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

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

In this short note many conjectures on partitions of integers as summations of prime numbers are presented, which are extension of Goldbach conjecture.

The paper introduces and utilizes a few new concepts: “nonstandard Peano arithmetic”, “complementary Peano arithmetic”, “Hilbert arithmetic”. They identify the foundations of both mathematics and physics demonstrating the equivalence of the newly introduced Hilbert arithmetic and the separable complex Hilbert space of quantum mechanics in turn underlying physics and all the world. That new both mathematical and physical ground can be recognized as information complemented and generalized by quantum information. A few fundamental mathematical problems of the present such as Fermat’s (...) last theorem, four-color theorem as well as its new-formulated generalization as “four-letter theorem”, Poincaré’s conjecture, “P vs NP” are considered over again, from and within the new-founding conceptual reference frame of information, as illustrations. Simple or crucially simplifying solutions and proofs are demonstrated. The link between the consistent completeness of the system mathematics-physics on the ground of information and all the great mathematical problems of the present (rather than the enumerated ones) is suggested. (shrink)

In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...) The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines. (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)

K denotes both the knowledge predicate satisfied by every currently known theorem and the finite set of all currently known theorems. The set K is time-dependent, publicly available, and contains theorems both from formal and constructive mathematics. Any theorem of any mathematician from past or present forever belongs to K. Mathematical statements with known constructive proofs exist in K separately and form the set K_c⊆K. We assume that mathematical sets are atemporal entities. They exist formally in ZFC theory although their (...) properties can be time-dependent (when they depend on K) or informal. The true statement "K is non-empty" is outside K forever because K is not a formal set. Paul Cohen proved in 1963 that the equality 2^{\aleph_0}=\aleph_1 is independent of ZFC. Before 1963, the statement "There is a known constructively defined integer n⩾1 such that 2^{\aleph_0}=\aleph_n" was outside K. Since 1963, this statement is outside K forever. The true statement "There exists a set X⊆{1,...,49} such that card(X)=6 and X never occurred as the winning six numbers in the Polish Lotto lottery" refers to the current non-mathematical knowledge and is outside K forever. In Martin-Löf's terminology, every currently known theorem is actually true whereas every theorem (known or unknown) is potentially true. Actual truth is knowledge dependent and tensed. Potential truth is knowledge independent and tenseless. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivially true statements on decidable sets X⊆N that belong to constructive and informal mathematics and refer to the current mathematical knowledge on X. For every such statement, its truth concerning the current mathematical knowledge is implied by a true statement of the form: (the conjunction of i conditions of the form α∈K)∧(the conjunction of j conditions of the form β∉K)∧(the conjunction of k conditions of the form γ∈K_c)∧(the conjunction of l conditions of the form δ∉K_c), where i,j,k,l∈N and α,β,γ,δ are mathematical statements. In constructive mathematics and the traditional Brouwerian intuitionism, the truth of a mathematical statement means that we know a constructive proof. Therefore, the truth of a mathematical statement depends on time, where the statement is formally stated in the classical mathematics without the predicate K. In this article, mathematical statements on decidable sets X⊆N refer to time because they refer to the current mathematical knowledge on X. They cannot be formally stated in the classical mathematics without the predicate K and their logical values may change in time. For a set X⊆N whose infiniteness 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) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(X)=ω" is outside K. (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. 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 the assumption of the above statement. We prove that the set X={n∈N: the interval [-1,n] contains more than 29.5+(11!/(3n+1))∙sin(n) primes of the form k!+1} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. We present a table that shows satisfiable conjunctions of the form #(Condition1)∧(Condition 2)∧#(Condition 3)∧(Condition 4)∧#(Condition 5), where # denotes the negation ¬ or the absence of any symbol. We prove that there exists a naturally defined set C⊆N which satisfies the following conditions (6)-(11). (6) A known and simple algorithm for every k∈N decides whether or not k∈C. (7) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(C)=ω" is outside K. (8) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(N\C)=ω" is outside K. (9) It is conjectured, though so far unproven, that C is infinite. (10) For every known algorithm A with no input, the statement "A returns an integer n satisfying card(C)<ω ⇒ C⊆(-∞,n]" is outside K. (11) For every known algorithm A with no input, the statement "A returns an integer m satisfying card(N\C)<ω ⇒ N\C⊆(-∞,m]" is outside K. The set C={k∈N: 2^{2^k}+1 is composite} is naturally defined and satisfies conditions (6)-(11). (shrink)

In this paper, I explore how theorists might navigate a course between the twin dangers of piety and excess cynicism when thinking critically about state apologies, by focusing on two government apologies to indigenous peoples: namely, those made by the Australian and Canadian Prime Ministers in 2008. Both apologies are notable for several reasons: they were both issued by heads of government, and spoken on record within the space of government: the national parliaments of both countries. Furthermore, in (...) each case, the object of the apology – that which was apologized for – comes closer to disrupting the idea both countries have of themselves, and their image in the global political community, than any previous apologies made by either government. Perhaps as a result, both apologies were surrounded by celebration and controversy alike, and tracing their consequences – even in the short term – is a difficult business. We avoid excessive piety or cynicism, I argue, when we take several things into account. First, apologies have multiple functions: they narrate particular histories of wrongdoing, they express disavowal of that wrongdoing, and they commit to appropriate forms of repair or renewal. Second, the significance and the success of each function must be assessed contextually. Third, when turning to official political apologies, in particular, appropriate assessment of their capacity to disavow or to commit requires that consider apologies both as performance and as political action. While there remain significant questions regarding the practice of political apology – in particular, its relationship to practices of reparation, forgiveness and reconciliation – this approach can provide a framework with which to best consider them. (shrink)

One type of deflationism about metaphysical modality suggests that it can be analysed strictly in terms of linguistic or conceptual content and that there is nothing particularly metaphysical about modality. Scott Soames is explicitly opposed to this trend. However, a detailed study of Soames’s own account of modality reveals that it has striking similarities with the deflationary account. In this paper I will compare Soames’s account of a posteriori necessities concerning natural kinds with the deflationary one, specifically Alan Sidelle’s account, (...) and suggest that Soames’s account is vulnerable to the deflationist’s critique. Furthermore, I conjecture that both the deflationary account and Soames’s account fail to fully explicate the metaphysical content of a posteriori necessities. Although I will focus on Soames, my argument may have more general implications towards the prospects of providing a meaning-based account of metaphysical modality. (shrink)

The opacity of some recent Machine Learning (ML) techniques have raised fundamental questions on their explainability, and created a whole domain dedicated to Explainable Artificial Intelligence (XAI). However, most of the literature has been dedicated to explainability as a scientific problem dealt with typical methods of computer science, from statistics to UX. In this paper, we focus on explainability as a pedagogical problem emerging from the interaction between lay users and complex technological systems. We defend an empirical methodology based on (...) field work, which should go beyond the in-vitro analysis of UX to examine in-vivo problems emerging in the field. Our methodology is also comparative, as it chooses to steer away from the almost exclusive focus on ML to compare its challenges with those faced by more vintage algorithms. Finally, it is also philosophical, as we defend the relevance of the philosophical literature to define the epistemic desiderata of a good explanation. This study was conducted in collaboration with Etalab, a Task Force of the French Prime Minister in charge of Open Data & Open Government Policies, dealing in particular with the enforcement of the right to an explanation. In order to illustrate and refine our methodology before going up to scale, we conduct a preliminary work of case studies on the main different types of algorithms used by the French administration: computation, matching algorithms and ML. We study the merits and drawbacks of a recent approach to explanation, which we baptize input-output black box reasoning or BBR for short. We begin by presenting a conceptual framework including the distinctions necessary to a study of pedagogical explainability. We proceed to algorithmic case studies, and draw model-specific and model-agnostic lessons and conjectures. (shrink)

Clayton and Stevens argue that political liberals should engage with the religiously unreasonable by offering religious responses and showing that their religious views are mistaken, instead of refusing to engage with them. Yet they recognize that political liberals will face a dilemma due to such religious responses: either their responses will alienate certain reasonable citizens, or their engagements will appear disingenuous. Thus, there should be a division of justificatory labour. The duty of engagement should be delegated to religious citizens. In (...) this comment, I will argue that the division of justificatory labour is indefensible. This dilemma can be avoided if politicians and political philosophers correctly use conjecture, a form of discourse that involves non-public reason. As a conditional response, conjecture avoids alienating any reasonable citizens. Also, if conjecture is given in a sincere and open-minded manner, then the problem of disingenuousness can be overcome. My comment concludes that while the engagement of politicians and political philosophers does not necessarily jeopardize overlapping consensus, they should be permitted, or perhaps even required, to engage with the religiously unreasonable due to the natural duty of justice. (shrink)

I argue that the empirical literature on priming effects does not warrant nor suggest the conclusion, drawn by prominent psychologists such as J. A. Bargh, that we have no free will or less free will than we might think. I focus on a particular experiment by Bargh – the ‘elderly’ stereotype case in which subjects that have been primed with words that remind them of the stereotype of the elderly walk on average slower out of the experiment’s room than control (...) subjects – and I show that we cannot say that subjects cannot help walking slower or that they are not free in doing do. I then illustrate how these cases can be reconciled and normalized within a Davidsonian theory of action to show that, in walking slower, subjects are acting intentionally. My argument applies across various experiments, including those of goal priming. In the final section I argue that the only cases in which priming effects are efficacious are so-called Buridan cases. (shrink)

Fetal reduction is the practice of reducing the number of fetuses in a multiple pregnancy, such as quadruplets, to a twin or singleton pregnancy. Use of assisted reproductive technologies increases the likelihood of multiple pregnancies, and many fetal reductions are done after in vitro fertilisation and embryo transfer, either because of social or health-related reasons. In this paper, I apply Joe Horton’s all or nothing problem to the ethics of fetal reduction in the case of a twin pregnancy. (...) I argue that in the case of a twin pregnancy, there are two intuitively plausible claims: abortion is morally permissible, and it is morally wrong to abort just one of the fetuses. But since we should choose morally permissible acts rather than impermissible ones, the two claims lead to another highly implausible claim: the woman ought to abort both fetuses rather than only one. Yet, this does not seem right. A plausible moral theory cannot advocate such a pro-death view. Or can it? I suggest ways to solve this problem and draw implications for each solution. There are no data in this work. (shrink)

It is often assumed that believing that p for a normative reason consists in nothing more than (i) believing that p for a reason and (ii) that reason’s corresponding to a normative reason to believe that p, where (i) and (ii) are independent factors. This is the Composite View. In this paper, we argue against the Composite View on extensional and theoretical grounds. We advocate an alternative that we call the Prime View. On this view, believing for a normative (...) reason is a distinctive achievement that isn’t exhausted by the mere conjunction of (i) and (ii). Its being an achievement entails that (i) and (ii) are not independent when one believes for a normative reason: minimally, (i) must hold because (ii) holds. Apart from its intrinsic interest, our discussion has important upshots for central issues in epistemology, including the analysis of doxastic justification, the epistemology of perception, and the place of competence in epistemology. (shrink)

Horgan and Timmons have argued that our intuitions about the semantics of non-moral language and moral language differ, and that while twin-earth semantic intuitions generate one result in Putnam´s twater case, moral twin-earth fails to generate comparable results for moral terms. Horgan and Timmon´s conclude from this that the semantic norms governing the use of natural kind terms differ from the semantic norms governing the use of moral terms. I will argue that Horgan and Timmons’ intuitive moral (...) class='Hi'>twin-earth argument fails to derail the new moral realism. Further, I will discuss Boyd’s semantic theory and raise problems for it that do not rely on the use of moral twin-earth. (shrink)

In a recent paper in this journal, McCall and Lowe (2003) argue that an understanding of Special Relativity reveals that the A theorist’s notion of temporal passage is consistent with the B theory of time. They arrive at this conclusion by considering the twins’ paradox, where one of two twins (T) travels to Alpha Centauri and back and upon her return has aged 30 years, while her earth-bound twin (S) has aged 40 years. This paper argues that their account (...) of temporal passage fails to reconcile the A theoretic notion of temporal passage with the B theory of time since the B theorist is at liberty to adopt this as an account of temporal passage as understood by the B theorist. (shrink)

A brief account of Putnam's Twin Earth thought experiment and its significance, written for a general audience. Sadly, I can't include Helen De Cruz's drawing of it - check out the beautiful book!

Horgan and Timmons, with their Moral Twin Earth arguments, argue that the new moral realism falls prey to either objectionable relativism or referential indeterminacy. The Moral Twin Earth thought experiment on which the arguments are based relies in crucial ways on the use of intuitions. First, it builds on Putnam’s well-known Twin Earth example and the conclusions drawn from that about the meaning of kind names. Further, it relies on the intuition that were Earthers and Twin (...) Earthers to meet, they would be able to have genuine moral disagreements. I will argue that the similarities with Putnam’s thought experiment are questionable and so the reliance on Putnam-like intuitions is questionable. I will then further argue that even if we accept the intuitions that Horgan and Timmons rely on, the anti-realist conclusion is not warranted due to there being more to the meaning of kind terms than the argument assumes. Once we develop the meaning of kind terms further we can acknowledge both that Earthers and Twin Earthers refer to different properties with their moral terms, and that in spite of that they can have a substantive disagreement due to a shared meaning component. (shrink)

In this paper I argue against Twin-Earth externalism. The mistake that Twin Earth arguments rest on is the failure to appreciate the force of the following dilemma. Some features of things around us do matter for the purposes of conceptual classification, and others do not. The most plausible way to draw this distinction is to see whether a certain feature enters the cognitive perspective of the experiencing subject in relation to the kind in question or not. If it (...) does, we can trace conceptual differences to internal differences. If it doesn’t, we do not have a case of conceptual difference. Neither case supports Twin Earth externalism. (shrink)

In special cases of partial twinning, two heads, each supporting a more-orless normal human mental life, emerge from a single torso. It is often argued that there must be two people in such a case, even if there is only one biological organism. That would pose a problem for ‘animalism’, the view that people are organisms. The paper argues that it is very hard to say what sort of non-organisms the people in such cases would be. Reflection on partial twinning (...) is no more comfortable for those who think we’re not organisms than for those who think we are. We may have to accept that a single person could have two separate mental lives. (shrink)

Moeser suggested participants default to linear ordering elements but they can be primed to impose either linear or partial ordering. This study seems problematic insofar as ‘greater than’ might be understood to incline participants to favor linear orderings. Recent follow-up studies strongly suggest participants do not default to linear ordering. It seems plausible, moreover, that the observed priming effect is far more pervasive than Moeser countenanced. The present work explores the extent to which priming for linear or partial orders conflicts (...) with the construction of linear or partial ordering lists. Our two experiments suggest friction between priming and task, and also show once the priming tasks are cleared of potentially confounding semantic content, participants perform equally with respect to constructing linear or partial orders under similar priming conditions. (shrink)

This is a conjecture about the conditions and operating structures that are required for the phenomenality of certain mental states. Specifically, full-blown phenomenality is assumed, as contrasted with constrained examples of phenomenal experience such as sensations of color and pain. Propositional attitudes and content, while not phenomenal per se, are standardly concurrent and may condition phenomenal states (e.g., when tied to false beliefs). It is conjectured that full phenomenality natively arises in coherent processes of situated sensory synthesis and representation (...) (with conceptual content) that are looped, mereologically whole and multi-dimensional. And that phenomenal states are typically phase-states within a parameterized conjoint structure of world and experiencer processes that are causally modulated across Markov blankets (which are conditionally independent and may be nested: cf. M. Kirchoff, et. al., 2017, 2018; and T. Burge, 2010, re: anti-individualism). Though they may, it is not accepted that phenomenally conscious states must be targets of higher-order representations (cf. A. Byrne, 2004). (shrink)

The two purposes of this essay. The general philosophical problem with most versions of social libertarianism and how this essay will proceed. The specific problem with liberty explained by a thought-experiment. The positive and abstract theory of interpersonal liberty-in-itself as ‘the absence of interpersonal initiated constraints on want-satisfaction’, for short ‘no initiated impositions’. The individualistic liberty-maximisation theory solves the problems of clashes, defences, and rectifications without entailing interpersonal utility comparisons or libertarian consequentialism. The practical implications of instantiating liberty: three rules (...) of liberty-in-practice, 1) initial ultimate control of one’s body, 2) initial ultimate control of one’s used resources, 3) consensual interpersonal interactions and resource transfers. These rules are economically efficient and maximise general want-satisfaction. Private property and legal remedies are additional practical institutional aspects, but to which ‘initiated impositions’ then apply prima facie. Libertarian law is often mistaken for complete libertarianism. Moral explanations are a separate issue. The three main moral theories imply libertarianism, but it can be morally posited independently of them. Critical rationalism and its application. No empirical or argumentative support for theories. An important ambiguity with ‘justification’. How the epistemology applies to the theory of liberty and its application but remains separable in principle. Conclusion: there are further published explanations but this should be enough to generate useful criticism. Appendix replying to some typical comments. (shrink)

Whether some condition is equivalent to a conjunction of some conditions has been a major issue in analytic philosophy. Examples include: knowledge, acting freely, causation, and justice. Philosophers have striven to offer analyses of these, and other concepts, by showing them equivalent to such a conjunction. Timothy Williamson offers a number of arguments for the idea that knowledge is ‘prime’, hence not equivalent to or composed by some such conjunction. I focus on one of his arguments: the requirement that (...) such conjuncts must be freely recombinable. Although there has been a great deal of discussion of Williamson's arguments, the flaw I describe has gone unnoticed. Williamson's argument is expressed in terms of conditions, and cases of the condition. Does the condition include specific information, or is the specific information only part of the case? His argument equivocates between more and less general specifications of the conditions. Once this distinction is clarified, his argument can be seen to be vitiated by this conflation. Neither option yields a sound argument for Williamson's desired conclusion. (shrink)

Mark Timmons and Terry Horgan have argued that the new moral realism, which rests on the causal theory of reference, is untenable. While I do agree that the new moral realism is untenable, I do not think that Timmons and Horgan have succeeded in showing that it is. I will lay out the case for new moral realism and Horgan and Timmons’ argument against it, and then argue that their argument fails. Further, I will discuss Boyd’s semantic theory as well (...) as attempts to improve upon it, raise serious problems for these semantic accounts, and suggest an alternative view that accounts for our use of moral terms. (shrink)

It is widely believed that Twin-Earth-style thought experiments show that the contents of a person's thoughts fail to supervene on her intrinsic properties. Several recent philosophers have made the further claim that Twin-Earth-style thought experiments produce metaphysically necessary conditions for the possession of certain concepts. I argue that the latter view is false, and produce counterexamples to several proposed conditions. My thesis is of particular interest because it undermines some attempts to show that externalism is incompatible with privileged (...) access. (shrink)

In this paper I revisit an important response to the Moral Twin Earth (MTE) challenge: The Common Functional Role strategy (CFR). I argue that CFR is open to a revenge problem. MTE-cases allegedly show that two linguistic communities can be in genuine disagreement even when they are regulated by distinct families of properties. CFR provides a way to reconcile the intuition that the two communities are in genuine disagreement with the claim that the use of moral terms by both (...) communities is causally regulated by different families of properties. This is done by identifying a functional role that those families of properties both fulfill. Still, even if CFR is successful, its proponents need to face a serious revenge problem. Roughly, it could be that the families of properties that regulate each community are equally perfect realizers of the relevant higher-order functional state. I suggest that the proponent of CFR faces a dilemma: either CFR has controversial implications about first-order moral theory, or CFR needs to be coupled with substantive and parochial empirical/metaphysical assumptions to avoid those implications. (shrink)

Determinism is established in quantum mechanics by tracing the probabilities in the Born rules back to the absolute (overall) phase constants of the wave functions and recognizing these phase constants as pseudorandom numbers. The reduction process (collapse) is independent of measurement. It occurs when two wavepackets overlap in ordinary space and satisfy a certain criterion, which depends on the phase constants of both wavepackets. Reduction means contraction of the wavepackets to the place of overlap. The measurement apparatus fans out the (...) incoming wavepacket into spatially separated eigenpackets of the chosen observable. When one of these eigenpackets together with a wavepacket located in the apparatus satisfy the criterion, the reduction associates the place of contraction with an eigenvalue of the observable. The theory is nonlocal and contextual. Keywords:. (shrink)

We ordinarily assume that we have reliable knowledge of our immediate surroundings, so much so that almost all the time we entrust our lives to the truth of what we take ourselves to know, without a moment’s thought. But if, as Karl Popper and others have maintained, all our knowledge is conjectural, then this habitual assumption that our common sense knowledge of our environment is secure and trustworthy would seem to be an illusion. Popper’s philosophy of science, in particular, fails (...) to do justice to the distinction we ordinarily draw between secure knowledge and mere conjecture. But Popper’s philosophy of science, in particular his attempted solution to the problem of induction, is defective. It fails to take into account that physics, in only accepting unified theories, even though endlessly empirically more successful disunified rivals are always available, makes the persistent metaphysical assumption that all disunified theories are false. Once this point is acknowledged, it becomes clear that a new conception of scientific method is required which sees science as making a hierarchy of metaphysical assumptions concerning the comprehensibility and knowability of the universe. This provides a framework of relatively unproblematic assumptions and associated methods of science within which much more problematic assumptions and associated methods can be critically assessed and improved. This hierarchical view seems at first to intensify the problem of distinguishing certainty from conjecture, in that it emphasizes that scientific knowledge, and even humble common sense knowledge, contain usually unacknowledged cosmological conjectures. But actually it explicates the basis we have for drawing the distinction between trustworthy knowledge and mere conjecture, and even goes some way towards providing a rationale for this distinction, in so far as one exists. (shrink)

This paper presents two cases demonstrating that theories allowing the environment to partially determine the content of moral concepts provide incorrect truth-conditions for moral terms. While typical Moral Twin Earth cases seek to establish that these theories fail to account formoral disagreement, neither case here essentially involves interpersonal disagreement. Both involve a single person retaining moral beliefs despite recognizing actual or potential mismatches with the purportedly content-determining facts. This lets opponents of such theories grant objections that standard Moral (...) class='Hi'>Twin Earth cases fail to demonstrate disagreement, and argue more straightforwardly that they generate implausible truth-conditions for moral claims. (shrink)

According to the target article authors, initial experience with a circumstance primes a relation that can subsequently be applied to a different circumstance to draw an analogy. While I broadly agree with their claim about the role of relational priming in early analogical reasoning, I put forward a few concerns that may be worthy of further reflection.

A collective understanding that traces a debate between ‘what is science?’ and ‘what is a science about?’ has an extraction to the notion of scientific knowledge. The debate undertakes the pursuit of science that hardly extravagance the dogma of pseudo-science. Scientific conjectures invoke science as an intellectual activity poured by experiences and repetition of the objects that look independent of any idealist views (believes in the consensus of mind-dependence reality). The realistic machinery employs in an empiricist exposition of the objective (...) phenomenon by synchronizing the general method to make observational predictions that cover all the phenomena of the particular entity without any exception. The formation of science encloses several epistemological purviews and a succession of conjectures cum refutation that a newer theorem could reinstate. My attempt is to advocate a holistic plea of scientific conjectures that outruns the restricted regulation of experience or testable hypothesis to render the validity of a chain of logical reasoning (deductive or inductive) of basic scientific statements. The milieu of scientific intensification integrates speculation that loads efficiency towards a new experimental dimension where the reality is not itself objective or observers relative; in fact the observed phenomenon divulges in the constructive progression of preferred methods of falsifiability and uncertainty. (shrink)

A collective understanding that traces a debate between 'what is science?’ and ‘what is a science about?’ has an extraction to the notion of scientific knowledge. The debate undertakes the pursuit of science that hardly extravagance the dogma of pseudo-science. Scientific conjectures invoke science as an intellectual activity poured by experiences and repetition of the objects that look independent of any idealist views (believes in the consensus of mind-dependence reality). The realistic machinery employs in an empiricist exposition of the objective (...) phenomenon by synchronizing the general method to make observational predictions that cover all the phenomena of the particular entity without any exception. The formation of science encloses several epistemological purviews and a succession of conjectures cum refutation that a newer theorem could reinstate. My attempt is to advocate a holistic plea of scientific conjectures that outruns the restricted regulation of experience or testable hypothesis to render the validity of a chain of logical reasoning (deductive or inductive) of basic scientific statements. The milieu of scientific intensification integrates speculation that loads efficiency towards a new experimental dimension where the reality is not itself objective or observers relative; in fact the observed phenomenon divulges in the constructive progression of preferred methods of falsifiability and uncertainty. (shrink)

Two very different forms of externalism about mental states appear prima facie unrelated: Williamson’s (1995, 2000) claim that knowledge is a mental state, and Clark & Chalmers’ (1998) extended mind hypothesis. I demonstrate, however, that the two approaches justify their radically externalist by appealing to the same argument from explanatory generality. I argue that if one accepts either Williamson’s claims or Clark & Chalmers’ claims on considerations of explanatory generality then, ceteris paribus, one should accept the other. This conclusion has (...) implications for philosophy of mind, epistemology, and cognitive science. (shrink)

Michael Scriven’s (1959) example of identical twins (who are said to be equal in fitness but unequal in their reproductive success) has been used by many philosophers of biology to discuss how fitness should be defined, how selection should be distinguished from drift, and how the environment in which a selection process occurs should be conceptualized. Here it is argued that evolutionary theory has no commitment, one way or the other, as to whether the twins are equally fit. This is (...) because the theory of natural selection is fundamentally about the fitnesses of traits, not the fitnesses of token individuals. A plausible philosophical thesis about supervenience entails that the twins are equally fit if they live in identical environments, but evolutionary biology is not committed to the thesis that the twins live in identical environments. Evolutionary theory is right to focus on traits, rather than on token individuals, because the fitnesses of token organisms (as opposed to their actual survivorship and degree of reproductive success) are almost always unknowable. This point has ramifications for the question of how Darwin’s theory of evolution and R. A. Fisher’s are conceptually different. (shrink)

Physicists Brian Greene and Max Tegmark both make variants of the claim that if the universe is infinite and matter is roughly uniformly distributed, then there are infinitely many “people with the same appearance, name and memories as you, who play out every possible permutation of your life choices.” In this paper I argue that--while our current best theories in astrophysics may allow one to conclude that we have infinitely many duplicates whose lives are identical to our own from start (...) to finish--without either further advances in physics or advances in fields like biology, psychology, neuroscience, and philosophy, Greene’s and Tegmark’s claims about the ways in which our duplicates lives will differ from our own are not a consequence of our best current scientific theories. Rather, I argue that Greene and Tegmark’s conclusions rely on philosophically imprecise usages of the language of “possibility.”. (shrink)

In this article, I examine a new concept of “Twin Memory’ which has emerged in memory classification research of conscious and unconscious memory representations. It is to analyse the presence of twin memory among the various memory systems, and also to provide a platform for the twin memory “anatomy” in the field of cognitive science, neuropsychology and neuroscience.

Time contraction is not a property of the moving body. Permanent contraction is against the constancy of the speed of light. Einstein uses wrong units of measurement and comes to wrong conclusions. We use the translation of the article "On the electrodynamics of moving bodies".

This paper presents folk impressions of the University of Manchester’s difficulties in becoming a great university, but by means of a fiction imitating a distinguished writer from the Indian subcontinent. The impressions concern past efforts and the difficulties they faced.

Sri Guru Granth Sahib, the holy scripture of the Sikhs, contains numerous references to the worship of the divine in Nature. The Sikh scripture declares that human beings' purpose is to achieve a blissful state and be in harmony with the Earth and all creation. Millions of Sikhs recite Gurbani daily wherein the divine is remembered using the symbolism from Nature, esp. air, water, sun, moon, trees, animals, and the Earth. The human mind loses communion with Nature and ultimately with (...) God by being self-conceited. It causes misery all around, is a repeated assertion of Sikhism. The contemporary environmental crisis is an outcome of the actions of such a self-conceited human mind. By affirming God's immanence and His presence in the creation, the Sikh religion imparts the spirit of self-righteousness to the entire subject of Nature. Sikhism is a remarkable religious and cultural phenomenon; several important themes emerge within its universe of beliefs. On the ecological front, the theology of Sikhism suggests that humans must live in harmony with Nature. The Sikh Gurus exemplified many of these teachings, and their examples continue to inspire contemporary social, religious, and environmental leaders in their efforts to protect the planet. In this presentation, the prime environmental teachings of Sikhism are shared with the community. (shrink)

The article examines the impact of the virtual public sphere on how urban spaces are experienced and conceived in our data-driven society. It places particular emphasis on urban scale digital twins, which are virtual replicas of cities that are used to simulate environments and develop scenarios in response to policy problems. The article also investigates the shift from the technical to the socio-technical perspective within the field of smart cities. Despite the aspirations of urban scale digital twins to enhance the (...) participation of citizens in the decision-making processes relayed to urban planning strategies, the fact that they are based on a limited set of variables and processes makes them problematic. The article aims to shed light on the tension between the real and the ideal at stake during this process of abstracting sets of variables and processes in the case of urban scale digital twins. (shrink)

This paper presents a new challenge for libertarianism. The problem, in a nutshell, is that libertarianism appears to self-destruct in cases where conjoined twins—who share body parts—disagree over what to do with them. The problem is explored, and some solutions are proposed. The verdict is that accepting any of them will make libertarianism harder to defend.

Let G be an additive subgroup of ℂ, let Wn = {xi = 1, xi + xj = xk: i, j, k ∈ {1, …, n }}, and define En = {xi = 1, xi + xj = xk, xi · xj = xk: i, j, k ∈ {1, …, n }}. We discuss two conjectures. If a system S ⊆ En is consistent over ℝ, then S has a real solution which consists of numbers whose absolute values belong to (...) [0, 22n –2]. If a system S ⊆ Wn is consistent over G, then S has a solution ∈ n in which |xj| ≤ 2n –1 for each j. (shrink)

In his recent book Physicalism, Daniel Stoljar argues that there is no version of physicalism that is both true and deserving of the name. His argument employs a variation of Hilary Putnam’s famous twin-earth story, which Stoljar calls “the twin-physics world.” In this paper, I challenge Stoljar’s use of the twin-physics world. The upshot of that challenge, I argue, is that Stoljar fails to show, concerning the versions of physicalism for which he grants the possibility of being (...) true, that none of them is deserving of the name. (shrink)

A lean hylomorphism stands as a metaphysical holy grail. An embarrassing feature of traditional hylomorphic ontologies is prime matter. Prime matter is both so basic that it cannot be examined (in principle) and its engagement with the other hylomorphic elements is far from clear. One particular problem posed by prime matter is how it is to be understood both as a principle of individuation for material substances and as pure potency. I present Thomas Aquinas’s way of squeezing (...) some intelligibility out of prime matter by modeling it on the idea of logical genus. Such a modeling provides insight into understanding prime matter as substratum, as maximally indeterminate, and as ontologically vague. One of the unusual but exciting things that fall out from this analysis of prime matter is the Entirety Thesis: “For any substance x, if x has prime matter then the prime matter of x is the same* as x,” where ‘same*’ is understood as “indeterminately identical.”. (shrink)

The two principal models of design in methodological circles in architecture—analysis/synthesis and conjecture/analysis—have their roots in philosophy of science, in different conceptions of scientific method. This paper explores the philosophical origins of these models and the reasons for rejecting analysis/synthesis in favour of conjecture/analysis, the latter being derived from Karl Popper’s view of scientific method. I discuss a fundamental problem with Popper’s view, however, and indicate a framework for conjecture/analysis to avoid this problem.