Abstract In the new millennium there have been important empirical developments in the philosophy of mathematics. One of these is the so-called “Empirical Philosophy of Mathematics”(EPM) of Buldt, Löwe, Müller and Müller-Hill, which aims to complement the methodology of the philosophy of mathematics with empirical work. Among other things, this includes surveys of mathematicians, which EPM believes to give philosophically important results. In this paper I take a critical look at the sociological part of EPM as a (...) case study of ... (shrink)

In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received (...) very little attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects. (shrink)

What were the reasons of the Copernican Revolution ? How did modern science (created by a bunch of ambitious intellectuals) manage to force out the old one created by Aristotle and Ptolemy, rooted in millennial traditions and strongly supported by the Church? What deep internal causes and strong social movements took part in the genesis, development and victory of modern science? The author comes to a new picture of Copernican Revolution on the basis of the elaborated model of scientific revolutions (...) that takes into account some recent advances in philosophy, sociology and history of science. The model was initially invented to describe Einstein’s Revolution of the XX century beginning. The model considers the growth of knowledge as interaction, interpenetration and unification of the research programmes, springing out of different cultural traditions. Thus, Copernican Revolution appears as a result of revealation and (partial) resolution of the dualism , of the gap between Ptolemy’s mathematical astronomy and Aristotelian qualitative physics. The works of Copernicus, Galileo, Kepler and Newton were all the stages of mathematics descendance from skies to earth and reciprocal extrapolation of earth physics on skies. The model elaborated enables to reassess the role of some social factors crucial for the scientific revolution. It is argued that initially modern science was a result of the development of Christian Weltanschaugung . Later the main support came from the absolute monarchies. In the long run the creators of modern science appeared to be the “apparatchics” of the “regime of truth” built-in state machine. Natural science became a part of ideological state apparatus providing not only scientific education but the internalization of values crucial for the functioning of state. -/- . (shrink)

Over the years, mathematics and statistics have become increasingly important in the social sciences1 . A look at history quickly confirms this claim. At the beginning of the 20th century most theories in the social sciences were formulated in qualitative terms while quantitative methods did not play a substantial role in their formulation and establishment. Moreover, many practitioners considered mathematical methods to be inappropriate and simply unsuited to foster our understanding of the social domain. Notably, the famous Methodenstreit also (...) concerned the role of mathematics in the social sciences. Here, mathematics was considered to be the method of the natural sciences from which the social sciences had to be separated during the period of maturation of these disciplines. All this changed by the end of the century. By then, mathematical, and especially statistical, methods were standardly used, and their value in the social sciences became relatively uncontested. The use of mathematical and statistical methods is now ubiquitous: Almost all social sciences rely on statistical methods to analyze data and form hypotheses, and almost all of them use (to a greater or lesser extent) a range of mathematical methods to help us understand the social world. Additional indication for the increasing importance of mathematical and statistical methods in the social sciences is the formation of new subdisciplines, and the establishment of specialized journals and societies. Indeed, subdisciplines such as Mathematical Psychology and Mathematical Sociology emerged, and corresponding journals such as The Journal of Mathematical Psychology (since 1964), The Journal of Mathematical Sociology (since 1976), Mathematical Social Sciences (since 1980) as well as the online journals Journal of Artificial Societies and Social Simulation (since 1998) and Mathematical Anthropology and Cultural Theory (since 2000) were established. What is more, societies such as the Society for Mathematical Psychology (since 1976) and the Mathematical Sociology Section of the American Sociological Association (since 1996) were founded. Similar developments can be observed in other countries. The mathematization of economics set in somewhat earlier (Vazquez 1995; Weintraub 2002). However, the use of mathematical methods in economics started booming only in the second half of the last century (Debreu 1991). Contemporary economics is dominated by the mathematical approach, although a certain style of doing economics became more and more under attack in the last decade or so. Recent developments in behavioral economics and experimental economics can also be understood as a reaction against the dominance (and limitations) of an overly mathematical approach to economics. There are similar debates in other social sciences. It is, however, important to stress that problems of one method (such as axiomatization or the use of set theory) can hardly be taken as a sign of bankruptcy of mathematical methods in the social sciences tout court. This chapter surveys mathematical and statistical methods used in the social sciences and discusses some of the philosophical questions they raise. It is divided into two parts. Sections 1 and 2 are devoted to mathematical methods, and Sections 3 to 7 to statistical methods. As several other chapters in this handbook provide detailed accounts of various mathematical methods, our remarks about the latter will be rather short and general. Statistical methods, on the other hand, will be discussed in-depth. (shrink)

It is commonly thought that such topics as Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason are disparate scientific physical or mathematical issues having little or nothing in common. I suggest that they are largely standard philosophical problems (i.e., language games) which were resolved by Wittgenstein over 80 years ago. -/- Wittgenstein also demonstrated the fatal error in regarding mathematics or language or our behavior in general as a unitary coherent logical ‘system,’ rather than (...) as a motley of pieces assembled by the random processes of natural selection. “Gödel shows us an unclarity in the concept of ‘mathematics’, which is indicated by the fact that mathematics is taken to be a system” and we can say (contra nearly everyone) that is all that Gödel and Chaitin show. Wittgenstein commented many times that ‘truth’ in math means axioms or the theorems derived from axioms, and ‘false’ means that one made a mistake in using the definitions, and this is utterly different from empirical matters where one applies a test. Wittgenstein often noted that to be acceptable as mathematics in the usual sense, it must be useable in other proofs and it must have real world applications, but neither is the case with Godel’s Incompleteness. Since it cannot be proved in a consistent system (here Peano Arithmetic but a much wider arena for Chaitin), it cannot be used in proofs and, unlike all the ‘rest’ of PA it cannot be used in the real world either. As Rodych notes “…Wittgenstein holds that a formal calculus is only a mathematical calculus (i.e., a mathematical language-game) if it has an extra- systemic application in a system of contingent propositions (e.g., in ordinary counting and measuring or in physics) …” Another way to say this is that one needs a warrant to apply our normal use of words like ‘proof’, ‘proposition’, ‘true’, ‘incomplete’, ‘number’, and ‘mathematics’ to a result in the tangle of games created with ‘numbers’ and ‘plus’ and ‘minus’ signs etc., and with -/- ‘Incompleteness’ this warrant is lacking. Rodych sums it up admirably. “On Wittgenstein’s account, there is no such thing as an incomplete mathematical calculus because ‘in mathematics, everything is algorithm [and syntax] and nothing is meaning [semantics]…” -/- I make some brief remarks which note the similarities of these ‘mathematical’ issues to economics, physics, game theory, and decision theory. -/- Those wishing further comments on philosophy and science from a Wittgensteinian two systems of thought viewpoint may consult my other writings -- Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle 2nd ed (2019), Suicide by Democracy 4th ed (2019), The Logical Structure of Human Behavior (2019), The Logical Structure of Consciousness (2019, Understanding the Connections between Science, Philosophy, Psychology, Religion, Politics, and Economics and Suicidal Utopian Delusions in the 21st Century 5th ed (2019), Remarks on Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason in Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, da Costa, Godel, Searle, Rodych, Berto, Floyd, Moyal-Sharrock and Yanofsky (2019), and The Logical Structure of Philosophy, Psychology, Sociology, Anthropology, Religion, Politics, Economics, Literature and History (2019). (shrink)

It is my contention that the table of intentionality (rationality, mind, thought, language, personality etc.) that features prominently here describes more or less accurately, or at least serves as an heuristic for, how we think and behave, and so it encompasses not merely philosophy and psychology, but everything else (history, literature, mathematics, politics etc.). Note especially that intentionality and rationality as I (along with Searle, Wittgenstein and others) view it, includes both conscious deliberative linguistic System 2 and unconscious automated (...) prelinguistic System 1 actions or reflexes. -/- I provide a critical survey of some of the major findings of two of the most eminent students of behavior of modern times, Ludwig Wittgenstein and John Searle, on the logical structure of intentionality (mind, language, behavior), taking as my starting point Wittgenstein’s fundamental discovery –that all truly ‘philosophical’ problems are the same—confusions about how to use language in a particular context, and so all solutions are the same—looking at how language can be used in the context at issue so that its truth conditions (Conditions of Satisfaction or COS) are clear. The basic problem is that one can say anything, but one cannot mean (state clear COS for) any arbitrary utterance and meaning is only possible in a very specific context. I analyze various writings by and about them from the modern perspective of the two systems of thought (popularized as ‘thinking fast, thinking slow’), employing a new table of intentionality and new dual systems nomenclature. I show that this is a powerful heuristic for describing behavior. -/- Thus, all behavior is intimately connected if one takes the correct viewpoint. The Phenomenological Illusion (oblivion to our automated System 1) is universal and extends not merely throughout philosophy but throughout life. I am sure that Chomsky, Obama, Zuckerberg and the Pope would be incredulous if told that they suffer from the same problem as Hegel, Husserl and Heidegger, (or that that they differ only in degree from drug and sex addicts in being motivated by stimulation of their frontal cortices by the delivery of dopamine (and over 100 other chemicals) via the ventral tegmentum and the nucleus accumbens), but it’s clearly true. While the phenomenologists only wasted a lot of people’s time, they are wasting the earth and their descendant’s future. -/- . (shrink)

The host of SUSY(supersymmetry) based string theories is considered. Superstrings are comprehended as possible candidates on Quantum Gravity basic objects. It is argued that superstring theories constitute mainly mathematical progress and can reconcile general relativity with quantum field theory at best. Yet they cannot provide the genuine synthesis. Superstring unification of all the four forces at hand is a formal one . It is contended that genesis and proliferation of superstrings can better be described not by philosophy of science models (...) but in terms of modern sociology of science. The formal character of gravity and quantum fields fusion and the lack of experimental verification make the transition to superstring theories ad hoc in Lakatosian standards. Possible way of explanation is proposed based on social interests conception of Andrew Pickering. -/- Key words: superstrings, unification, Kaluza-Klein, sociology of science . (shrink)

The paper explicates the stages of the author’s philosophical evolution in the light of Kopnin’s ideas and heritage. Starting from Kopnin’s understanding of dialectical materialism, the author has stated that category transformations of physics has opened from conceptualization of immutability to mutability and then to interaction, evolvement and emergence. He has connected the problem of physical cognition universals with an elaboration of the specific system of tools and methods of identifying, individuating and distinguishing objects from a scientific theory domain. The (...) role of vacuum conception and the idea of existence (actual and potential, observable and nonobservable, virtual and hidden) types were analyzed. In collaboration with S.Crymski heuristic and regulative functions of categories of substance, world as a whole as well as postulates of relativity and absoluteness, and anthropic and self-development principles were singled out. Elaborating Kopnin’s view of scientific theories as a practically effective and relatively true mapping of their domains, the author in collaboration with M. Burgin have originated the unified structure-nominative reconstruction (model) of scientific theory as a knowledge system. According to it, every scientific knowledge system includes hierarchically organized and complex subsystems that partially and separately have been studied by standard, structuralist, operationalist, problem-solving, axiological and other directions of the current philosophy of science. 1) The logico-linguistic subsystem represents and normalizes by means of different, including mathematical, languages and normalizes and logical calculi the knowledge available on objects under study. 2) The model-representing subsystem comprises peculiar to the knowledge system ways of their modeling and understanding. 3) The pragmatic-procedural subsystem contains general and unique to the knowledge system operations, methods, procedures, algorithms and programs. 4) From the viewpoint of the problem-heuristic subsystem, the knowledge system is a unique way of setting and resolving questions, problems, puzzles and tasks of cognition of objects into question. It also includes various heuristics and estimations (truth, consistency, beauty, efficacy, adequacy, heuristicity etc) of components and structures of the knowledge system. 5) The subsystem of links fixes interrelations between above-mentioned components, structures and subsystems of the knowledge system. The structure-nominative reconstruction has been used in the philosophical and comparative case-studies of mathematical, physical, economic, legal, political, pedagogical, social, and sociological theories. It has enlarged the collection of knowledge structures, connected, for instance, with a multitude of theoreticity levels and with an application of numerous mathematical languages. It has deepened the comprehension of relations between the main directions of current philosophy of science. They are interpreted as dealing mainly with isolated subsystems of scientific theory. This reconstruction has disclosed a variety of undetected knowledge structures, associated also, for instance, with principles of symmetry and supersymmetry and with laws of various levels and degrees. In cooperation with the physicist Olexander Gabovich the modified structure-nominative reconstruction is in the processes of development and justification. Ideas and concepts were also in the center of Kopnin’s cognitive activity. The author has suggested and elaborated the triplet model of concepts. According to it, any scientific concept is a dependent on cognitive situation, dynamical, multifunctional state of scientist’s thinking, and available knowledge system. A concept is modeled as being consisted from three interrelated structures. 1) The concept base characterizes objects falling under a concept as well as their properties and relations. In terms of volume and content the logical modeling reveals partially only the concept base. 2) The concept representing part includes structures and means (names, statements, abstract properties, quantitative values of object properties and relations, mathematical equations and their systems, theoretical models etc.) of object representation in the appropriate knowledge system. 3) The linkage unites a structures and procedures that connect components from the abovementioned structures. The partial cases of the triplet model are logical, information, two-tired, standard, exemplar, prototype, knowledge-dependent and other concept models. It has introduced the triplet classification that comprises several hundreds of concept types. Different kinds of fuzziness are distinguished. Even the most precise and exact concepts are fuzzy in some triplet aspect. The notions of relations between real scientific concepts are essentially extended. For example, the definition and strict analysis of such relations between concepts as formalization, quantification, mathematization, generalization, fuzzification, and various kinds of identity are proposed. The concepts «PLANET» and «ELEMENTARY PARTICLE» and some of their metamorphoses were analyzed in triplet terms. The Kopnin’s methodology and epistemology of cognition was being used for creating conception of the philosophy of law as elaborating of understanding, justification, estimating and criticizing legal system. The basic information on the major directions in current Western philosophy of law (legal realism, feminism, criticism, postmodernism, economical analysis of law etc.) is firstly introduced to the Ukrainian audience. The classification of more than fifty directions in modern legal philosophy is suggested. Some results of historical, linguistic, scientometric and philosophic-legal studies of the present state of Ukrainian academic science are given. (shrink)

This essay examines the quantitative aspects of Greco-Roman science, represented by a group of established disci¬plines, which since the fourth century BC were called mathēmata or mathē¬ma¬tikai epistē¬mai. In the group of mathēmata that in Antiquity normally comprised mathematics, mathematical astronomy, harmonics, mechanics and optics, we have also included geography. Using a dataset based on The Encyclopaedia of Ancient Natural Scientists, our essay considers a community of mathēmatikoi (as they called themselves), or ancient scientists (as they are defined for (...) the purposes of the present paper) from a sociological point of view, focusing on the size of the scientific population known to us and its disciplinary, temporal and geographical distribution. A diachronic comparison of neighboring and partly overlapping communities, ancient scientists and philosophers, allows the pattern of their interrelationship to be traced. An examination of centers of science throughout ancient history reveals that there were five major centers – Athens, Alexandria, Rhodes, Rome and Byzantium/Constantinople – that appear and replace one another in succession as leaders. These conclusions serve to reopen the issue of the place of mathēmata and mathēmatikoi in ancient society. (shrink)

A proof P of a theorem T is transferable when a typical expert can become convinced of T solely on the basis of their prior knowledge and the information contained in P. Easwaran has argued that transferability is a constraint on acceptable proof. Meanwhile, a proof P is fixable when it’s possible for other experts to correct any mistakes P contains without having to develop significant new mathematics. Habgood-Coote and Tanswell have observed that some acceptable proofs are both fixable (...) and in need of fixing, in the sense that they contain nontrivial mistakes. The claim that acceptable proofs must be transferable seems quite plausible. The claim that some acceptable proofs need fixing seems plausible too. Unfortunately, these attractive suggestions stand in tension with one another. I argue that the transferability requirement is the problem. Acceptable proofs need only satisfy a weaker requirement I call “corrigibility”. I explain why, despite appearances, the corrigibility standard is preferable to stricter alternatives. (shrink)

The need for revolution in modern physics is a well known and often broached subject, however, the precision and success of current models narrows the possible changes to such a great degree that there appears to be no major change possible. We provide herein, the first step toward a possible solution to this paradox via reinterpretation of the conceptual-theoretical framework while still preserving the modern art and tools in an unaltered form. This redivision of concepts and redistribution of the data (...) can revolutionize expectations of new experimental outcomes. This major change within finely tuned constraints is made possible by the fact that numerous mathematically equivalent theories were direct precursors to, and contemporaneous with, the modern interpretations. In this first of a series of papers, historical investigation of the conceptual lineage of modern theory reveals points of exacting overlap in physical theories which, while now considered cross discipline, originally split from a common source and can be reintegrated as a singular science again. This revival of an an older associative hierarchy, combined with modern insights, can open new avenues for investigation. This reintegration cross-disciplinary theories and tools is defined as the “Neoclassical Interpretation.” . (shrink)

Until the late 19th century scientists almost always assumed that the world could be described as a rule-based and hence deterministic system or as a set of such systems. The assumption is maintained in many 20th century theories although it has also been doubted because of the breakthrough of statistical theories in thermodynamics (Boltzmann and Gibbs) and other fields, unsolved questions in quantum mechanics as well as several theories forwarded within the social sciences. Until recently it has furthermore been assumed (...) that a rule-based and deterministic system was also predictable if only the rules were known, but this assumption has now been undermined by modern chaos-theory describing rule-based and deterministic, but unpredictable systems, while catastrophe-theory delivers a set of types describing various kinds of instability and conditions for the stability of a given system. Hence the main trait in the theoretical development in the 20th-century science can be described as a basic modification and limitation of some of the fundamental and strong assumptions forwarded in the previous epochs of modern science. Ironically, the very same process has been a process in which the human capacity to intervene in nature has expanded dramatically and mainly with the help of the very same theories, and not least because they allow nature to be described and made manipulable on a lower level and a more fine-grained scale. While the overall theoretical consistency between the various theories has gone, the reach of human intervention in nature has increased based on quite new dimensions whether in the area of physics (e.g.: energy technologies, chemical technologies, nanotechnologies etc.) or biology (ge¬netic manipulation) or in the area of psychology, sociology and culture (artificial simulations of mental processes, new means of communication, implying changes in the social infrastructure and cultural behaviour etc.). While some of these changes and new conditions can be reflected from within the conceptual framework of rule-based systems, albeit more complex than formerly recognized, others seem to give rise to the question of whether there are »systems« and relations between different systems in the world which are not rule-based? For instance, it seems to be obvious that the notion of instability represents a major conceptual break with former theories of rule-based systems, as the stability of the latter is an axiomatically given property implied in the very notion of rule-based systems, while instability can only be the result of external influence which should be explained as the result of another rule-based sy¬stem. While there are no difficulties implied concerning the stability of rule-based systems, the notion of unstable states of a system raises the question of how there can be a system at all if there are no invariant stabilising principles? This is the first question which I will address. And I shall do so by taking two examples of such systems as my point of departure. The first example will be the computer and the second will be ordinary language. In both cases I will argue that the stability of these systems (which are both defined by the existence/presence of human intentions) are provided by the help of - differently organised - redundancy functions which both allow the maintenance of systems in unstable macro-states, suspension of previous rules, underdetermination and overdetermination and generation/emergence/creation of new rules more or less independent of previous rules by the help of optional recursions to the permanently accessible underlying levels as for instance the level of binary representation in computers. Since the notion of redundancy is both controversial as such and often avoided, the concept is discussed (as defined in Claude Shannon's mathematical theory of information and in the semiotic framework of J. J. Greimas) and leading to a more general definition in which the redundancy functions serve to overcome noisy conditions, but at the cost of rule-based stability, determination, and predictability. A second question will be how the notion of rule-generating systems relates to the notion of anticipatory systems and it will be argued that rule-generating systems share some features with an¬ticipatory systems and that the former from a certain viewpoint can be seen as a subclass of the latter, although anticipative features are not necessarily a part of the definition of rule-generating systems. On the other hand, it will be discussed whether anticipatory systems which are not rule-generating systems can exist and it will be argued that the capacity to anticipate is strongly limited if it is not part of a rule-generating system. Therefore, it is concluded that the most powerful anticipatory systems need to be rule-generating systems. (shrink)

A philosophical exploration is presented that considers entities such as atoms, electrons, protons, reasoned (in existing physics theories) by induction, to be other than universal building blocks, but artifacts of a sociological struggle that in elemental description is identical with that of all processes of matter and energy. In a universal context both men and materials, when stressed, struggle to accomplish/maintain the free state. The space occupied by cognition, inferred to be the result of the inequality of spaces, is an (...) integral component of both processes and process interpretation; arbitration space, ubiquitous throughout nature, occurred to a vast number of vastnesses, a manifestation of the existence of time dependent mass/number/amount, is argued to be located to the same judging criteria with which principles are determined for sociological purposes: the processes of mind are determined (excuse the pun) to occur as a free state that is reflectively equal to what is construed by the intellect as universe. Scientifically determined states are not free states. (shrink)

Horwich gives a fine analysis of Wittgenstein (W) and is a leading W scholar, but in my view they all fall short of a full appreciation, as I explain at length in this review and many others. If one does not understand W (and preferably Searle also) then I don't see how one could have more than a superficial understanding of philosophy and of higher order thought and thus of all complex behavior(psychology, sociology, anthropology, history, literature, society). In a (...) nutshell, W demonstrated that when you have shown how a sentence is used in the context of interest, there is nothing more to say. I will start with a few notable quotes and then give what I think are the minimum considerations necessary to understand Wittgenstein, philosophy and human behavior. -/- First one might note that putting “meta” in front of any word should be suspect. W remarked e.g., that metamathematics is mathematics like any other. The notion that we can step outside philosophy (i.e., the descriptive psychology of higher order thought) is itself a profound confusion. Another irritation here (and throughout academic writing for the last 4 decades) is the constant reverse linguistic sexism of “her” and “hers” and “she” or “he/she” etc., where “they” and “theirs” and “them” would do nicely. Likwise the use of the French word 'repertoire' where the English 'repertory' will do quite well. The major deficiency is the complete failure (though very common) to employ what I see as the hugely powerful and intuitive two systems view of HOT and Searle’s framework which I have outlined above. This is especially poignant in the chapter on meaning p111 et seq.(esp. in footnotes 2-7), where we swim in very muddy water without the framework of automated true only S1, propositional dispositional S2, COS etc. One can also get a better view of the inner and the outer by reading e.g., Johnston or Budd (see my reviews). Horwich however makes many incisive comments. I especially liked his summary of the import of W’s antitheoretical stance on p65. Horwich is first rate and his work well worth the effort. One hopes that he (and everyone) will study Searle and some modern psychology as well as Hutto, Read, Hutchinson, Stern, Moyal-Sharrock, Stroll, Hacker and Baker etc. to attain a broad modern view of behavior. Most of their papers are on academia.edu but for PMS Hacker see http://info.sjc.ox.ac.uk/scr/hacker/DownloadPapers.html. -/- Finally, let me suggest that with the perspective I have encouraged here, W is at the center of contemporary philosophy and psychology and is not obscure, difficult or irrelevant, but scintillating, profound and crystal clear and that to miss him is to miss one of the greatest intellectual adventures possible. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my article The Logical Structure of Philosophy, Psychology, Mind and Language as Revealed in Wittgenstein and Searle 59p(2016). For all my articles on Wittgenstein and Searle see my e-book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Wittgenstein and Searle 367p (2016). Those interested in all my writings in their most recent versions may consult my e-book Philosophy, Human Nature and the Collapse of Civilization - Articles and Reviews 2006-2016’ 662p (2016). -/- All of my papers and books have now been published in revised versions both in ebooks and in printed books. -/- Talking Monkeys: Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet - Articles and Reviews 2006-2017 (2017) https://www.amazon.com/dp/B071HVC7YP. -/- The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle--Articles and Reviews 2006-2016 (2017) https://www.amazon.com/dp/B071P1RP1B. -/- Suicidal Utopian Delusions in the 21st century: Philosophy, Human Nature and the Collapse of Civilization - Articles and Reviews 2006-2017 (2017) https://www.amazon.com/dp/B0711R5LGX . (shrink)

The article contains a critical analysis of the skeptical solution to the rule- following problem. The skeptical solution denies the existence of “superlative” R-facts that would make statements of the form “P means R by ‘+’ ” true. The role of the sources for the meaning of ‘+’ here is played by the patterns of solidarity behavior of members of some community to which P belongs. The correct use of ‘+’ would be one that is approved by the competent majority (...) of this community, and there can be no other sense in which it would be correct or wrong. Boyd’s hypothesis denies the communal character of the ‘+’ meaning. While there are no “superlative” R-facts, there should be C-facts not about the R as the standard that P or its community follows in their practice of using ‘+’, but about whether they do it correctly. The proof of the Boyd hypothesis is based on the example of an imaginary Ω-community, whose agents use a finite set of simple symbols for the needs of their arithmetic: ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’, ‘G’, ‘H’, ‘J’. Each symbol denotes a subset of identical, from the Ω-community point of view, numerical values. The symbol ‘A’ is used, for ex- ample, for a subset of the natural numbers 1, 10, 19, 28, 37, 46, etc.; ‘B’ for 2, 11, 20, 29, 38, 47, etc.; ‘C’ for 3, 12, 21, 30, 39, 48, etc. The Ω-community’s arithmetic uses the only local function ⊕ whose range of values forms a finite set of mathematical propositions {α} that are true. The Ω-community’s arithmetic, like our own, is open to many skeptical challenges. Is there a fact that determines the meaning of ‘⊕’? What do agents do when they calculate with ‘⊕’ (say, solve examples ‘A⊕B = ?’, ‘C⊕E=?’, etc.)? Do they Add, Badd or Dadd? To answer them would require a “superlative” R-fact. For the calculation practice with ‘⊕’, it could be a certain R-fact that determines the only possible order for the sequence of numerals ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’, ‘G’, ‘H’, ‘J’ such that {α} is true. An analysis of the calculation practice using the local arithmetic function ⊕ shows that for it there are no such R-facts that would determine the only correct standard R – even if the agents in the Ω-community were trained in such calculations on a full set of cases for the application of that function. However, for such practice there are C-facts (independent in their existence from R-facts) that make it possible to distinguish between what seems to be right and what is right. The solitary agent P and the Ω-community are in the same position regarding the knowledge of C-facts. The Ω-community’s point of view has no advantage in matters of C-facts knowledge over the solitary agent P’s point of view. The Ω-community arithmetic shows that if a solitary agent P had the suitable knowledge of C-facts about the practice of calculations with ‘⊕’, it would allow him/her to disagree with the not correct answers of other members of the community even when they would constitute an absolute majority. (shrink)

This collection of articles was written over the last 10 years and the most important and longest within the last year. Also I have edited them to bring them up to date (2016). The copyright page has the date of this first edition and new editions will be noted there as I edit old articles or add new ones. All the articles are about human behavior (as are all articles by anyone about anything), and so about the limitations of having (...) a recent monkey ancestry (8 million years or much less depending on viewpoint) and manifest words and deeds within the framework of our innate psychology as presented in the table of intentionality. As famous evolutionist Richard Leakey says, it is critical to keep in mind not that we evolved from apes, but that in every important way, we are apes. If everyone was given a real understanding of this (i.e., human ecology and psychology) in school, maybe civilization would have a chance. -/- In my view these articles and reviews have many novel and highly useful elements, in that they use my own version of the recently (ca. 1980’s) developed dual systems view of our brain and behavior to lay out a logical system of rationality (personality, psychology, mind, language, behavior, thought, reasoning, reality etc.) that is sorely lacking in the behavioral sciences (psychology, philosophy, literature, politics, anthropology, history, economics, sociology etc.). The philosophy centers around the two writers I have found the most important, Ludwig Wittgenstein and John Searle, whose ideas I combine and extend within the dual system (two systems of thought) framework that has proven so useful in recent thinking and reasoning research. As I note, there is in my view essentially complete overlap between philosophy, in the strict sense of the enduring questions that concern the academic discipline, and the descriptive psychology of higher order thought (behavior). Once one has grasped Wittgenstein’s insight that there is only the issue of how the language game is to be played, one determines the Conditions of Satisfaction (what makes a statement true or satisfied etc.) and that is the end of the discussion. -/- Now that I think I understand how the games work I have mostly lost interest in philosophy, which of course is how Wittgenstein said it should be. But since they are the result of our innate psychology, or as Wittgenstein put, it due to the lack of perspicuity of language, the problems run throughout all human discourse, so there is endless need for philosophical analysis, not only in the ‘human sciences’ of philosophy, sociology, anthropology, political science, psychology, history, literature, religion, etc., but in the ‘hard sciences’ of physics, mathematics, and biology. It is universal to mix the language game questions with the real scientific ones as to what the empirical facts are. Scientism is ever present and the master has laid it before us long ago, i.e., Wittgenstein (hereafter W) beginning principally with the Blue and Brown Books in the early 1930’s. -/- "Philosophers constantly see the method of science before their eyes and are irresistibly tempted to ask and answer questions in the way science does. This tendency is the real source of metaphysics and leads the philosopher into complete darkness." (BBB p18) -/- Nevertheless, a real understanding of Wittgenstein’s work, and hence of how our psychology functions, is only beginning to spread in the second decade of the 21st century, due especially to P.M.S. Hacker (hereafter H) and Daniele Moyal-Sharrock (hereafter DMS),but also to many others, some of the more prominent of whom I mention in the articles. -/- When I read ‘On Certainty’ a few years ago I characterized it in an Amazon review as the Foundation Stone of Philosophy and Psychology and the most basic document for understanding behavior, and about the same time DMS was writing articles noting that it had solved the millennia old epistemological problem of how we can know anything for certain. I realized that W was the first one to grasp what is now characterized as the two systems or dual systems of thought, and I generated a dual systems (S1 and S2) terminology which I found to be very powerful in describing behavior. I took the small table that John Searle (hereafter S) had been using, expanded it greatly, and found later that it integrated perfectly with the framework being used by various current workers in thinking and reasoning research. -/- Since they were published individually, I have tried to make the book reviews and articles stand by themselves, insofar as possible, and this accounts for the repetition of various sections, notably the table and its explanation. I start with a short article that presents the table of intentionality and briefly describes its terminology and background. Next, is by far the longest article, which attempts a survey of the work of W and S as it relates to the table and so to an understanding or description (not explanation as W insisted) of behavior. -/- The key to everything about us is biology, and it is obliviousness to it that leads millions of smart educated people like Obama, Chomsky, Clinton and the Pope to espouse suicidal utopian ideals that inexorably lead straight to Hell On Earth. As W noted, it is what is always before our eyes that is the hardest to see. We live in the world of conscious deliberative linguistic System 2, but it is unconscious, automatic reflexive System 1 that rules. This is Searle’s The Phenomenological Illusion (TPI), Pinker’s Blank Slate and Tooby and Cosmides Standard Social Science Model. Democracy and equality are wonderful ideals, but without strict controls, selfishness and stupidity gain the upper hand and soon destroy any nation and any world that adopts them. The monkey mind steeply discounts the future, and so we sell our children’s heritage for temporary comforts. -/- The astute may wonder why we cannot see System 1 at work, but it is clearly counterproductive for an animal to be thinking about or second guessing every action, and in any case there is no time for the slow, massively integrated System 2 to be involved in the constant stream of split second ‘decisions’ we must make. As W noted, our ‘thoughts’ (T1 or the thoughts of System 1) must lead directly to actions. It is my contention that the table of intentionality (rationality, mind, thought, language, personality etc.) that features prominently here describes more or less accurately, or at least serves an heuristic for how we think and behave, and so it encompasses not merely philosophy and psychology but everything else (history, literature, mathematics, politics etc.). Note especially that intentionality and rationality as I (along with Searle, Wittgenstein and others) view it,includes both conscious deliberative System 2 and unconscious automated System 1 actions or reflexes. -/- Thus all the articles, like all behavior, are intimately connected if one knows how to look at them. As I note, The Phenomenological Illusion (oblivion to our automated System 1) is universal and extends not merely throughout philosophy but throughout life. I am sure that Chomsky, Obama, Zuckerberg and the Pope would be incredulous if told that they suffer from the same problem as Hegel, Husserl and Heidegger, but it’s clearly true. While the phenomenologists only wasted a lot of people’s time, they are wasting the earth. -/- My writings are available in updated versions as paperbacks and Kindles on Amazon. -/- Talking Monkeys: Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet - Articles and Reviews 2006-2017 (2017) ASIN B071HVC7YP. -/- The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle--Articles and Reviews 2006-2016 (2017) ASIN B071P1RP1B. -/- Suicidal Utopian Delusions in the 21st century: Philosophy, Human Nature and the Collapse of Civilization - Articles and Reviews 2006-2017 (2017) 2nd printing with corrections (Feb 2018) ASIN B0711R5LGX -/- Suicide by Democracy: an Obituary for America and the World (2018) ASIN B07CQVWV9C . (shrink)

In August 2002, three Indian computer scientists published a paper, ‘PRIMES is in P’, online. It presents a ‘deterministic algorithm’ which determines in ‘polynomial time’ if a given number is a prime number. The story was quickly picked up by the general press, and by this means spread through the scientific community of complexity theorists, where it was hailed as a major theoretical breakthrough. This is although scientists regarded the media reports as vulgar popularizations. When the paper was published in (...) a peer-reviewed journal only two years later, the three scientists had already received wide recognition for their accomplishment. Current sociological theory challenges the ability to clearly distinguish on independent epistemic grounds between distorted and non-distorted scientific knowledge. It views the demarcation lines between such forms of presentation as contextual and unstable. In my paper, I challenge this view. By systematically surveying the popular press coverage of the ‘PRIMES is in P’ affair, I argue--against the prevailing new orthodoxy--that distorted simplifications of scientific knowledge are distinguishable from non-distorted simplifications on independent epistemic grounds. I argue that in the ‘PRIMES is in P’ affair, the three scientists could ride on the wave of the general press-distorted coverage of their algorithm, while counting on their colleagues’ ability to distinguish genuine accounts from distorted ones. Thus, their scientific reputation was unharmed. This suggests that the possibility of the existence of independent epistemic standards must be incorporated into the new SSK model of popularization. (shrink)

This collection of articles was written over the last 10 years and the most important and longest within the last year. Also I have edited them to bring them up to date (2016). All the articles are about human behavior (as are all articles by anyone about anything), and so about the limitations of having a recent monkey ancestry (8 million years or much less depending on viewpoint) and manifest words and deeds within the framework of our innate psychology as (...) presented in the table of intentionality. As famous evolutionist Richard Leakey says, it is critical to keep in mind not that we evolved from apes, but that in every important way, we are apes. If everyone was given a real understanding of this (i.e., human ecology and psychology) in school, maybe civilization would have a chance. In my view these articles and reviews have many novel and highly useful elements, in that they use my own version of the recently (ca. 1980’s) developed dual systems view of our brain and behavior to lay out a logical system of rationality (personality, psychology, mind, language, behavior, thought, reasoning, reality etc.) that is sorely lacking in the behavioral sciences (psychology, philosophy, literature, politics, anthropology, history, economics, sociology etc.). (shrink)

In my view all behavior is an expression of our evolved psychology and so intimately connected to religion, morals and ethics, if one knows how to look at them. -/- Many will find it strange that I spend little time discussing the topics common to most discussions of religion, but in my view it is essential to first understand the generalities of behavior and this necessitates a good understanding of biology and psychology which are mostly noticeable by their absence in (...) works on religion, politics, history, morals and ethics, etc. In my view most such efforts have no grasp at all of the operation of System 2, the slow cortical functions of the brain which can be equated to linguistic behavior or the mind, and which I call the Descriptive Psychology of Higher Order Thought and which I regard as the province of philosophy in the narrow sense. -/- It is my contention that the table of intentionality (rationality, mind, thought, language, personality etc.) that features prominently here describes more or less accurately, or at least serves as an heuristic for, how we think and behave, and so it encompasses not merely philosophy and psychology, but everything else (religion, history, literature, mathematics, politics etc.). Note especially that intentionality and rationality as I (along with Searle, Wittgenstein and others) view it, includes both conscious deliberative System 2 and unconscious automated System 1 actions or reflexes. -/- This collection of articles was written over the last 10 years and revised to bring them up to date (2019). All the articles are about human behavior (as are all articles by anyone about anything), and so about the limitations of having a recent monkey ancestry (8 million years or much less depending on viewpoint) and manifest words and deeds within the framework of our innate psychology as presented in the table of intentionality. As famous evolutionist Richard Leakey says, it is critical to keep in mind not that we evolved from apes, but that in every important way, we are apes. If everyone was given a real understanding of this (i.e., of human ecology and psychology to actually give them some control over themselves), maybe civilization would have a chance. As things are however the leaders of society have no more grasp of things than their constituents and so collapse into anarchy is inevitable is spite of the near universal views that religion, politics or technology can save us. See my Suicidal Utopian Delusions in the 21st Century 5th ed (2019), for a detailed exposition of this view. -/- It is critical to understand why we behave as we do and so I start with a brief review of the logical structure of rationality, which provides some heuristics for the description of language (mind, rationality, personality) and gives some suggestions as to how this relates to the evolution of social behavior. This centers around the two writers I have found the most important in this regard, Ludwig Wittgenstein and John Searle, whose ideas I combine and extend within the dual system (two systems of thought) framework that has proven so useful in recent thinking and reasoning research. As I note, there is in my view essentially complete overlap between philosophy, in the strict sense of the enduring questions that concern the academic discipline, and the descriptive psychology of higher order thought (behavior). Once one has grasped Wittgenstein’s insight that there is only the issue of how the language game is to be played, one determines the Conditions of Satisfaction (what makes a statement true or satisfied etc.) and that is the end of the discussion. No neurophysiology, no metaphysics, no postmodernism, no theology. -/- Along with many, I see it as the basic religious or moral issue of our times that America and the world are in the process of collapse from excessive population growth, most of it for the last century, and now all of it, due to 3rd world people. Consumption of resources and the addition of 3 billion more ca. 2100 will collapse industrial civilization and bring about starvation, disease, violence and war on a staggering scale. The earth loses at least 1% of its topsoil every year, so as it nears 2100, most of its food growing capacity will be gone. Billions will die and nuclear war is all but certain. In America, this is being hugely accelerated by massive immigration and immigrant reproduction, combined with abuses made possible by democracy. Depraved human nature inexorably turns the dream of democracy and diversity into a nightmare of crime and poverty. China will continue to overwhelm America and the world, as long as it maintains the dictatorship which limits selfishness and permits long term planning. The root cause of collapse is the inability of our innate psychology to adapt to the modern world, which leads people to treat unrelated persons as though they had common interests (which I suggest may be regarded as an unrecognized -- but the commonest and most serious-- psychological problem -- Inclusive Fitness Disorder). This, plus ignorance of basic biology and psychology, leads to the social engineering delusions of the partially educated who control democratic societies. Few understand that if you help one person you harm someone else—there is no free lunch and every single item anyone consumes destroys the earth beyond repair. Consequently, social policies everywhere are unsustainable and one by one all societies without stringent controls on selfishness will collapse into anarchy or dictatorship. Without dramatic and immediate changes, there is no hope for preventing the collapse of America, or any country that follows a democratic system, especially now that the Neomarxist Third World Supremacists are taking control of the USA and other Western Democracies, and helping the Seven Sociopaths who run China to succeed in their plan to eliminate peace and freedom and religion worldwide. Hence my concluding essays. Of course, it is an easily defensible point of view that Artificial Intelligence (aka Artificial Stupidity or Artificial Sociopathy) researchers are even more evil than the Democrats and the CCP, and I make brief comments on this as well. -/- Several articles touch on The One Big Happy Family Delusion, i.e., that we are genetically selected for cooperation with everyone, and that the euphonious ideals of Democracy, Diversity, Equality and Religion will lead us into utopia, if we just manage things correctly (the possibility of politics). Again, the No Free Lunch Principle ought to warn us it cannot be true, and we see throughout history and all over the contemporary world, that without strict controls, selfishness and stupidity gain the upper hand and soon destroy any nation that embraces these delusions. In addition, the monkey mind steeply discounts the future, and so we cooperate in selling our descendant’s heritage for temporary comforts, greatly exacerbating the problems. -/- I describe versions of this delusion (i.e., that we are basically ‘friendly’ if just given a chance) as it appears in some recent books on sociology/biology/economics. Even Sapolsky’s otherwise excellent “Behave” (2017) embraces leftist politics and group selection and gives space to a discussion of whether humans are innately violent. I end with two essays on the great tragedy playing out in America and the world, which can be seen as a direct result of our evolved psychology manifested as the inexorable machinations of System 1. Our psychology, eminently adaptive and eugenic on the plains of Africa from ca. 6 million years ago, when we split from chimpanzees, to ca. 50,000 years ago, when many of our ancestors left Africa (i.e., in the EEA or Environment of Evolutionary Adaptation), is now maladaptive and dysgenic and the source of our Suicidal Utopian Delusions. So, like all discussions of behavior (theology, philosophy, psychology, sociology, biology, anthropology, politics, law, literature, history, economics, soccer strategies, business meetings, etc.), this book is about evolutionary strategies, selfish genes and inclusive fitness (kin selection, natural selection), though of course few grasp this, regardless of whether they are academics or peasants, atheists or fundamentalists. (shrink)

This is a review of The Turing Guide (2017), written by Jack Copeland, Jonathan Bowen, Mark Sprevak, Robin Wilson, and others. The review includes a new sociological approach to the problem of computability in physics.

The 20th Century is the starting point for the most ambitious attempts to extrapolate human life into artificial systems. Norbert Wiener’s Cybernetics, Claude Shannon’s Information Theory, John von Neumann’s Cellular Automata, Universal Constructor to the Turing Test, Artificial Intelligence to Maturana and Varela’s Autopoietic Organization, all shared the goal of understanding in what sense humans resemble a machine. This scientific and technological movement has embraced all disciplines without exceptions, not only mathematics and physics but also biology, sociology, psychology, (...) economics etc. New terms were developed, such as “information”, “organization”, “entropy”, “communication”, “encryption”, “computation” and “algorithmics” to mention a few, all which had an enormous impact on artificial systems. Our work follows this historical track but with a reversed order of priorities. Instead of deducing a reduced group of human acts into an artificial environment, we deduce the human aspects of machines by extrapolating algorithmic methodologies into everyday life acts. The present informational theories were insufficiently powered to achieve this objective without developing a new theoretical approach. Hence, our research is directed towards an expansion of the current informational theories. (shrink)

ABSTRACT This article distinguishes nine senses of polarization and provides formal measures for each one to refine the methodology used to describe polarization in distributions of attitudes. Each distinct concept is explained through a definition, formal measures, examples, and references. We then apply these measures to GSS data regarding political views, opinions on abortion, and religiosity—topics described as revealing social polarization. Previous breakdowns of polarization include domain-specific assumptions and focus on a subset of the distribution’s features. This has conflated multiple, (...) independent features of attitude distributions. The current work aims to extract the distinct senses of polarization and demonstrate that by becoming clearer on these distinctions we can better focus our efforts on substantive issues in social phenomena. (shrink)

Focusing on the history of prehistoric archaeology in the 20th century, this papers shows (1) that statistical multidimensional analyses were carried out by a new kind of actors who challenged the previous common language shared by prehistorians. This fundamental change was important, considering that (2) language is a fundamental point for the epistemology of archaeology. However, a comparison of multidimensional analyses applications over time shall make clear that (3) the differences are mostly a generational matter: the transmission processes between them (...) will be addressed. (shrink)

Language suggestive of natural law ethics, similar to the Catholic understanding of ethical foundations, is prevalent in a number of disciplines. But it does not always issue in a full-blooded commitment to objective ethics, being undermined by relativist ethical currents. In law and politics, there is a robust conception of "human rights", but it has become somewhat detached from both the worth of persons in themselves and from duties. In education, talk of "values" imports ethical considerations but hints at a (...) subjectivist view of them. In the psychology and sociology of drug use, ethically thin concepts of "harm minimisation" and "selfimage" dominate discussion and distract attention from the virtue of temperance and the training of character. A more forceful assertion of an ethics based on the worth of persons in these cases would be most desirable. Arguments against objectivity in the fundamentals may be replied to by examining the parallel between ethics and the discipline whose objectivity has been least challenged by relativist arguments, mathematics. (shrink)

This article focuses on two developments in nineteenth-century (philosophy of) social science: Moritz Lazarus’s and Heymann Steinthal’s Völkerpsychologie and Georg Simmel’s early sociology of knowledge. The article defends the following theses. First, Lazarus and Steinthal wavered between a “strong” and a “weak” program for Völkerpsychologie. Ingredients for the strong program included methodological neutrality and symmetry; causal explanation of beliefs based on causal laws; a focus on groups, interests, tradition, culture, or materiality; determinism; and a self-referential model of social institutions. (...) Second, elements of the weak program were the blurring of explanatory and normative interests, an emphasis on freedom of the will, and antirelativism and antimaterialism. Third, later research projects keeping the label “Völkerpsychologie” followed the weak program. Fourth, in the 1880s and 1890s, Simmel tried to build on some of the elements of the strong program. Finally, and fifth, part of the explanation for why Simmel did not succeed in his attempt had to do with the social-political situation of German academia around 1900. (shrink)

Analytical philosophy defines mathematics as an extension of logic. This research will restructure the progress in mathematical philosophy made by analytical thinkers like Wittgenstein, Russell, and Frege. We are setting up a new theory of mathematics and arithmetic’s familiar to Wittgenstein’s philosophy of language. The analytical theory proposed here proves that mathematics can be defined with non-logical terms, like numbers, theorems, and operators. We’ll explain the role of the arithmetical operators and geometrical theorems to be foundational in (...) mathematics. Our position states that mathematical operators and theorems are tautologies. Here numbers are arbitrary signs of magnitudes whose meaning is arbitrated by the mathematical operator. We will prove that set theory in mathematics doesn’t form a branch of logic and operators arbitrarily form sets into units. Herein are the foundations of numbers. (shrink)

This collection of articles was written over the last 10 years and edited them to bring them up to date (2017). All the articles are about human behavior (as are all articles by anyone about anything), and so about the limitations of having a recent monkey ancestry (8 million years or much less depending on viewpoint) and manifest words and deeds within the framework of our innate psychology as presented in the table of intentionality. As famous evolutionist Richard Leakey says, (...) it is critical to keep in mind not that we evolved from apes, but that in every important way, we are apes. If everyone was given a real understanding of this (i.e., of human ecology and psychology to actually give them some control over themselves), maybe civilization would have a chance. As things are however the leaders of society have no more grasp of things than their constituents and so collapse into anarchy is inevitable. -/- It is critical to understand why we behave as we do and so the first section presents articles that try to describe (not explain as Wittgenstein insisted) behavior. Section one starts with a brief review of the logical structure of rationality which provides some heuristics for the description of language (mind) and gives some suggestions as to how this relates to the evolution of social behavior. This centers around the two writers I have found the most important in this regard, Ludwig Wittgenstein and John Searle, whose ideas I combine and extend within the dual system (two systems of thought) framework that has proven so useful in recent thinking and reasoning research. As I note, there is in my view essentially complete overlap between philosophy, in the strict sense of the enduring questions that concern the academic discipline, and the descriptive psychology of higher order thought (behavior). Once one has grasped Wittgenstein’s insight that there is only the issue of how the language game is to be played, one determines the Conditions of Satisfaction (what makes a statement true or satisfied etc.) and that is the end of the discussion. -/- Since philosophical problems are the result of our innate psychology, or as Wittgenstein put it, due to the lack of perspicuity of language, they run throughout human discourse, so there is endless need for philosophical analysis, not only in the ‘human sciences’ of philosophy, sociology, anthropology, political science, psychology, history, literature, religion, etc., but in the ‘hard sciences’ of physics, mathematics, and biology. It is universal to mix the language game questions with the real scientific ones as to what the empirical facts are. Scientism is ever present and the master has laid it before us long ago, i.e., Wittgenstein (hereafter W) beginning with the Blue and Brown Books in the early 1930’s. -/- "Philosophers constantly see the method of science before their eyes and are irresistibly tempted to ask and answer questions in the way science does. This tendency is the real source of metaphysics and leads the philosopher into complete darkness." (BBB p18) -/- The key to everything about us is biology, and it is obliviousness to it that leads millions of smart educated people like Obama, Chomsky, Clinton and the Pope to espouse suicidal utopian ideals that inexorably lead straight to Hell On Earth. As W noted, it is what is always before our eyes that is the hardest to see. We live in the world of conscious deliberative linguistic System 2, but it is unconscious, automatic reflexive System 1 that rules. This is the source of the universal blindness described by Searle’s The Phenomenological Illusion (TPI), Pinker’s Blank Slate and Tooby and Cosmides’ Standard Social Science Model. -/- The astute may wonder why we cannot see System 1 at work, but it is clearly counterproductive for an animal to be thinking about or second guessing every action, and in any case there is no time for the slow, massively integrated System 2 to be involved in the constant stream of split second ‘decisions’ we must make. As W noted, our ‘thoughts’ (T1 or the ‘thoughts’ of System 1) must lead directly to actions. -/- It is my contention that the table of intentionality (rationality, mind, thought, language, personality etc.) that features prominently here describes more or less accurately, or at least serves as an heuristic for, how we think and behave, and so it encompasses not merely philosophy and psychology, but everything else (history, literature, mathematics, politics etc.). Note especially that intentionality and rationality as I (along with Searle, Wittgenstein and others) view it, includes both conscious deliberative System 2 and unconscious automated System 1 actions or reflexes. -/- Thus all the articles, like all behavior, are intimately connected if one knows how to look at them. As I note, The Phenomenological Illusion (oblivion to our automated System 1) is universal and extends not merely throughout philosophy but throughout life. I am sure that Chomsky, Obama, Zuckerberg and the Pope would be incredulous if told that they suffer from the same problem as Hegel, Husserl and Heidegger, (or that that they differ only in degree from drug and sex addicts in being motivated by stimulation of their frontal cortices by the delivery of dopamine via the ventral tegmentum and the nucleus accumbens) but it’s clearly true. While the phenomenologists only wasted a lot of people’s time, they are wasting the earth and their descendant’s future. Section one continues with other views of behavior which my reviews attempt to correct and put in context with minimal theory. -/- The next section describes the digital delusions which confuse the language games of System 2 with the automatisms of System one, and so cannot distinguish biological machines (i.e., people) from other kinds of machines (i.e., computers). The ‘reductionist’ claim is that one can ‘explain’ behavior at a ‘lower’ level, but what actually happens is that one does not explain human behavior but a ‘stand in’ for it. Hence the title of Searle’s classic review of Dennett’s book (“Consciousness Explained”)— “Consciousness Explained Away”. In most contexts ‘reduction’ of higher level emergent behavior to brain functions, biochemistry, or physics is incoherent. Even for chemistry or physics the path is blocked by chaos and uncertainty. Anything can be ‘represented’ by equations, but when they ‘represent’ higher order behavior, it is not clear what the ‘results’ mean. Reductionist metaphysics is a joke but most scientists and philosophers lack the appropriate sense of humor. -/- Another hi-tech delusion is that the we will be saved from the pure evil (selfishness) of System 1 by computers/AI/robotics/ nanotech/genetic engineering created by System 2. The No Free Lunch principal tells us there will be serious and possibly fatal consequences. The adventurous may regard this principle as a higher order emergent expression of the Second Law of Thermodynamics. -/- The last section describes The One Big Happy Family Delusion , i.e., that we are selected for cooperation with everyone and that the euphonious ideals of Democracy, Diversity and Equality will lead us into utopia. Again the No Free Lunch Principle ought to warn us it cannot be true, and we see throughout history and all over the contemporary world, that without strict controls, selfishness and stupidity gain the upper hand and soon destroy any nation that embraces it. In addition, the monkey mind steeply discounts the future, and so we sell our descendant’s heritage for temporary comforts greatly exacerbating the problems. -/- I describe versions of this delusion (i.e., that we are basically ‘friendly’ if just given a chance) as it appears in some recent books on sociology/biology/economics. I end with an essay on the great tragedy playing out in America and the world, which can be seen as a direct result of our evolved psychology manifested as the inexorable machinations of System 1. Our evolved psychology, eminently adaptive and eugenic on the plains of Africa ca. 50,000 years ago, when many of our ancestors left Africa, to ca. 6 million years ago, when we split from chimpanzees (i.e., in the EEA or Environment of Evolutionary Adaptation), but now maladaptive and dysgenic and the source of our Suicidal Utopian Delusions. So, like all discussions of behavior, this book is about evolutionary strategies, selfish genes and inclusive fitness. (shrink)

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts (...) of the physical world and are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge. (shrink)

Dans 'Godel’s Way', trois éminents scientifiques discutent de questions telles que l’indécidabilité, l’incomplétude, le hasard, la calculabilité et la paraconsistence. J’aborde ces questions du point de vue de Wittgensteinian selon lesquelles il y a deux questions fondamentales qui ont des solutions complètement différentes. Il y a les questions scientifiques ou empiriques, qui sont des faits sur le monde qui doivent être étudiés de manière observationnelle et philosophique quant à la façon dont le langage peut être utilisé intelligiblement (qui incluent certaines (...) questions en mathématiques et en logique), qui doivent être décidés en regardant un comment nous utilisons réellement des mots dans des contextes particuliers. Lorsque nous obtenons clair sur le jeu de langue que nous jouons, ces sujets sont considérés comme des questions scientifiques et mathématiques ordinaires comme les autres. Les idées de Wittgenstein ont rarement été égalées et jamais dépassées et sont aussi pertinentes aujourd’hui qu’elles l’étaient il y a 80 ans lorsqu’il a dicté les Livres Bleus et Brown. Malgré ses défauts, vraiment une série de notes plutôt qu’un livre fini, c’est une source unique du travail de ces trois savants célèbres qui travaillent aux confins de la physique, des mathématiques et de la philosophie depuis plus d’un demi-siècle. Da Costa et Doria sont cités par Wolpert (voir ci-dessous ou mes articles sur Wolpert et mon examen de Yanofsky 'The Outer Limits of Reason') depuis qu’ils ont écrit sur le calcul universel, et parmi ses nombreuses réalisations, Da Costa est un pionnier dans la paraconsistence. -/- Ceux qui souhaitent un cadre complet à jour pour le comportement humain de la vue moderne de deux système peuvent consulter mon livre 'The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle' 2nd ed (2019). Ceux qui s’intéressent à plus de mes écrits peuvent voir «Talking Monkeys --Philosophie, Psychologie, Science, Religion et Politique sur une planète condamnée --Articles et revues 2006-2019 » 3e ed (2019) et Suicidal Utopian Delusions in the 21st Century 4th ed (2019) et autres. (shrink)

Author's response to: Raphael Sassower, 'Heidegger and the Sociologists: A Forced Marriage?,' Social Epistemology Review and Reply Collective 7, no. 5 (2018): 30-32. -- Part of a book-review symposium on: Jeff Kochan (2017), Science as Social Existence: Heidegger and the Sociology of Scientific Knowledge (Cambridge UK: Open Book Publishers).

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the (...) mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of “geometric judgments” from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) “space” should be revisited for the purposes of life sciences. (shrink)

According to Steiner (1998), in contemporary physics new important discoveries are often obtained by means of strategies which rely on purely formal mathematical considerations. In such discoveries, mathematics seems to have a peculiar and controversial role, which apparently cannot be accounted for by means of standard methodological criteria. M. Gell-Mann and Y. Ne׳eman׳s prediction of the Ω− particle is usually considered a typical example of application of this kind of strategy. According to Bangu (2008), this prediction is apparently based (...) on the employment of a highly controversial principle—what he calls the “reification principle”. Bangu himself takes this principle to be methodologically unjustifiable, but still indispensable to make the prediction logically sound. In the present paper I will offer a new reconstruction of the reasoning that led to this prediction. By means of this reconstruction, I will show that we do not need to postulate any “reificatory” role of mathematics in contemporary physics and I will contextually clarify the representative and heuristic role of mathematics in science. (shrink)

Value dimensions of mature theory change in science are considered. It is argued that the interaction of the values of the cross-theories constitutes the major mechanism of theory change in this dimension. Examples from history of science describing the details of the mechanism are given.

This essay offers a strategic reinterpretation of Kant’s philosophy of mathematics in Critique of Pure Reason via a broad, empirically based reconception of Kant’s conception of drawing. It begins with a general overview of Kant’s philosophy of mathematics, observing how he differentiates mathematics in the Critique from both the dynamical and the philosophical. Second, it examines how a recent wave of critical analyses of Kant’s constructivism takes up these issues, largely inspired by Hintikka’s unorthodox conception of Kantian (...) intuition. Third, it offers further analyses of three Kantian concepts vitally linked to that of drawing. It concludes with an etymologically based exploration of the seven clusters of meanings of the word drawing to gesture toward new possibilities for interpreting a Kantian philosophy of mathematics. (shrink)

The city of Kruja (Albania)contains three types of dwellings that date back to different periods of time: the historic ones, the socialist ones, the modern ones. This paper has to deal only with the historic building's typology. The questionnaire that is applied will be considered for the development of mathematical regression based on specific data for this category. Variation between the relevant variables of the questionnaire is fairly or inverse-linked with a certain percentage of influence. The aim of this study (...) is to have better insights into the important role of building occupancy, people's lifestyle, economic level, and the quality of life of the residents in the inner medieval citadel, the physics characteristics, and the energy efficiency of the historical dwellings. The variables such as the number of residents, quality of life, the surface of the dwellings, heating instruments and time spent in the dwelling, current living conditions, monthly bills, level of satisfaction, restoration, and building improvements, interact with each other with probabilities with different positive or negative percentages. (shrink)

What is the ontological status of mathematical structures? Michael Resnic, Stewart Shapiro and Gianluigi Oliveri, are contemporaries of American philosophers on mathematics, they give Platonic answers on this question.

Throughout his work, John Dewey seeks to emancipate philosophical reflection from the influence of the classical tradition he traces back to Plato and Aristotle. For Dewey, this tradition rests upon a conception of knowledge based on the separation between theory and practice, which is incompatible with the structure of scientific inquiry. Philosophical work can make progress only if it is freed from its traditional heritage, i.e. only if it undergoes reconstruction. In this study I show that implicit appeals to the (...) classical tradition shape prominent debates in philosophy of mathematics, and I initiate a project of reconstruction within this field. (shrink)

It is undeniable Poincaré was a very famous and influential scientist. So, possibly because of it, it was relatively easy for him to participate in the heated discussions of the foundations of mathematics in the early 20th century. We can say it was “easy” because he didn't get involved in this subject by writing great treatises, or entire books about his own philosophy of mathematics (as other authors from the same period did). Poincaré contributed to the philosophy of (...) mathematics by writing short essays and letters. (shrink)

In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all mathematics, (...) at least according to some speculative research programs. (shrink)

I claim that a relatively new position in philosophy of mathematics, pluralism, overlaps in striking ways with the much older Jain doctrine of anekantavada and the associated doctrines of nyayavada and syadvada. I first outline the pluralist position, following this with a sketch of the Jain doctrine of anekantavada. I then note the srrong points of overlaps and the morals of this comparison of pluralism and anekantavada.

In this paper, I present and discuss critically the main elements of Mario Bunge’s philosophy of mathematics. In particular, I explore how mathematical knowledge is accounted for in Bunge’s systemic emergent materialism.

Until recently, discussion of virtues in the philosophy of mathematics has been fleeting and fragmentary at best. But in the last few years this has begun to change. As virtue theory has grown ever more influential, not just in ethics where virtues may seem most at home, but particularly in epistemology and the philosophy of science, some philosophers have sought to push virtues out into unexpected areas, including mathematics and its philosophy. But there are some mathematicians already there, (...) ready to meet them, who have explicitly invoked virtues in discussing what is necessary for a mathematician to succeed. In both ethics and epistemology, virtue theory tends to emphasize character virtues, the acquired excellences of people. But people are not the only sort of thing whose excellences may be identified as virtues. Theoretical virtues have attracted attention in the philosophy of science as components of an account of theory choice. Within the philosophy of mathematics, and mathematics itself, attention to virtues has emerged from a variety of disparate sources. Theoretical virtues have been put forward both to analyse the practice of proof and to justify axioms; intellectual virtues have found multiple applications in the epistemology of mathematics; and ethical virtues have been offered as a basis for understanding the social utility of mathematical practice. Indeed, some authors have advocated virtue epistemology as the correct epistemology for mathematics (and perhaps even as the basis for progress in the metaphysics of mathematics). This topical collection brings together several of the researchers who have begun to study mathematical practices from a virtue perspective with the intention of consolidating and encouraging this trend. (shrink)

Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show (...) that diagrams form genuine notational systems, and I argue that this explains why they can play a role in the inferential structure of proofs without undermining their reliability. I then consider whether diagrams can be essential to the proofs in which they appear. (shrink)

This study delved into the perceptions of Mathematics’ student teachers regarding the implementation of gamification in secondary schools at Nasugbu, Batangas. This research investigates the rising global trend of implementing gamification in education, particularly in Mathematics teaching, to address contemporary learner needs by examining student teachers' use of gamified activities, their design factors, encountered challenges, and perceived benefits. Purposive sampling was utilized in a multiple-case study approach to select ten (10) secondary school Mathematics’ student teachers engaged in (...) practice teaching in Nasugbu, Batangas. Qualitative findings revealed common gamified activities employed by student teachers, emphasizing the importance of student-centered design, alignment with learning objectives, student engagement, assessment, and adaptation to the classroom context. Challenges faced by student teachers in integrating gamification included technical limitations, sustaining engagement, time management, and addressing diverse learning styles. Despite these challenges, integrating gamification showed benefits such as increased engagement, improved learning outcomes, reduced math anxiety, and enhanced attitudes towards Mathematics. In conclusion, gamified activities play a significant role in enhancing student engagement and learning outcomes in Mathematics classrooms. The findings suggest student teachers to explore and integrate gamified activities into Mathematics lessons to create engaging environments supporting student success. (shrink)

Mathematical objects are divided into (1) those which are autonomous, i.e., not dependent for their existence upon mathematicians’ conscious acts, and (2) intentional objects, which are so dependent. Platonist philosophy of mathematics argues that all objects belong to group (1), Brouwer’s intuitionism argues that all belong to group (2). Here we attempt to develop a dualist ontology of mathematics (implicit in the work of, e.g., Hilbert), exploiting the theories of Meinong, Husserl and Ingarden on the relations between autonomous (...) and intentional objects. In particular we develop a phenomenology of mathematical works, which has the stratified intentional structure discovered by Ingarden in his study of the literary work. (shrink)

Mathematics is everywhere and yet its objects are nowhere. There may be five apples on the table but the number five itself is not to be found in, on, beside or anywhere near the apples. So if not in space and time, where are numbers and other mathematical objects such as perfect circles and functions? And how do we humans discover facts about them, be it Pythagoras’ Theorem or Fermat’s Last Theorem? The metaphysical question of what numbers are and (...) the epistemological question of how we know about them are central to the philosophy of mathematics. These and related philosophical questions are of particular interest because of mathematics’ unusual status. Mathematics is exceptional in that, on the one hand, it appears unhesitatingly true—no one doubts that 2 + 3 = 5—but on the other, as just noted, it is not about the physical world. This ambivalent status is what gives the philosophy of mathematics its special interest. The philosophy of mathematics is also one of the oldest academic fields, more or less coeval with philosophy itself. But contemporary philosophy of mathematics is rather different from its pre-twentieth-century antecedents, largely for three reasons. The first is that since the seventeenth century, mathematics has become integral to science. Science has over the past few centuries become increasingly mathematical, and indeed the fundamental science of nature, physics, is today recognised as a branch of applied mathematics. The second is that mathematics underwent a transformation in the course of nineteenth century: having started the century as a rather traditional-looking science of quantity it emerged a hundred years later a radically transformed abstract theory of structure. The final factor in the transformation of the philosophy of mathematics is the rise of modern logic. Developed by Frege, Cantor and others in the late nineteenth century, modern logic pervades contemporary mathematics, philosophy and computer science, and has had an immeasurable effect on the philosophy of mathematics. These volumes will collect the major works in this major field, with a focus on the last few decades. The anthology will include technical work, which interprets philosophically significant mathematical results or subfields of mathematics, as well as purely philosophical writing, aimed at those without advanced mathematics. The collection should be of interest to both philosophers and mathematicians, as well as to anyone who is susceptible to wondering what the main intellectual tool used in science, economics and finance, and indeed everyday life is ultimately about. (shrink)

Fefermans argument is indeed convincing in a certain context, it can be dissolved entirely by modifying the context appropriately.