquire some disposition D toward X itself. This broadly behavioral perceptual theory explains perceptual intentionality and correct versus incorrect, plus successful versus unsuccessful, perception in a plausible evolutionary framework. The theory also undermines cognitive and perceptual modularity assumptions, including informational or purely epistemic views of perception in that, according to (...) the RTP, any X-caused and X-directed dispositions are genuinely perceptual—including affective, attitudinal, and immediately activated purely action-directed behavioral dispositions. Thus the RTP has the potential to provide the foundations for a broadly behavioral counter-revolution in cognitive science. (shrink)

I here defend a theory consisting of four claims about ‘property’ and properties, and argue that they form a coherent whole that can solve various serious problems. The claims are (1): ‘property’ is defined by the principles (PR): ‘F-ness/Being F/etc. is a property of x iff F’ and (PA): ‘F-ness/Being F/etc. is a property’; (2) the function of ‘property’ is to increase the expressive power of English, roughly by mimicking quantification into predicate position; (3) property talk should be understood (...) at face value: apparent commitments are real and our apparently literal use of ‘property’ is really literal; (4) there are no properties. In virtue of (1)–(2), this is a deflationist theory and in virtue of (3)–(4), it is an error theory. (1) is fleshed out as a claim about understanding conditions, and it is argued at length, and by going through a number of examples, that it satisfies a crucial constraint on meaning claims: all facts about ‘property’ can be explained, together with auxiliary facts, on its basis. Once claim (1) has been expanded upon, I argue that the combination of (1)–(3) provides the means for handling several problems: they help giving a happy-face solution to what I call the paradox of abstraction , they form part of a plausible account of the correctness of committive sentences, and, most importantly, they help respond to various indispensability arguments against nominalism. (shrink)

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical (...) theory of categories, dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. (shrink)

I defend Haze’s argument against the Breckenridge-Magidor theory of instantial reasoning from an objection by Meléndez Gutiérrez. According to Breckenridge and Magidor, in reasoning like ‘Some x is mortal. Let n be such an x…’, the ‘n’ refers to a particular object but we cannot know which. This surprisingly defensible view poses an obvious threat to widespread notions in the philosophy of language. Haze argues that the theory leads to absurdity in cases like ‘Some x is unreferred-to by (...) any expression. Let n be such an x…’ and should therefore be rejected. Meléndez Gutiérrez counters that Haze’s argument is just a case of Berry-like paradox and thus fails to refute the Breckenridge-Magidor theory. I argue that the analogy breaks down: unlike the intuitively compelling and widely believed well-ordering principle about positive integers, the principle drawn from Breckenridge and Magidor that plays a supposedly analogous role enjoys no such status, and is instead simply shown to be false by Haze’s reductio. The possibility of such a response is obscured when Meléndez Gutiérrez portrays Haze’s argument as involving a stipulation that ‘n’ is to refer to an unreferred-to object. On the contrary, Haze’s argument does not assume that expressions like ‘n’ work by means of referring at all, and simply lets stipulations like ‘Let n be such an x’ be themselves, without imposing a theory on them. Once this is clarified, we can see that Haze’s argument is unaffected by Meléndez Gutiérrez’s objection. (shrink)

Let f(1)=2, f(2)=4, and let f(n+1)=f(n)! for every integer n≥2. Edmund Landau's conjecture states that the set P(n^2+1) of primes of the form n^2+1 is infinite. Landau's conjecture implies the following unproven statement Φ: card(P(n^2+1))<ω ⇒ P(n^2+1)⊆[2,f(7)]. Let B denote the system of equations: {x_j!=x_k: i,k∈{1,...,9}}∪{x_i⋅x_j=x_k: i,j,k∈{1,...,9}}. The system of equations {x_1!=x_1, x_1 \cdot x_1=x_2, x_2!=x_3, x_3!=x_4, x_4!=x_5, x_5!=x_6, x_6!=x_7, x_7!=x_8, x_8!=x_9} has exactly two solutions in positive integers x_1,...,x_9, namely (1,...,1) and (f(1),...,f(9)). No known system S⊆B with a finite (...) number of solutions in positive integers x_1,...,x_9 has a solution (x_1,...,x_9)∈(N\{0})^9 satisfying max(x_1,...,x_9)>f(9). For every known system S⊆B, if the finiteness/infiniteness of the set {(x_1,...,x_9)∈(N\{0})^9: (x_1,...,x_9) solves S} is unknown, then the statement ∃ x_1,...,x_9∈N\{0} ((x_1,...,x_9) solves S)∧(max(x_1,...,x_9)>f(9)) remains unproven. Let Λ denote the statement: if the system of equations {x_2!=x_3, x_3!=x_4, x_5!=x_6, x_8!=x_9, x_1 \cdot x_1=x_2, x_3 \cdot x_5=x_6, x_4 \cdot x_8=x_9, x_5 \cdot x_7=x_8} has at most finitely many solutions in positive integers x_1,...,x_9, then each such solution (x_1,...,x_9) satisfies x_1,...,x_9≤f(9). The statement Λ is equivalent to the statement Φ. It heuristically justifies the statement Φ . This justification does not yield the finiteness/infiniteness of P(n^2+1). We present a new heuristic argument for the infiniteness of P(n^2+1), which is not based on the statement Φ. Algorithms always terminate. We explain the distinction between existing algorithms (i.e. algorithms whose existence is provable in ZFC) and known algorithms (i.e. algorithms whose definition is constructive and currently known). Assuming that the infiniteness of a set X⊆N is false or unproven, we define which elements of X are classified as known. No known set X⊆N satisfies Conditions (1)-(4) and is widely known in number theory or naturally defined, where this term has only informal meaning. *** (1) A known algorithm with no input returns an integer n satisfying card(X)<ω ⇒ X⊆(-∞,n]. (2) A known algorithm for every k∈N decides whether or not k∈X. (3) No known algorithm with no input returns the logical value of the statement card(X)=ω. (4) There are many elements of X and it is conjectured, though so far unproven, that X is infinite. (5) X is naturally defined. The infiniteness of X is false or unproven. X has the simplest definition among known sets Y⊆N with the same set of known elements. *** Conditions (2)-(5) hold for X=P(n^2+1). The statement Φ implies Condition (1) for X=P(n^2+1). The set X={n∈N: the interval [-1,n] contains more than 29.5+\frac{11!}{3n+1}⋅sin(n) primes of the form k!+1} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. 501893∈X. Condition (1) holds with n=501893. card(X∩[0,501893])=159827. X∩[501894,∞)= {n∈N: the interval [-1,n] contains at least 30 primes of the form k!+1}. We present a table that shows satisfiable conjunctions of the form #(Condition 1) ∧ (Condition 2) ∧ #(Condition 3) ∧ (Condition 4) ∧ #(Condition 5), where # denotes the negation ¬ or the absence of any symbol. No set X⊆N will satisfy Conditions (1)-(4) forever, if for every algorithm with no input, at some future day, a computer will be able to execute this algorithm in 1 second or less. The physical limits of computation disprove this assumption. (shrink)

The article first rehearses three deflationary theories of reference, (1) disquotationalism, (2) propositionalism (Horwich), and (3) the anaphoric theory (Brandom), and raises a number of objections against them. It turns out that each corresponds to a closely related theory of truth, and that these are subject to analogous criticisms to a surprisingly high extent. I then present a theory of my own, according to which the schema “That S(t) is about t” and the biconditional “S refers to (...) x iff S says something about x” are exhaustive of the notions of aboutness and reference. An account of the usefulness of “about” is then given, which, I argue, is superior to that of Horwich. I close with a few considerations about how the advertised theory relates to well-known issues of reference, the conclusions of which is (1) that the issues concern reference and aboutness only insofar as the words “about” and “refer” serve to generalise over the claims that are really at issue, (2) that the theory of reference will not settle the issues, and (3) that it follows from (2) that the issues do not concern the nature of aboutness or reference. (shrink)

The closing chapters of Aristotle’s Nicomachean Ethics x are regularly described as “puzzling,” “extremely abrupt,” “awkward,” or “surprising” to readers. Whereas the previous nine books described—sometimes in lavish detail—the multifold ethical virtues of an embodied person situated within communities of family, friends, and fellow-citizens, NE x 6-8 extol the rarified, god-like and solitary existence of a sophos or sage (1179a32). The ethical virtues that take up approximately the first half of the Ethics describe moral exempla who experience fear fighting for (...) their communities, are sensitive to the esteem and recognition of others, and feel love for a desire to live together with a wide variety of kinds of friends. Such good people take pleasure in prudently expending sums to improve their communities—communities in which they exchange goods and participate in ruling and being ruled in a cooperative fashion. The exemplum of x 7-8, by contrast, is a person whose activity consists almost entirely in exercising his or her mind (nous)—a part of one’s soul that Aristotle explicitly notes is disconnected from human emotions and that can be exercised, insofar as one as wise, in a wholly solitary fashion (1178a15-16, a19-20; 1177a33-34). Although Aristotle’s claim that a “life in accord with the mind” is best and most pleasant (1178a6-7) may jar the intuitions of many people—he himself endorses Anaxagoras’ claim that the happy person will appear as “someone who is absurd” (atopos, 1179a15) to most people—it is false to claim that his conclusions in NE x 6-8 are unexpected or unanticipated, or that the text is in any way discontinuous with what precedes it. The Nicomachean Ethics exhibits aspects of ring-composition both within the work as a whole and within book 10. In NE i 5 Aristotle introduces his rendition of a trope that he inherits (most immediately) from Plato, viz. that the problem of the good can be considered like a contest between three different kinds of life—the life of enjoyment (apolaustikos), the life of politics (politikos), and the life of contemplation (theôrêtikos). NE x 6-8 returns to that contest, rendering a verdict about which life takes first, second, and third place. As the opening lines of NE x 6 note, that verdict presupposes central claims articulated between the first and last books of the Ethics, specifically about the nature of the virtues, the nature of friendship, and the nature of pleasure. NE i 5 and x 6-8 thus serve as “bookends” which encase arguments and proposition located between them. Book 10 exhibits a similar ring-composition. NE x opens with methodological reflection on the gap between the theoretical positions that thinkers articulate and the way they live their lives (especially in the case of scolds who simultaneously criticize pleasure on a scientific level but seek it on a practical level [1172a33-b8]). Chapter 8 concludes with an explicit reiteration of the methodological point, a reiteration that underscores how Aristotle’s treatment of the contest of lives incorporates central aspects of the discussion of pleasure in NE x 1-5. Aristotle’s reiteration of the problem of a gap between theory and practice also draws attention to the centrality of his treatment of pleasure in his adjudication of the three lives. Although the life of pleasure takes a distant third in the contest of lives, the contemplative life wins the contest in part because it itself is the most pleasant form of life. The central philosophical problem looming behind Aristotle’s treatment of the contest of lives concerns the relationship between the notion of activity (energeia) and the notion of a way of life (bios). In the last four decades, much of the scholarship on NE x 6-8 has sought to address the question of what activities a certain way of life includes or excludes. “Monistic” or “dominant” end interpretations of the best life have viewed it as including only contemplative activities whereas “inclusivist” end interpretations of the best life have viewed it as including non-contemplative activities. Although this chapter largely side-steps this debate—partially because there are ample recent first-rate introductory treatments of the debate, partially because I have addressed the question elsewhere in my own writing —I argue that focusing solely on the contest between the two best ways of life overshadows the way that Aristotle incorporates insights from the third way of life into the best way of life. Although the notion of a contest among different kinds of lives presupposes that the lives are mutually exclusive, Aristotle has no problem saying that the contemplative life trumps the life of pleasure because the contemplative life is more pleasant. I proceed in two parts. In the first part I examine what I will call the “outer” ring of the Ethics, namely the relationship between the contest of lives proposed in NE i 5 and its overall resolution in x 6-8. I show how i 5 and x 6 establish the framework for the contest, how x 7 adjudicates that contest in large part by relying upon premises articulated in the interim between books 1 and 10, and how x 6 and x 8 determine the second and third place positions in the contest. In the second part I focus on what I will call the “inner” ring of NE x. More than half of NE x struggles with the nature of pleasure, its role in a happy life, and the methodological problems of examining pleasure within a practical science. I show how x 1 and x 8 are “bookends” that underscore the methodological problem of examining pleasure and how the contest of lives draws upon the proximate conclusions concerning the nature of pleasure in NE x 1-5. (shrink)

An important problem with machine learning is that when label number n>2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G (...) class='Hi'>theory consists of a group of truth functions or membership functions. In comparison with likelihood functions, Bayesian posteriors, and Logistic functions used by popular methods, membership functions can be more conveniently used as learning functions without the above problem. In Logical Bayesian Inference (LBI), every label’s learning is independent. For Multilabel learning, we can directly obtain a group of optimized membership functions from a big enough sample with labels, without preparing different samples for different labels. A group of Channel Matching (CM) algorithms are developed for machine learning. For the Maximum Mutual Information (MMI) classification of three classes with Gaussian distributions on a two-dimensional feature space, 2-3 iterations can make mutual information between three classes and three labels surpass 99% of the MMI for most initial partitions. For mixture models, the Expectation-Maxmization (EM) algorithm is improved and becomes the CM-EM algorithm, which can outperform the EM algorithm when mixture ratios are imbalanced, or local convergence exists. The CM iteration algorithm needs to combine neural networks for MMI classifications on high-dimensional feature spaces. LBI needs further studies for the unification of statistics and logic. (shrink)

The idea that normative statements implicitly refer to standards has been around for quite some time. It is usually defended by normative antirealists, who tend to be attracted to Humean theories of reasons. But this is an awkward combination: 'A ought to X' entails that there are reasons for A to X, and 'A ought to X all things considered' entails that the balance of reasons favours X-ing. If the standards implicitly referred to are not those of the agent, then (...) why would these entailments hold? After all, Humeanism says that 'A has a reason to X' is true if and only if A has some desire which is furthered by X-ing. In this paper, I develop a standard-relational theory of 'ought' and a non-Humean theory of reasons (oughtism). Together, they explain why 'A ought to X' entails not only that there are reasons for A to X, but also that the balance of reasons favours X-ing. The latter explanation depends on a theory of weight, in which the weight of a reason depends on the position of a rule (standard) in an order of priorities. The theories are truth-conditional, but do not require objective normative facts for the truth of 'ought' judgments and judgments about reasons. (shrink)

The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition (...) for granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter. According to that, both papers (1930; 1931) can be seen as advocating Russell’s logicism or the intensional propositional logic versus both extensional arithmetic and set theory. Reconstructing history of philosophy, Aristotle’s logic and doctrine can be opposed to those of Plato or the pre-Socratic schools as establishing ontology or intensionality versus extensionality. Husserl’s phenomenology can be analogically realized including and particularly as philosophy of mathematics. One can identify propositional logic and set theory by virtue of Gödel’s completeness theorem (1930: “Satz VII”) and even both and arithmetic in the sense of the “compactness theorem” (1930: “Satz X”) therefore opposing the latter to the “incompleteness paper” (1931). An approach identifying homomorphically propositional logic and set theory as the same structure of Boolean algebra, and arithmetic as the “half” of it in a rigorous construction involving information and its unit of a bit. Propositional logic and set theory are correspondingly identified as the shared zero-order logic of the class of all first-order logics and the class at issue correspondingly. Then, quantum mechanics does not need any quantum logics, but only the relation of propositional logic, set theory, arithmetic, and information: rather a change of the attitude into more mathematical, philosophical, and speculative than physical, empirical and experimental. Hilbert’s epsilon calculus can be situated in the same framework of the relation of propositional logic and the class of all mathematical theories. The horizon of Part III investigating Hilbert mathematics (i.e. according to the Pythagorean viewpoint about the world as mathematical) versus Gödel mathematics (i.e. the usual understanding of mathematics as all mathematical models of the world external to it) is outlined. (shrink)

A RELATIVISTIC THEORY OF PHENOMENOLOCICAL CONSTITUTION: A SELF-REFERENTIAL, TRANSCENDENTAL APPROACH TO CONCEPTUAL PATHOLOGY. (Vol. I: French; Vol. II: English) -/- Steven James Bartlett -/- Doctoral dissertation director: Paul Ricoeur, Université de Paris Other doctoral committee members: Jean Ladrière and Alphonse de Waehlens, Université Catholique de Louvain Defended publically at the Université Catholique de Louvain, January, 1971. -/- Universite de Paris X (France), 1971. 797pp. -/- The principal objective of the work is to construct an analytically precise methodology which can (...) serve to identify, eliminate, and avoid a certain widespread _conceptual fault_ or _misconstruction_, called a "projective misconstruction" or "projection" by the author. It is argued that this variety of error in our thinking (i) infects a great number of our everyday, scientific, and philosophical concepts, claims, and theories, (ii) has largely been undetected, and (iii), when remedied, leads to a less controversial and more rigorous elucidation of the transcendental preconditions of human knowledge than has traditionally been possible. The dissertation identifies, perhaps for the first time, a _projective_ variety of self-referential inconsistency, and proposes an innovative, self-reflexive approach to transcendental argument in a logical and phenomenological context. The strength of the approach lies, it is claimed, in the fact that a rejection of the approach is possible only on pain of self-referential inconsistency. The argument is developed in the following stages: A general introduction identifies the central theme of the work, defines the scope of applicability of the results reached, and sketches the direction of the studies that follow. The preliminary discussion culminates in a recognition of the need for a _critique of impure reason_. The body of the work is divided into two parts: Section I seeks to develop a methodology, on a purely formal basis, which is, on the one hand, capable of being used to study the transcendental foundations of the special sciences, including its own proper transcendental foundation. On the other hand, the methodology proposed is intended as a diagnostic and therapeutic tool for dealing with _projective_ uses of concepts. The approach initiates an analysis of concepts from a perspective which views _knowledge as coordination_. Section I describes formal structures that possess the status of preconditions in such a coordinative account of knowledge. Special attention is given to the preconditions of _identifying reference_ to logical particulars. The first section attempts, then, to provide a self-referential, transcendental methodology which is essentially revisionary in that it is motivated by a concern for conceptual error-elimination. Phenomenology, considered in its unique capacity as a self-referential, transcendental discipline, is of special relevance to the study. Section II accordingly examines a group of concepts which come into question in connection with the central theme of _phenomenological constitution_. The "_de-projective methodology_" developed in Section I is applied to these concepts that have a foundational importance in transcendental phenomenology. A translation is, in effect, proposed from the language of consciousness to a language in which preconditions of referring are investigated. The result achieved is the elimination of self-defeating, projective concepts from a rigorous, phenomenological study of the constitutive foundations of science. The dissertation was presented in a two volume, double-language format for the convenience of French and English researchers. Each volume contains an analytical index. (shrink)

Is knowledge consistent with literally any credence in the relevant proposition, including credence 0? Of course not. But is credence 0 the only credence in p that entails that you don’t know that p? Knowledge entails belief (most epistemologists think), and it’s impossible to believe that p while having credence 0 in p. Is it true that, for every value of ‘x,’ if it’s impossible to know that p while having credence x in p, this is simply because it’s impossible (...) to believe that p while having credence x in p? If so, is it possible to believe that p while having (say) credence 0.4 in p? These questions aren’t standard epistemological fare, at least in part because many epistemologists think their answers are obvious, but they have unanticipated consequences for epistemology. Let ‘improbabilism’ name the thesis that it’s possible to know that p while having a credence in p below 0.5. Improbabilism will strike many epistemologists as absurd, but careful reflection on these questions reveals that, if improbabilism is false, then all of the most plausible theories of knowledge are also false. Or so I argue in this paper. Since improbabilism is widely rejected by epistemologists (at least implicitly), this paper reveals a tension between all of the most plausible theories of knowledge and a widespread assumption in epistemology. (shrink)

This article offers a critical overview of a set of normative theories, namely Tianxia 天下 (all-under-heaven), whose purpose is to provide a renewed conceptual framework for the improvement of the world system. First, the article introduces the origins, main features, and differences within Tianxia, before discussing two major criticisms leveled against it. The article then argues that the most powerful parts of these criticisms come from the challenges posed against Tianxia’s legitimacy. The article elaborates on this and introduces two additional (...) challenges of the same kind which were not discussed before. While the article leaves open the question of whether Tianxia is a realistic utopia, it insists that meaningful discussion of Tianxia must take legitimacy challenges seriously. It ends with a discussion concerning whether China can be understood as a civilization-state and how this understanding affects Tianxia’s reception as a realistic utopia. (shrink)

It is well known that the following features hold of AR + T under the strong Kleene scheme, regardless of the way the language is Gödel numbered: 1. There exist sentences that are neither paradoxical nor grounded. 2. There are 2ℵ0 fixed points. 3. In the minimal fixed point the weakly definable sets (i.e., sets definable as {n∣ A(n) is true in the minimal fixed point where A(x) is a formula of AR + T) are precisely the Π1 1 sets. (...) 4. In the minimal fixed point the totally defined sets (sets weakly defined by formulae all of whose instances are true or false) are precisely the ▵1 1 sets. 5. The closure ordinal for Kripke's construction of the minimal fixed point is ωCK 1. In contrast, we show that under the weak Kleene scheme, depending on the way the Gödel numbering is chosen: 1. There may or may not exist nonparadoxical, ungrounded sentences. 2. The number of fixed points may be any positive finite number, ℵ0, or 2ℵ0 . 3. In the minimal fixed point, the sets that are weakly definable may range from a subclass of the sets 1-1 reducible to the truth set of AR to the Π1 1 sets, including intermediate cases. 4. Similarly, the totally definable sets in the minimal fixed point range from precisely the arithmetical sets up to precisely the ▵1 1 sets. 5. The closure ordinal for the construction of the minimal fixed point may be ω, ωCK 1, or any successor limit ordinal in between. In addition we suggest how one may supplement AR + T with a function symbol interpreted by a certain primitive recursive function so that, irrespective of the choice of the Godel numbering, the resulting language based on the weak Kleene scheme has the five features noted above for the strong Kleene language. (shrink)

The ninth and tenth chapters of the Origin mark a profound, if perhaps difficult to detect, shift in the book’s argumentative structure. In the previous few chapters and in the ninth, Darwin has been exploring a variety of objections to natural selection, some more obvious (where are all the fossils of transitional forms?) and some showing careful attention to challenging consequences of evolution (could selection really produce instincts?). Starting in the tenth, however, Darwin turns to showing us what kinds of (...) new and unexpected results evolutionary theory might be able to offer us, again in domains both predictable (extinction) and unexpected (biogeography, embryology). It is notable that it is the fossil record that serves as this pivot point, being both a source of potentially powerful objections to evolutionary theory and home to some of its most compelling new explanations. In this chapter, I present both sets of arguments and consider what role Darwin gave to fossil evidence, in the process attempting to discover why it might have played this unique role in two different parts of Darwin’s “long argument” for evolution by natural selection. Geology’s special place, I argue, derives at least in part from its particular importance in Darwin’s social and intellectual context. (shrink)

This is a review of a book by Shan Gao called "The meaning of the wave function", Cambridge: Cambridge University Press, 2017.

In Rational Powers in Action, Sergio Tenenbaum sets out a new theory of instrumental rationality that departs from standard discussions of means-ends coherence in the literature on structural rationality in at least two interesting ways: it takes intentional action (as opposed to intention) to be what puts in place the relevant instrumental requirements, and it applies to both necessary and non-necessary means. I consider these two developments in more detail. On the first, I argue that Tenenbaum’s theory is (...) too narrow since there could be instrumental irrationality with respect to an intention to X even if one is not yet engaged in any relevant intentional action. On the second, I argue against Tenenbaum’s claim that “an agent is instrumentally irrational if she knowingly fails to pursue some sufficient means to an end she is pursuing.”. (shrink)

Over time, research programs focusing on the processes that underlie dissonance and regret diverged to the point that the present literature only occasionally draws explicit connections between regret and consistency seeking processes. One of our aims in this chapter is to reestablish the connection between regret and consistency within the context of a theory that examines two independent factors that critically interact to enhance or diminish regret. The first of these is opportunity, which includes both perceptions of past opportunities (...) to make alternative choices and future opportunities to take corrective actions, and the second is mitigation, which is the ability to justify one's actions or otherwise engage regulatory processes that allow for the diminishment of regret. We examine both opportunity and mitigation separately before describing how the two may interact to elicit differential experiences of regret. (shrink)

In the contemporary free will debate between compatibilism — the thesis that free will is compatible with determinism, and incompatibilism — that free will is incompatible with determinism, many scholars are sympathetic to compatibilism, yet disagree in how the position is best characterized. As one of the most important branches of source compatibilism, reasons-responsive theories attempt to address an important issue, namely, what type of person can be regarded as moral agents. There are several controversial points within the theory. (...) This paper aims to show that reasons-responsive theories fail as a solution to the free will debate, to the extent that they remain silent on the issue of the nature of reasons. It is this silence and inadequacy that constitute a rebuttal to reasons-responsive theories. In what follows I will propose a dilemma to reasons-responsive theories: if moral reasons are objective in the sense that one could be wrong about them, it appears that one must be a moral expert to possess the so-called “reasons-reactivity”, a necessary condition for the possession of free will. This will later be shown to be deeply implausible. If moral reasons are instead subjective in the sense that whether one has a moral reason to do X crucially depends on his mental states, then reasons-responsiveness seems to have no connection with free will at all. In addition, there are independent grounds on which the subjective account of the nature of reason can be challenged. Therefore, no matter which road reasons-responsive theorists choose to go down, there are serious objections that cast doubt on their plausibility. At the end of the paper, I will touch on the question of why reasons-responsive theories are doomed to failure due to their lack of concern with the agent’s own psychology. (shrink)