It is widely recognized that computational theories of learning must posit the existence of a priori constraints on hypothesis selection. The present article surveys the theoretical options available for modelling the dynamic process whereby the constraints have their effect. According to the 'simplicity' theory (exemplified by Fodor's treatment), hypotheses are preference-ordered in terms of their syntactic or semantic properties. It is argued that the same explanatory power can be obtained with a weaker (hence better) theory, the 'minimalist' theory, which dispenses (...) with the preference ordering. According to the 'finitistic' theory, the learner is capable of generating only finitely many hypotheses for evaluation. Chomsky maintains that the occurrence of errorless learning in language acquisition necessitates a finististic explanation. Once again, there is a weaker theory that explains the same data. Finally, Goodman's argument to the effect that there cannot be a computational theory of learning is examined and rejected. (shrink)

The purpose of this paper is to discuss the role of financial practice in the development of mathematics as applied in human judgement. The basis of the paper is in historical research from the 1990s that argues that the monetisation of western commerce, which abstracted value into quantified price, was synthesised with scholastic analysis resulting in a “mathematical mechanistic world picture” that led to the widespread use of mathematics in science from the seventeenth century. An aspect of this process was (...) the quantification of chance that led to the development of mathematical probability, the branch of mathematics most relevant to judgement and the focus of this paper. Ideas from this historical research are related to the fundamental theorem of asset pricing, the foundational theory of contemporary financial mathematics. The paper observes that vestiges of medieval scholastic attitudes to financial ethics can be discerned in the FTAP, offering a novel interpretation of the mathematical theorem. The paper then considers the Dutch book argument, the most popular justification for subjective probability. The paper’s main contribution is in describing the significance of financial practice in validating the DBA and the paper explains how the FTAP addresses some criticisms of how the DBA represents beliefs. The conclusions emphasise the distinction between pure and practical reasoning and that this should be mirrored in a distinction between the mathematics of physica and practica. This point is important as mathematics is becoming more widespread in modelling, and directing, social systems. (shrink)

A global pandemic on the scale of Covid-19 upsets all standard decision protocols. Pressure from politicians to "open up" the economy presumes that individuals grant credible trust to politicians and merchants eager to recover customers. The asymmetric concern for safety compounds normal heuristics. The Peircean pragmatic maxim reminds us that it is the perceived effects of a post-pandemic society and economy that will drive human volition in the aftermath of Covid-19. Opening up does not equal showing up.

According to the instrumentalism of Friedman and Machlup it is irrelevant whether the explanatory principles or “assumptions” of a theory satisfy any criterion of “plausibility,” “realism,” “credibility,” or “soundness.” In this view the main or only criterion for selecting theories is whether a theory yields empirically testable implications that turn out to be consistent with observations. All we should require or expect from a theory is that it is a useful instrument for the purpose of prediction. Considerations of the “efficiency” (...) of a theory for the purpose of ordering our experiences are permitted, but considerations of “plausibility” are not. “Explanatory assumptions” are not really explanatory in the sense that they claim to represent underlying causal processes in reality; they only serve to generate, by deduction, implications that are in accordance with as many observations as possible. (shrink)

The principle of clinical equipoise requires that, aside from certain exceptional cases, second generation treatments ought to be tested against standard therapy. In violation of this principle, placebo-controlled trials (PCTs) continue to be used extensively in the development and licensure of second-generation treatments. This practice is typically justified by appeal to methodological arguments that purport to demonstrate that active-controlled trials (ACTs) are methodologically flawed. Foremost among these arguments is the so called assay sensitivity argument. In this paper, I take a (...) closer look at this argument. Following Duhem, I argue that all trials, placebo-controlled or not, rely on external information for their meaningful interpretation. Pending non-circular empirical evidence that we can trust the findings of PCTs to a greater degree than the findings of ACTs, I conclude that the assay sensitivity argument fails to demonstrate that placebo-controlled trials are preferable, methodologically or otherwise, to active-controlled trials. Contrary to the intentions of its authors, the fundamental lesson taught by the assay sensitivity argument is Duhemian: the validity of all clinical trials depends on external information. (shrink)

This fourteenth volume of Collected Papers is an eclectic tome of 87 papers in Neutrosophics and other fields, such as mathematics, fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, information fusion, robotics, statistics, or extenics, comprising 936 pages, published between 2008-2022 in different scientific journals or currently in press, by the author alone or in collaboration with the following 99 co-authors (alphabetically ordered) from 26 countries: Ahmed B. Al-Nafee, Adesina Abdul Akeem Agboola, Akbar Rezaei, Shariful Alam, Marina Alonso, Fran Andujar, (...) Toshinori Asai, Assia Bakali, Azmat Hussain, Daniela Baran, Bijan Davvaz, Bilal Hadjadji, Carlos Díaz Bohorquez, Robert N. Boyd, M. Caldas, Cenap Özel, Pankaj Chauhan, Victor Christianto, Salvador Coll, Shyamal Dalapati, Irfan Deli, Balasubramanian Elavarasan, Fahad Alsharari, Yonfei Feng, Daniela Gîfu, Rafael Rojas Gualdrón, Haipeng Wang, Hemant Kumar Gianey, Noel Batista Hernández, Abdel-Nasser Hussein, Ibrahim M. Hezam, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Muthusamy Karthika, Nour Eldeen M. Khalifa, Madad Khan, Kifayat Ullah, Valeri Kroumov, Tapan Kumar Roy, Deepesh Kunwar, Le Thi Nhung, Pedro López, Mai Mohamed, Manh Van Vu, Miguel A. Quiroz-Martínez, Marcel Migdalovici, Kritika Mishra, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohammed Alshumrani, Mohamed Loey, Muhammad Akram, Muhammad Shabir, Mumtaz Ali, Nassim Abbas, Munazza Naz, Ngan Thi Roan, Nguyen Xuan Thao, Rishwanth Mani Parimala, Ion Pătrașcu, Surapati Pramanik, Quek Shio Gai, Qiang Guo, Rajab Ali Borzooei, Nimitha Rajesh, Jesús Estupiñan Ricardo, Juan Miguel Martínez Rubio, Saeed Mirvakili, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, Ahmed A. Salama, Nirmala Sawan, Gheorghe Săvoiu, Ganeshsree Selvachandran, Seok-Zun Song, Shahzaib Ashraf, Jayant Singh, Rajesh Singh, Son Hoang Le, Tahir Mahmood, Kenta Takaya, Mirela Teodorescu, Ramalingam Udhayakumar, Maikel Y. Leyva Vázquez, V. Venkateswara Rao, Luige Vlădăreanu, Victor Vlădăreanu, Gabriela Vlădeanu, Michael Voskoglou, Yaser Saber, Yong Deng, You He, Youcef Chibani, Young Bae Jun, Wadei F. Al-Omeri, Hongbo Wang, Zayen Azzouz Omar. (shrink)

The question of David Armstrong's recent book, What Is a Law of Nature? would seem to have little point unless there really are laws of nature. However that may be, so much philosoFhical thinking has utilized this concept, that an inquiry of this sort was needed whether there are or not. The book begins with a devastating attack on so-called Regularity views of law, and then proceeds with an exposition of Armstrong's own answer to the question. I wish to raise (...) here some difficulties for Armstrong's answer, concentrating on his account of probabilistic laws where I see the severest problems. To locate myself with respect to his approach, however, I shall first enter some lesser demurrals. (shrink)

Quine’s eliminativist theory has largely been ignored by the philosophical community. This is highly regrettable because Quine’s theory is probably close to correct. Now, the probable correctness of Quine’s theory has an important consequence since, according to the theory, there are no mental entities (events, states, phenomena, properties, etc.) nor do such entities play any role in a scientific account of the relevant phenomena. But the hundreds or probably thousands of publications that deal with issues such as mental causation, the (...) nature of qualia, supervenience of the mental, or multiple realizability, presume the existence of, or at least attribute a positive role to, mental entities. The probable correctness of Quine’s theory therefore suggests that all these publications are worthless and reading them is a waste of time just as reading studies about how crystal spheres can move planets is considered nowadays a waste of time. (shrink)

Quine’s eliminativist theory has largely been ignored by the philosophical community. This is highly regrettable because Quine’s theory is probably close to correct. Now, the probable correctness of Quine’s theory has an important consequence since, according to the theory, there are no mental entities (events, states, phenomena, properties, etc.) nor do such entities play any role in a scientific account of the relevant phenomena. But the hundreds or probably thousands of publications that deal with issues such as mental causation, the (...) nature of qualia, supervenience of the mental, or multiple realizability, presume the existence of, or at least attribute a positive role to, mental entities. The probable correctness of Quine’s theory therefore suggests that all these publications are worthless and reading them is a waste of time just as reading studies about how crystal spheres can move planets is considered nowadays a waste of time. (shrink)

One usually speaks of Hume's problem of induction in the singular, as if Hume had called our attention to only one problem which affects the justification of inductive inferences. But Hume shows that this justification depends on two assumptions which are not logically valid. In most studies about the justification of inductive inferences, Hume's approach to base the justification on two assumptions has not been discussed. This seems to have been a mistake, however. Not only do these assumptions play different (...) roles in the justification, but by distinguishing between them, one of them can be shown to be scientifically (though not logically) valid. (shrink)

The author makes an introduction to non-standard analysis, then extends the dialectics to “neutrosophy” – which became a new branch of philosophy. This new concept helps in generalizing the intuitionistic, paraconsistent, dialetheism, fuzzy logic to “neutrosophic logic” – which is the first logic that comprises paradoxes and distinguishes between relative and absolute truth. Similarly, the fuzzy set is generalized to “neutrosophic set”. Also, the classical and imprecise probabilities are generalized to “neutrosophic probability”.

Hilary Putnam has famously undergone some radical changes of mind with regard to the issue of scientific realism and its wider epistemological bearings. In this paper I defend the arguments put forward by early Putnam in his essays on the causal theory of reference as applied to natural-kind terms, despite his own later view that those arguments amounted to a form of 'metaphysical' realism which could not be sustained against various lines of sceptical attack. I discuss some of the reasons (...) for Putnam's retreat, first to the theory of 'internal (or framework-relative) realism proposed in his middle-period writings, and then to a commonsensepragmatist stance which claims to resituate this whole discussion on ground that has not been trorldden into ruts by the contending philosophical schools. In particular I examine his protracted engagement with various forms of anti-realist doctrine (Michael Dummett's most prominent among them), with Wittgenstein's thinking about language-games or meaning-as-use, and with a range of sceptical- relativist positions adopted in the wake of Quine's influential attack on the two last 'dogmas' of logical empiricism. My paper seeks to show that Putnam has been over-impressed by some of the arguments — from these and other sources — which he takes to constitute a knock-down case against the kind of extemalist and causal-realist approach developed in his early essays. It concludes by re-stating that position in summary form and relating it to other, more recent defences of causal realism in epistemology and philosophy of science. (shrink)