We attribute three major insights to Hegel: first, an understanding of the real numbers as the paradigmatic kind of number ; second, a recognition that a quantitative relation has three elements, which is embedded in his conception of measure; and third, a recognition of the phenomenon of divergence of measures such as in second-order or continuous phase transitions in which correlation length diverges. For ease of exposition, we will refer to these three insights as the R First Theory, Tripartite Relations, (...) and Divergence of Measures. Given the constraints of space, we emphasize the first and the third in this paper. (shrink)

A work on the philosophy of mathematics (2017) -/- ‘Number’, such a simple idea, and yet it fascinated and absorbed the greatest proportion of human geniuses over centuries, not to mention the likes of Pythagoras, Euclid, Newton, Leibniz, Descartes and countless maths giants like Euler, Gauss and Hilbert, etc.. Einstein thought of pure maths as the poetry of logical ideas, the exactitude of which, although independent of experience, strangely seems to benefit the study of the objects of reality. And, (...) interestingly as well as surprisingly we are nowhere near any clear understandings of numbers despite discoveries of many productive usages of numbers. This is - rightly or wrongly - a humble attempt to approach the subject from an angle hitherto unthought-of. (shrink)

In the paper “Math Anxiety,” Aden Evens explores the manner by means of which concepts are implicated in the problematic Idea according to the philosophy of Gilles Deleuze. The example that Evens draws from Difference and Repetition in order to demonstrate this relation is a mathematics problem, the elements of which are the differentials of the differential calculus. What I would like to offer in the present paper is an historical account of the mathematical problematic that Deleuze deploys (...) in his philosophy, and an introduction to the role that this problematic plays in the develop- ment of his philosophy of difference. One of the points of departure that I will take from the Evens paper is the theme of “power series.”2 This will involve a detailed elaboration of the mechanism by means of which power series operate in the differential calculus deployed by Deleuze in Difference and Repetition. Deleuze actually constructs an alternative history of mathematics that establishes an historical conti- nuity between the differential point of view of the infinitesimal calculus and modern theories of the differential calculus. It is in relation to the differential point of view of the infinitesimal calculus that Deleuze determines a differential logic which he deploys, in the form of a logic of different/ciation, in the development of his proj- ect of constructing a philosophy of difference. (shrink)

In a lot of domains in metaphysics the tacit assumption has been that whichever metaphysical principles turn out to be true, these will be necessarily true. Let us call necessitarianism about some domain the thesis that the right metaphysics of that domain is necessary. Necessitarianism has flourished. In the philosophy of maths we find it held that if mathematical objects exist, then they do of necessity. Mathematical Platonists affirm the necessary existence of mathematical objects (see for instance Hale and (...) Wright 1992 and 1994; Wright 1983 and 1988; Schiffer 1996; Resnik 1997; Shapiro 1997 and Zalta 1988) while mathematical nominalists, usually in the form of fictionalists, hold that necessarily such objects fail to exist (see for instance Balaguer 1996 and 1998; Rosen 2001 and Yablo 2005). In metaphysics more generally, until recently it was more or less assumed that whatever the right account of composition—the account of under what conditions some xs compose a y—that account will be necessarily true (for a discussion of theories of composition see Simons 1987 and van Inwagen 1987 and 1990; the modal status of the composition relation is explicitly addressed in Schaffer 2007; Parsons 2006 and Cameron 2007). Similarly, it has generally been assumed that whatever the right account is of the nature of properties, whether they be universals, tropes, or whether nominalism is true, that account will be necessarily true (though see Rosen 2006 for a recent suggestion to the contrary). In considering theories of persistence it has been widely held that whether objects endure or perdure through time is a matter of necessity (Sider 2001; though see Lewis 1999 p227 who defends contingent perdurantism). And with respect to theories of time it is frequently held that whichever of the A- or B-theory is true is necessarily true. A-theorists often argue that there is time in a world only if the A-theory is true at that world (see for instance McTaggart 1903; Markosian 2004; Bigelow 1996; Craig 2001) while B-theorists often argue that the A-theory is internally inconsistent (Smart 1987; Mellor 1998; Savitt 2000 and Le Poidevin 1991). Once again, we find a few recent contingentist dissenters. Bourne (2006) suggests that it is a contingent feature of time that it is tensed, and thus that the A-theory is contingently true. Worlds in which there exist only B-theoretic properties are worlds with time, it is just that time in those worlds time is radically different to the way it is actually. Other defenders of the B-theory, though not expressly contingentists, do offer arguments against versions of the A-theory that try to show that such A-theories theories are inconsistent with the actual laws of nature (see for instance Saunders 2002 and Callender 2000); these arguments, at least, leave room for the possibility that the A-theories in question are contingently false (at least on the assumption that the laws of nature are themselves contingent, an assumption that not everyone accepts). Despite some notable exceptions, necessitarianism has flourished in many, if not most, domains in metaphysics. One such exception is Lewis’ famous defence of Humean supervenience as a contingent claim about our world. Lewis does not argue that necessarily, the supervenience base for all matters of fact in a world is nothing but a vast mosaic of local matters of particular fact. Rather, he thinks that we have reason to think that our world is one in which Humean supervenience holds (see Lewis 1986 p9-10 and 1994). Another exception to the necessitarian orthodoxy is to be found in the lively debate about the modal status of the laws of nature. Here, if anything, contingentism has been the dominating force, with it generally being held that there are possible worlds in which different laws of nature hold (this view is defended by, among others, Lewis 1986 and 2010; Schaffer 2005 and Sidelle 2002). Necessitarian dissenters hold that the laws of nature are necessary, frequently because they think it is necessary that fundamental properties have the causal or nomic profiles they do (see for instance Shoemaker 1980 and 1988; Swoyer 1982; Bird 1995; Ellis and Lierse 1994). Nevertheless, when it comes to thinking about the nature of the laws themselves, the necessitarian presumption is back on firm footing. Though there is disagreement about whether the laws are generalisations that feature in the most virtuous true axiomatisation of all the particular matters of fact (often known as the Humean view of laws and defended by Ramsey 1978; Lewis 1986 and Beebee 2000) or whether laws are relations of necessity that hold between universals (a view defended by Armstrong 1983; Dretske 1977; Tooley 1977 and Carroll 1990) no one has seriously suggested that it might be a contingent matter which of these is the right account of laws. The necessitarian orthodoxy is not surprising since metaphysics is largely an a priori process. While a priori reasoning may be used to determine whether a proposition is necessary or contingent, it is not well placed (in the absence of a posteriori evidence) to determine whether a contingent proposition is actually true or false. Since metaphysicians aim to tell us which principles are true in which worlds, on the face of it the discovery that metaphysical principles are contingent seems to make part of the task of metaphysics epistemically intractable. In what follows I consider two reasons one might end up embracing contingentism and whether this would lead one into epistemic difficulty. The following section considers a route to contingent metaphysical truths that proceeds via a combination of conceptual necessities and empirical discoveries. Section 3 considers whether there might be synthetic contingent metaphysical truths, and the final section raises the question of whether if there were such truths we would be well placed to come to know them. (shrink)

Nietzsche has a surprisingly significant and strikingly positive assessment of mathematics. I discuss Nietzsche's theory of the origin of mathematical practice in the division of the continuum of force, his theory of numbers, his conception of the finite and the infinite, and the relations between Nietzschean mathematics and formalism and intuitionism. I talk about the relations between math, illusion, life, and the will to truth. I distinguish life and world affirming mathematical practice from its ascetic perversion. For Nietzsche, (...) class='Hi'>math is an artistic and moral activity that has an essential role to play in the joyful wisdom. (shrink)

Peer review is often taken to be the main form of quality control on academic research. Usually journals carry this out. However, parts of maths and physics appear to have a parallel, crowd-sourced model of peer review, where papers are posted on the arXiv to be publicly discussed. In this paper we argue that crowd-sourced peer review is likely to do better than journal-solicited peer review at sorting papers by quality. Our argument rests on two key claims. First, crowd-sourced peer (...) review will lead on average to more reviewers per paper than journal-solicited peer review. Second, due to the wisdom of the crowds, more reviewers will tend to make better judgments than fewer. We make the second claim precise by looking at the Condorcet Jury Theorem as well as two related jury theorems developed specifically to apply to peer review. (shrink)

Much has been written about the free energy principle (FEP), and much misunderstood. The principle has traditionally been put forth as a theory of brain function or biological self-organisation. Critiques of the framework have focused on its lack of empirical support and a failure to generate concrete, falsifiable predictions. I take both positive and negative evaluations of the FEP thus far to have been largely in error, and appeal to a robust literature on scientific modelling to rectify the situation. A (...) prominent account of scientific modelling distinguishes between model structure and model construal. I propose that the FEP be reserved to designate a model structure, to which philosophers and scientists add various construals, leading to a plethora of models based on the formal structure of the FEP. An entailment of this position is that demands placed on the FEP that it be falsifiable or that it conform to some degree of biological realism rest on a category error. To this end, I deliver first an account of the phenomenon of model transfer and the breakdown between model structure and model construal. In the second section, I offer an overview of the formal elements of the framework, tracing their history of model transfer and illustrating how the formalism comes apart from any interpretation thereof. Next, I evaluate existing comprehensive critical assessments of the FEP, and hypothesise as to potential sources of existing confusions in the literature. In the final section, I distinguish between what I hold to be the FEP—taken to be a modelling language or modelling framework—and what I term “FEP models.”. (shrink)

It’s sometimes suggested that we can (in a sense) settle the truth-value of some statements in the language of number theory by stipulation, adopting either φ or ¬φ as an additional axiom. For example, in Clarke-Doane (2020b) and a series of recent APA presentations, Clarke-Doane suggests that any Σ01 sound expansion of our current arithmetical practice would express a truth. In this paper, I’ll argue that (given a certain popular assumption about the model-theoretic representability of languages like ours) we can’t (...) know ourselves to have any such freedom. (shrink)

Sber Science Award 2023 winner in the “Digital Universe” category, full member of the Russian Academy of Sciences, Doctor of Physics and Mathematics, Head of the Chair of Computational Technology and Modeling of the Department of Computational Mathematics and Cybernetics of Moscow State University, Director of the Marchuk Institute for Computational Mathematics of the Russian Academy of Sciences Evgeny Evgenyevich Tyrtyshnikov dedicated his lecture entitled “Dimension: Is it a curse or a blessing?” to methods of presentation of multi-dimensional data based (...) on the idea of separation of variables and to algorithms that even now successfully help resolve problems that are beyond the capabilities of supercomputers. -/- The lecture was followed by a panel discussion attended by: Evgeny Evgenyevich Tyrtyshnikov, full member of the Russian Academy of Sciences, Doctor of Physics and Mathematics, Director of the Institute for Computational Mathematics of the Russian Academy of Sciences; Alexander Vladimirovich Gasnikov, Doctor of Physics and Mathematics, President of Innopolis University; Gleb Gennadyevich Gusev, PhD of Physics and Mathematics, Head of Sberbank’s Artificial Intelligence Laboratory. The discussion was moderated by Albert Ruvimovich Efimov, PhD of Philosophy, Vice President, Director of the Research and Innovation Division of Sberbank. (shrink)

Variable quality essays dominated by reductionist nonsense. This is a followup to Hofstadter´s famous Godel, Escher, Bach (1980). Like its predecessor, it is concerned largely with the foundations of artificial intelligence, but it is composed mostly of stories, essays and extracts from a wide range of people, with a few essays by DH and DD and comments to all of the contributions by one or the other of them. For my views on the attempts of D and H to understand (...) behaviour see my review of D's " I am a Strange Loop. " Much of it is very reductionistic in tone (ie, " explains " everything in terms of physics/math and denies " reality " of psychology) but as Hofstadter notes, the quantum field equations of a water molecule are too complex to solve (and so is a vacuum)and nobody has a clue about how to explain the way properties emerge(eg, water properties from H2 and 02) as you go up the scale from the vacuum to the brain, so reductionism, like holism, requires a great deal of faith and in fact is incoherent as one cannot even frame it's arguments without presupposing the coherence of higher order thought. Additional problems for reductionism are the uncertainty principle, chaos (eg, no way to predict how a pile of sand will fall) and the logically necessary incompleteness of math (and all thought). In sum, though there are many interesting comments, like nearly all writing on behavior this work lacks any coherent account of the logical structure of rationality which I give in my more recent writings. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

How the universe came to be what it is now is a key philosophical question. The hypothesis that it came from nothing or śūnya (as proposed by Stephen Hawking, among others) proves to be dissembling, since the quantum vacuum can hardly be considered a void (śūnya). In modern science, it is generally assumed that matter existed before the universe came to be. Modern science hypothesizes that the manifestation of life on earth is nothing but a mere increment in the complexity (...) of matter – and hence is an outcome of evolution of matter (chemical evolution) following the Big Bang. After the manifestation of life, modern science believed that chemical evolution transformed itself into biological evolution, which then had caused the entire biodiversity on our planet. In the framework of materialism, the major attention is to find general organizational laws stimulated by physical sciences, ignoring the uniqueness of life. The main goal of materialism is to reduce consciousness to natural processes, which in turn can be translated into the language of math, physics, and chemistry. Following this approach, scientists have made several attempts to deny the living organism of its veracity as an immortal soul, in favor of genes, molecules, atoms, and so on. However, advancement in various fields of biology has repeatedly given rise to questions against such a denial and has supplied more and more evidence against the completely misleading ideological imposition that living entities are particular states of matter. In the recent past, however, the realization has arisen that cognitive nature of life at all levels has begun presenting significant challenges to the views of materialism in biology and has created a more receptive environment for the soul hypothesis (Shanta BN. Commun Integr Biol 8(5):e1085138, 2015). Therefore, instead of adjudicating different aprioristic claims, the development of an authentic theory of origin of life and universe needs both proper scientific knowledge and the appropriate tools of philosophical analysis of life. This talk will highlight the uniqueness of biological systems that offers a considerable challenge to the mainstream materialism and proposes the Vedāntic philosophical view as a viable alternative for development of a theory worthy of origin of life and universe. (shrink)

This book tries to present math to the millions and does a pretty good job. It is simple and sometimes witty but often the literary allusions intrude and the text bogs down in pages of relentless math--lovely if you like it and horrid if you don´t. If you already know alot of math you will still probably find the discussions of general math, geometry, projective geometry, and infinite series to be a nice refresher. If you don´t (...) know any and don´t have a natural talent for it, you will find it very dense or impossible. Being somewhere in the middle I skimmed thru most of it and slowed down when it got interesting. If you have only a little time I would suggest the last chapter ´The Abyss` about Georg Cantor and transfinite arithmetic. -/- At points they wax philosophical and ask the perennial question: is math is out there in the world or in here in our heads. Why not ask this about art or music or literature or computer programs or philosophy itself? In a very general way math must come from the same place that words and ideas and images come from---our brain evolved to make them and they must in many ways (every way?) reflect the structure of our brains, which reside in our DNA, which was shaped by natural selection, which was shaped by the geology of the earth and the structure of our universe, which comes from particle physics which comes from the laws of nature which are just there. -/- I have written extensively on the nature of math and language and mind and how they are all one in my many other reviews so please see them if these topics interest you. 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)

A philosophical system that aims to explain the structure of nature from the perspective of the framework of human consciousness, and thus the foundations of mathematics and physics.

This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any of these (...) notions and proposes a more physical treatment of mathematical objects separating the objects from tools used to study them. It both offers a possibility to create new numerical methods using infinities and infinitesimals in floating-point computations and allows one to study certain mathematical objects dealing with infinity more accurately than it is done traditionally. In these notes, we explain that even though both methodologies deal with infinities and infinitesimals, they are independent and represent two different philosophies of Mathematics that are not in a conflict. It is proved that texts :539–555, 2017; Gutman and Kutateladze in Sib Math J 49:835–841, 2008; Kutateladze in J Appl Ind Math 5:73–75, 2011) asserting that the ①-based methodology is a part of non-standard analysis unfortunately contain several logical fallacies. Their attempt to show that the ①-based methodology can be formalized within non-standard analysis is similar to trying to show that constructivism can be reduced to the traditional Mathematics. (shrink)

Writing philosophy well is an essential skill in our discipline. Philosophical writing must aim for clarity, precision, and rigor, but in doing so, it can often wind up dry, long-winded and boring. It can take many drafts to produce a paper that is suitable for publication in a journal, and many aspiring (and accomplished!) academic philosophers find the process of writing arduous and frustrating. Still, some people make it look easy – if you’ve read anything by Alan Hájek, you’ve (...) probably noticed his breezy style that effortlessly communicates complex ideas in simple terms. His concise and witty prose makes even formal epistemology, a notoriously complicated, math-heavy subject, accessible and engaging to readers. However, while it might look effortless, Hájek’s spirited style is in fact born out of deep and thoughtful engagement with the craft of writing. His motto is: “Work hard for your readers, so that they don’t have to.” Hájek’s approach is decidedly anti-genius: he believes that having good ideas and communicating them well can be taught, and he has devoted considerable energy to helping his graduate students improve their writing. He has written multiple articles about philosophical creativity, as well as an unpublished lengthy manuscript on the mechanics of writing. I have benefited myself from his advice – at least I believe I have, readers may judge for themselves. My aim in this article is to share a few of his insights that I have found most helpful for myself and for my students. I won’t try to summarize all of Hájek’s advice, and I also don’t claim that all of this is totally new. Rather, I will offer a small collection of greatest hits. I will cover eight aspects of philosophical writing, and for each one, I will explain the basic idea, and then discuss some ways of implementing it for oneself and one’s students. (shrink)

Randomness, a core concept of gambling, is seen in problem gambling as responsible for the formation of the math-related cognitive distortions, especially the Gambler’s Fallacy. In problem-gambling research, the concept of randomness was traditionally referred to as having a mathematical nature and categorized and approached as such. Randomness is not a mathematical concept, and I argue that its weak mathematical dimension is not decisive at all for the randomness-related issues in gambling and problem gambling, including the correction of the (...) misconceptions and fallacies about probability and statistical concepts applied in gambling. I distinguish between mathematical and nonmathematical dimensions of randomness (the epistemic, the theoretical-methodological, the functional, and the ethical) falling within the general concept, and I argue that both the studies having as object the math-related cognitive distortions among gamblers and the educational programs aiming at correcting them should employ this distinction in their design and content. (shrink)

In a recent article in this journal [Phil. Math., II, v.4 (1989), n.2, pp.?- ?] J. Fang argues that we must not be fooled by A.J. Ayer (God rest his soul!) and his cohorts into believing that mathematical knowledge has an analytic a priori status. Even computers, he reminds us, take some amount of time to perform their calculations. The simplicity of Kant's infamous example of a mathematical proposition (7+5=12) is "partly to blame" for "mislead[ing] scholars in the direction (...) of neglecting the temporal element"; yet a brief instant of time is required to grasp even this simple truth. If Kant were alive today, "and if he had had a little more mathematical savvy", Fang explains, he could have used the latest example of the largest prime number (391,581 x 2 216,193 - 1) as a better example of the "synthetic a priori" character of mathematics. The reason Fang is so intent upon emphasizing the temporal character of mathematics is that he wishes to avoid "the uncritical mixing of ... a theology and a philosophy of mathematics." For "in the light of the Computer Age today: finitism is king!" Although Kant's aim was explicitly "to study the 'human' ... faculty", Fang claims that even he did not adequatley emphasize "the clearly and concretely distinguishable line of demarcation between the human and divine faculties.". (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

A mixed bag dominated by H & D's reductionist nonsense. This is a follow-up to Hofstadter´s famous (or infamous as I would now say, considering its unrelenting nonsense) Godel, Escher, Bach (1980). Like its predecessor, it is concerned largely with the foundations of artificial intelligence, but it is composed mostly of stories, essays and extracts from a wide range of people, with a few essays by DH and DD and comments to all of the contributions by one or the other (...) of them. For my views on the attempts of D and H to understand behavior see my review of Hofstadter's ‘I am a Strange Loop’ and other writings. -/- Much of it is very reductionistic in tone (i.e., " explains " everything in terms of physics/math and denies " reality " of psychology) but as Hofstadter notes, the quantum field equations of a water molecule are too complex to solve (and so is a vacuum)and nobody has a clue about how to explain the way properties emerge (e.g., water properties from H2 and 02) as you go up the scale from the vacuum to the brain, so reductionism, like holism, requires a great deal of faith and in fact is incoherent as one cannot even frame it's arguments without presupposing the coherence of higher order thought. Additional problems for reductionism are the uncertainty principle, chaos (e.g., no way to predict how a pile of sand will fall), the logically necessary incompleteness of math (and all thought) and the impossibility of matching higher order behaviors (e.g., language) with lower order phenomena (e.g., biochemistry), i.e., the combinatorial explosion or underdetermination. In sum, though there are many interesting comments, like nearly all writing on behavior, this work lacks any coherent account of the logical structure of rationality, which I try to give in my writings. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019) and Suicidal Utopian Delusions in the 21st Century 4th ed (2019) . (shrink)

The Einstein of the New Age holds forth in his unique and brilliant style on the history of world views and how to put spirit back in our life. If you have the patience to learn his jargon and read slowly there is alot of serious brainfood here. I read this and his Sex, Ecology and Spirituality(1995) with Hofstadter´s famous Godel, Escher, Bach(GEB) written in 1980(both of which I have reviewed here). Wilber´s work has many parallels with GEB, both of (...) them massive works attempting to tie together disparate fields and different views of life. Unlike Hofstadter, who was mainly interested in the nature of intelligence, Wilber does not treat math, music or DNA, and he concentrates on world views that have a spiritual relevance but like Hofstadter he lacks any grasp of the logical structure of rationality, the dual systems of thought or the works of Wittgenstein and Searle, which obviates much of his work. For an account of those see my articles. He spent a vast amount of time working out the relationships between ideas and how they relate to individual and society, spirit and science. If you don´t have the time or patience for the whole book, read Superconsciousness Parts 1 and 2 which are an excellent summary. His shortest book, `The Marriage of Self andSoul is a much easier read that gives you a good idea of his style and purpose. He details alot of intellectual history (philosophy, psychology, religion, ecology, feminism, sociology, etc) and shows where nearly everyone went too far in the direction of Ascent (to the spirit) or Descent (to science,materialism, reductionism or Flatland). He trys to show how to heal the rifts by combining sense and soul (spiritual and material life, science and religion, internal and external, individual and social). Everything is related to everything else (holons in holarchies). The Age of Enlightenment denied the the spirit, the individual and the interior life but developed art, morals and science and led to democracy, feminism, equality and ecology, but this reductionism compressed the intellect and the spirit into the Flatland of science, rationality and materialism. He sees the loss of the spiritual point of view with the Age of Enlightenment as the major factor responsible for the malaise of modern times, but real spirituality or ìntelligent religion (i.e., the quest for enlightenment) as opposed to primitive religion (everything else-see my review of Boyer´s 'Religion Explained') was always rare. It is intelligent religion he sees as the panacea, but it is primitive religion that the masses understand, and it too has only materialistic goals. In sum, in spite of its shortcomings it is still unique and well worth the effort. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

"There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact" Mark Twain-Life on the Mississippi -/- This is a lovely book full of fascinating info on the evolution of physics and cosmology. Its main theme is how the idea of higher dimensional geometry created by Riemann, recently extended to 24 dimensions by string theory, has revolutionized our understanding of the universe. Everyone knows that Riemann created multidimensional geometry in 1854 (...) but it is amazing to learn that he also was a physicist who believed that it held the key to explaining the fundamental laws of physics. Maxwell´s equations did not exist then and Riemann´s untimely death at age 39 prevented his pursuit of these ideas. Both he and his British translator Clifford believed that magnetic and electric fields resulted from the bending of space in the 4th dimension-more than 50 years before Einstein! The fourth dimension became a standard subject in the popular media for the next 50 years with several stories by HG Wells using it and even Lenin wrote about it. The American mathematician Hinton had widely publicized his idea that light is a vibration in the 4th spatial dimension. Amazingly, physicists and most mathematicians forgot about it and when Einstein was looking for the math needed to encompass general relativity 60 years later, he had never heard of Riemannian geometry. He spent 3 years trying to find the equations for general relativity and only after a math friend told him about Riemann was he able to complete his work. Riemann´s equations with four dimensional metric tensors describing every point in space were incorporated almost unchanged into relativity. And on and on it goes. Since this review I have written a great deal on the language games of math and science, uncertainty, incompleteness, the limits of computation etc., so those interested should find them useful since this volume like most science frequently wanders across the line into philosophy (scientism). -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

I start with some famous comments by the philosopher (psychologist) Ludwig Wittgenstein because Pinker shares with most people (due to the default settings of our evolved innate psychology) certain prejudices about the functioning of the mind and because Wittgenstein offers unique and profound insights into the workings of language, thought and reality (which he viewed as more or less coextensive) not found anywhere else. The last quote is the only reference Pinker makes to Wittgenstein in this volume, which is most (...) unfortunate considering that he was one of the most brilliant and original analysts of language. -/- In the last chapter, using the famous metaphor of Plato’s cave, he beautifully summarizes the book with an overview of how the mind (language, thought, intentional psychology) –a product of blind selfishness, moderated only slightly by automated altruism for close relatives carrying copies of our genes--works automatically, but tries to end on an upbeat note by giving us hope that we can nevertheless employ its vast capabilities to cooperate and make the world a decent place to live. -/- Pinker is certainly aware of but says little about the fact that far more about our psychology is left out than included. Among windows into human nature that are left out or given minimal attention are math and geometry, music and sounds, images, events and causality, ontology (classes of things), dispositions (believing, thinking, judging, intending etc) and the rest of intentional psychology of action, neurotransmitters and entheogens, spiritual states (e.g, satori and enlightenment, brain stimulation and recording, brain damage and behavioral deficits and disorders, games and sports, decision theory (incl. game theory and behavioral economics), animal behavior (very little language but a billion years of shared genetics). Many books have been written about each of these areas of intentional psychology. The data in this book are descriptions, not explanations that show why our brains do it this way or how it is done. How do we know to use the sentences in their various way (i.e., know all their meanings)? This is evolutionary psychology that operates at a more basic level –the level where Wittgenstein is most active. And there is scant attention to context. -/- Nevertheless this is a classic work and with these cautions is still well worth reading. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

Can we do science without numbers? How much contingency is there? These seemingly unrelated questions--one in the philosophy of math and science and the other in metaphysics--share an unexpectedly close connection. For as it turns out, a radical answer to the second leads to a breakthrough on the first. The radical answer is new view about modality called compossible immutabilism. The breakthrough is a new strategy for doing science without numbers. One of the chief benefits of the new (...) strategy is that, unlike the existing substantialism approach from Field (1980), the new strategy naturally generalizes to theories formulated in terms of state space. (shrink)

The movement called Experimental Philosophy (‘x-Phi’) has now passed its tenth anniversary. Its central insight is compelling: When an argument hinges on accepting certain ‘facts’ about human perception, knowledge, or judging, the evoking of relevant intuitions by thought experiments is intended to make those facts seem obvious. But these intuitions may not be shared universally. Experimentalists propose testing claims that traditionally were intuition-based using real experiments, with real samples. Demanding that empirical claims be empirically supported is certainly reasonable; though (...) experiments are not necessarily the only means available. When experiments are conducted, adequately interpreting their results requires understanding the study’s design (and possibly flaws) that produced them. Experiment-based reports should document the design clearly. If Plato, writing his Meno, replaced accounts of Socrates demonstrating geometry to a slave-boy, with a survey of 100 real boys—some grasping his demonstrations, others not—what conclusions could be reached? Before answering, the reader needs details on key design questions, including (among others): (a) What population are these samples intended to represent? (E.g., ‘all slave boys’?; ‘math-ignorant people’?; ‘everyone’?) (b) What statistical tests were conducted, on what assumptions? (c) How was ‘significance’ of results determined? (d) Was the test instrument’s validity established? For readers wishing to explore x-Phi’s potentials, as contributors or as interpreters of their findings, this paper offers some cautionary considerations. Throughout their literature, examples can be found casting doubt on some experimentalists’ findings, due to design-related issues. Increased awareness of methodological questions would tighten the x-phi literature, going forward . (shrink)

Since Gintis is a senior economist and I have read some of his previous books with interest, I was expecting some more insights into behavior. Sadly he makes the dead hands of group selection and phenomenology into the centerpieces of his theories of behavior, and this largely invalidates the work. Worse, since he shows such bad judgement here, it calls into question all his previous work. The attempt to resurrect group selection by his friends at Harvard, Nowak and Wilson, a (...) few years ago was one of the major scandals in biology in the last decade, and I have recounted the sad story in my article ‘Altruism, Jesus and the End of the World—how the Templeton Foundation bought a Harvard Professorship and attacked Evolution, Rationality and Civilization -- A review of E.O. Wilson 'The Social Conquest of Earth' (2012) and Nowak and Highfield ‘SuperCooperators’ (2012).’ Unlike Nowak, Gintis does not seem to be motivated by religious fanaticism, but by the strong desire to generate an alternative to the grim realities of human nature, made easy by the (near universal) lack of understanding of basic human biology and blank slateism of behavioral scientists, other academics, and the general public. -/- Gintis rightly attacks (as he has many times before) economists, sociologists and other behavioral scientists for not having a coherent framework to describe behavior. Of course the framework needed to understand behavior is an evolutionary one. Unfortunately he fails to provide one himself (according to his many critics and I concur), and the attempt to graft the rotten corpse of group selection onto whatever economic and psychological theories he has generated in his decades of work, merely invalidates his entire project. Although Gintis makes a valiant effort to understand and explain the genetics, like Wilson and Nowak, he is far from an expert, and like them, the math just blinds him to the biological impossibilities and of course this is the norm in science. As Wittgenstein famously noted on the first page of Culture and Value “There is no religious denomination in which the misuse of metaphysical expressions has been responsible for so much sin as it has in mathematics.” -/- It has always been crystal clear that a gene that causes behavior which decreases its own frequency cannot persist, but this is the core of the notion of group selection. Furthermore, it has been well known and often demonstrated that group selection just reduces to inclusive fitness (kin selection), which, as Dawkins has noted, is just another name for evolution by natural selection. Like Wilson, Gintis has worked in this arena for about 50 years and still has not grasped it, but after the scandal broke, it took me only 3 days to find, read and understand the most relevant professional work, as detailed in my article. It is mind boggling to realize that Gintis and Wilson were unable to accomplish this in nearly half a century. -/- I discuss the errors of group selection and phenomenology that are the norm in academia as special cases of the near universal failure to understand human nature that are destroying America and the world. -/- Those who wish to read all my articles please consult the ebook here Philosophy, Human Nature and the Collapse of Civilization -- Articles and Reviews 2006-2016 by Michael Starks 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)

In attempt to provide an answer to the question of origin of deductive proofs, I argue that Aristotle’s philosophy of math is more accurate opposed to a Platonic philosophy of math, given the evidence of how mathematics began. Aristotle says that mathematical knowledge is a posteriori, known through induction; but once knowledge has become unqualified it can grow into deduction. Two pieces of recent scholarship on Greek mathematics propose new ways of thinking about how mathematics began (...) in the Greek culture. Both claimed there was a close relationship between the culture and mathematicians; mathematics was understood through imaginative processes, experiencing the proofs in tangible ways, and establishing a consistent unified form of argumentation. These pieces of evidence provide the context in which Aristotle worked and their contributions lend support to the argument that mathematical premises as inductively available is a better way of understanding the origins of deductive practices, opposed to the Platonic tradition. (shrink)

Since Benacerraf’s ‘What Numbers Could Not Be, ’ there has been a growing interest in mathematical structuralism. An influential form of mathematical structuralism, modal structuralism, uses logical possibility and second order logic to provide paraphrases of mathematical statements which don’t quantify over mathematical objects. These modal structuralist paraphrases are a useful tool for nominalists and realists alike. But their use of second order logic and quantification into the logical possibility operator raises concerns. In this paper, I show that the work (...) of both these elements can be done by a single natural generalization of the logical possibility operator. (shrink)

Nowak is (or was) a respected Harvard professor of mathematical biology with numerous well regarded publications. Sadly, he has chosen to launch an arrogant attack on science motivated by religious fervor. His recent actions show the evil consequences when universities accept money from religious groups, science journals are so awed by big names that they avoid proper peer review, and egos are permitted to get out of control. Most of this book is good, but it repeats the utterly misconceived attacks (...) on inclusive fitness in favor of group selection which he and his much more famous Harvard colleague E.O.Wilson have been making the last 5 years, so it is on that chapter of the book that I will concentrate. This takes us into the nature of evolution, the basics of scientific methodology, how math relates to science, what constitutes a law or a theory, and what attitudes to religion and generosity are appropriate as we inexorably approach the collapse of industrial civilization. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

I give a detailed review of 'The Outer Limits of Reason' by Noson Yanofsky 403(2013) from a unified perspective of Wittgenstein and evolutionary psychology. I indicate that the difficulty with such issues as paradox in language and math, incompleteness, undecidability, computability, the brain and the universe as computers etc., all arise from the failure to look carefully at our use of language in the appropriate context and hence the failure to separate issues of scientific fact from issues of how (...) language works. I discuss Wittgenstein's views on incompleteness, paraconsistency and undecidability and the work of Wolpert on the limits to computation. -/- Those wishing a comprehensive up to date account of Wittgenstein, Searle and their analysis of 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 (2016). Those interested in all my writings in their most recent versions may download from this site my e-book ‘Philosophy, Human Nature and the Collapse of Civilization Michael Starks (2016)- Articles and Reviews 2006-2016’ by Michael Starks First Ed. 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)

This paper is about teaching probability to students of philosophy who don’t aim to do primarily formal work in their research. These students are unlikely to seek out classes about probability or formal epistemology for various reasons, for example because they don’t realize that this knowledge would be useful for them or because they are intimidated by the material. However, most areas of philosophy now contain debates that incorporate probability, and basic knowledge of it is essential even for (...) philosophers whose work isn’t primarily formal. In this paper, I explain how to teach probability to students who are not already enthusiastic about formal philosophy, taking into account the common phenomena of math anxiety and the lack of reading skills for formal texts. I address course design, lesson design, and assignment design. Most of my recommendations also apply to teaching formal methods other than probability theory. (shrink)

Some people believe that critical thinking is not a modern science, but its roots are old and deeply rooted in the history of philosophy. Its roots date back to Aristotle, the inventor of logic and who was called the first teacher by virtue of this invention. Aristotle was impressed by the language of mathematics and wanted to invent a language to logic similar to the language of Mathematics. What encouraged Aristotle to do so is that Math language is (...) quite different from daily life language. For example , when you say one in Mathematics language, what is this one you mean or intend? That is what is one? Is it a specific man or an animal or something abstract or any creature of the creatures of the natural world? The one we are talking about is neither this nor that and you can use it to talk about one human being or one animal or one creature. Therefore, the concept of the one is something abstract and it is so far from the creatures of the exterior world. Geometry has the same case. Triangle, quarter and rectangle as such are mere geometrical shapes and are far away from real life language. But when we use them in our daily life language we give them specific life meanings. -/- As I said, Aristotle was impressed by the language of Mathematics and wanted to build a similar language for logic .The rationale behind this is to get away from the language of ambiguity caused by the use of daily life language .One word or utterance in a language has many usages in one language or when translated into other languages , and therefore it causes many problems in usage instead of simplifying it and this is what Aristotle tried to avoid. Aristotle chose letters instead of words, the letter is part of the word, and the letter is meaningless unless it is a part of the word. The meaning of a letter depends on its occurrence in the word. If you compose a word from a group of letters and use it , it becomes ambiguous because it becomes part of the used language. -/- However, Aristotle did not combine letters in a word but he used them as abstract letters and gave them meanings in the language of logic where there is no divergence about its use. Aristotle used them in syllogism and they mean the limits of reason . Until recently critical thinking was part of formal logic and learning it means that you have logical background or at least you are familiar with the rules and fundamentals of logic. But critical thinking theorists soon took the initiative to separate it from logic because the latter started to suffer from its rules which are difficult to understand and which require some awareness and thoughts on the part of the scholar to understand. Hence , critical thinking is not supposed to possess a background of logic and it adopts a specific questioning approach where it suggests a number of questions the practitioner of critical thinking has to successively answer since he has to make sure that the opinion he reaches does not rely on any subjective considerations. This is how the skills that are acquired on a continuum of related critical questions are established ,this is not to mention that the concept of critical thinking itself is usually defined in this context as the awareness of such kinds of questions and the ability to arouse and answer them at appropriate times. My paper explains, How to be able to implement these skills in high education and what are the benefits of these skills? The paper includes; Critical Thinking and Logic Socrates `s Approach The impact of critical thinking on teaching methods Questioning How questions are organized in the light of critical thinking? Using Critical Thinking in Problem-Solving Use of Non-Oral language in Critical Thinking. (shrink)

Frans de Waal (1948-2024) transformed our understanding of primate cognition and social behavior, shaping the perspectives of scientists, philosophers, and the general public through his groundbreaking research and engaging popular books.

What is reasoning? What is logic? What is math? Common sense tells us that concepts such as numbers, relations, and logical structures feel inherently familiar—almost intuitive. They seem so obvious, but why? Do they have deeper origins? What is the number? What is addition? Why do they work in this way? Basic axioms of math, their foundation seems to be very intuitive, but absolutely mysteriously appear to the human mind out of nowhere. In a way their true essence (...) magically slips away unnoticed from the consciousness, in an attempt to pinpoint its foundation. This paper delves into the fundamental nature of mathematics, logic, and rational reasoning, examining their "unreasonable effectiveness" in understanding and shaping the world. By drawing parallels between advancements in artificial neural networks and human cognition, the work introduces a novel perspective on intuition as the cornerstone of higher cognitive systems. Intuition is presented not only as a tool for pattern recognition but as the foundation upon which complex reasoning processes, such as mathematical abstraction and logical frameworks are constructed. This perspective redefines the role of consciousness, highlighting its capacity for innovation and exploration within abstract domains. Beyond theoretical insights, the paper outlines potential pathways for advancing artificial general intelligence by leveraging the interplay between intuition and conscious reasoning. (shrink)

Within this text is The Proof, beyond an ounce of doubt, by way of the language of the Universe: Mathematics, that The Triune God is The One True God and The Holy Bible is His Word.

I start with some famous comments by the philosopher (psychologist) Ludwig Wittgenstein because Pinker shares with most people (due to the default settings of our evolved innate psychology) certain prejudices about the functioning of the mind, and because Wittgenstein offers unique and profound insights into the workings of language, thought and reality (which he viewed as more or less coextensive) not found anywhere else. There is only reference to Wittgenstein in this volume, which is most unfortunate considering that he was (...) the most brilliant and original analyst of language. -/- In the last chapter, using the famous metaphor of Plato’s cave, he beautifully summarizes the book with an overview of how the mind (language, thought, intentional psychology) –a product of blind selfishness, moderated only slightly by automated altruism for close relatives carrying copies of our genes (Inclusive Fitness)--works automatically, but tries to end on an upbeat note by giving us hope that we can nevertheless employ its vast capabilities to cooperate and make the world a decent place to live. -/- Pinker is certainly aware of but says little about the fact that far more about our psychology is left out than included. Among windows into human nature that are left out or given minimal attention are math and geometry, music and sounds, images, events and causality, ontology (classes of things or what we know), most of epistemology (how we know), dispositions (believing, thinking, judging, intending etc.) and the rest of intentional psychology of action, neurotransmitters and entheogens, spiritual states (e.g, satori and enlightenment, brain stimulation and recording, brain damage and behavioral deficits and disorders, games and sports, decision theory (incl. game theory and behavioral economics), animal behavior (very little language but a billion years of shared genetics). Many books have been written about each of these areas of intentional psychology. The data in this book are descriptions, not explanations that show why our brains do it this way or how it is done. How do we know to use the sentences in their various way (i.e., know all their meanings)? This is evolutionary psychology that operates at a more basic level –the level where Wittgenstein is most active. And there is scant attention to the context in which words are used = an arena which Wittgenstein pioneered. -/- Nevertheless, this is a classic work and with these cautions is still well worth reading. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019) . (shrink)

TLP is a remarkable document which continues to seduce some the best minds in philosophy, with new books and articles dealing partly or entirely with it appearing frequently over a century after it was first conceived. The first thing to note is that W later rejected it entirely for reasons he spent the rest of his life explaining. He was doing philosophy (descriptive psychology) as though the mind was a logical mathematical machine that processed facts, and behavior was (...) the result. Thus, long before computers W gave the ultimate statement of what was half a century later to become known as strong AI, CTM (Computational Theory of Mind) and most recently DSM (Dynamic Systems Theory). Eventually, W realized that perception and memory were the raw material acted upon by our innate psychology (EP) and logic and math were some of the results. Being able to say or understand anything presupposed EP and trying to make logic primary leads to incoherence, as is evident throughout TLP (and the explanation for its many bizarre statements-see e.g. Hutto). Even so, one can “understand” TLP in the sense that one can state the confusions he labored under and which most of the world still does. I briefly review Wittgenstein’s work in modern context. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

TLP is a remarkable document which continues to seduce some the best minds in philosophy, with new books and articles dealing partly or entirely with it appearing frequently over a century after it was first conceived. The first thing to note is that W later rejected it entirely for reasons he spent the rest of his life explaining. He was doing philosophy (descriptive psychology) as though the mind was a logical mathematical machine that processed facts, and behavior was (...) the result. Thus, long before computers W gave the ultimate statement of what was half a century later to become known as strong AI, CTM (Computational Theory of Mind) and most recently DSM (Dynamic Systems Theory). Eventually, W realized that perception and memory were the raw material acted upon by our innate psychology (EP) and logic and math were some of the results. Being able to say or understand anything presupposed EP and trying to make logic primary leads to incoherence, as is evident throughout TLP (and the explanation for its many bizarre statements-see e.g. Hutto). Even so, one can “understand” TLP in the sense that one can state the confusions he labored under and which most of the world still does. I briefly review Wittgenstein’s work in modern context. -/- 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). (shrink)

Austria, by the end of the nineteenth century, clearly lagged behind its more developed Western neighbours in matters of intellect and science. The Empire had witnessed a relatively late process of urbanization, bringing also a late development of those liberal habits and values which would seem to be a presupposition of the modern, scientific attitude. It therefore lacked institutions of scientific research of the sort that had been founded in Germany since the time of von Humboldt. On the other hand, (...) as more liberal ways began to be established in Austria - effectively in the second half of the nineteenth century - the desire to enjoy the trappings of a modern enlightened culture made itself felt. The Austrians were not of course in a position to summon forth the means to create reputable institutions and traditions of science in the narrow sense, and this created a vacuum which the theory of a practice so attractively pursued elsewhere could then fill. (shrink)

November 4th-5th, 2012 at Kyoto University. Organizers: Hisashi Nakao & Pierre-Alain Braillard.

This work is a attempt to describe various braches of mathematics and the analogies betwee them. Namely: 1) Symbolic Analogic 2) Lateral Algebraic Expressions 3) Calculus of Infin- ity Tensors Energy Number Synthesis 4) Perturbations in Waves of Calculus Structures (Group Theory of Calculus) 5) Algorithmic Formation of Symbols (Encoding Algorithms) The analogies between each of the branches (and most certainly other branches) of mathematics form, ”logic vectors.” Forming vector statements of logical analogies and semantic connections between the di↵erentiated branches (...) of math- ematics is useful. It’s useful, because it gives us a linguistic notation from which we can derive other insights. These combined insights from the logical vector space connections yield a combination of Numeric Energy and the logic space. Thus, I have derived and notated many of the most useful tangent ideas from which even more correlations and connections ca be drawn. Using AI, these branches can be used to form even more connections through training of lan- guage engines on the derived models. Through the vector logic space and the discovery of new sheaf (Limbertwig), vast combinations of novel, mathematical statements are derived. This paves the way for an AGI that is not rigid, but flex- ible, like a Limbertwig. The Limbertwig sheaf is open, meaning it can receive other mathematical logic vectors with di↵erent designated meanings (of infi- nite or finite indicated elements). Furthermore, the articulation of these syntax forms evolves language away from imperative statements into a mathematically emotive space. Indeed, shown within, we see how the supramanifold of logic is shared with the supramanifold of space-time mathematically. Developing clean mathematical spaces can help meditation, thought pro- cess, acknowledgment of ideas spoken into that cognitive-spacetime and in turn, methods by which paradoxes can be resolved linguistically. This toolkit should be useful to all in the sciences as well as those bridging the humantities to mathematics. Using our memories as a toolkit to aggregate these ideas breaks down bound- aries between them in a new, exciting way. Merging philosophy and Quantum Mechanics together through the lens of symbolic analogies gives the tools to unravel this mystery of all mysteries. Mathematics thus exists as a bridge al- beit a complex one between the two disciplines, giving life to a composite art of problem-solving. Furthermore, mathematics yields to millions of other applications that are potentially limited only by our imagination. From massive data sets used for predictive analytics to emerging fields in medicine, mathematics is an energy and force at the center of possibilities. The power of mathematics to help manage life exists in its ability to shape and model the world in which we live and interact with one another. In conclusion, mathematics is a powerful tool that creates bridges and con- nections between many disciplines and serves as a powerful form of analytical data consumption. It provides language-rich bridges from which to assemble vast fields of theoretical investigations and create groundbreaking innovations. As we approach new horizons in the technology timeline, mathematics will con- tinue to be a powerful driver of creativity and progress. (shrink)

Why study notations, diagrams, or more broadly the variety of nonverbal “representations” or “signs” that are used in mathematical practice? This chapter maps out recent work on the topic by distinguishing three main philosophical motivations for doing so. First, some work (like that on diagrammatic reasoning) studies signs to recover norms of informal or historical mathematical practices that would get lost if the particular signs that these practices rely on were translated away; work in this vein has the potential to (...) broaden our view of the specific normativity of mathematics beyond logical proof. Second, some work focuses on signs to highlight the open-ended and “nonrigorous” aspects of mathematical practice, and the role of these aspects in the historical development of mathematics. The third motivation is based on the following observation: the reason differences in signs matter in mathematics is that humans are finite agents, with cognitive and computational limitations. Accordingly, studying signs can be a way to study how human computational constraints shape the mathematics that we do, and to tackle the topic of mathematical understanding. (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)

In a 1978 lecture in Tokyo, Foucault drew a comparison between his own philosophical methodology and that of ‘Anglo-Saxon analytic philosophy’, claiming the label ‘analytic philosophy of politics’ for his own approach. This may seem like a somewhat surprising comparison given the gulf between contemporary analytic and continental philosophy, but I argue that it is a very productive one which indeed might help us reconsider this gulf. I proceed through a comparison between Foucault and the speech act (...) theory of J. L. Austin, one of the analytic philosophers Foucault had in mind in his Tokyo lecture. By focusing on the methodological commonalities between Foucault and Austin, this article identifies the core of a philosophical methodology that cuts across the analytic/continental divide in philosophy in general while constituting a powerful alternative to the methods applied by analytic political philosophers specifically. This approach, which I term ‘analytic critique’, is one that starts from a critical analysis of what happens in ordinary lived experience and theorizes ‘bottom-up’ in an avowedly politically engaged way – thereby challenging the conceptual and political aloofness of contemporary political philosophy in the liberal-Rawlsian tradition. Foucault’s appropriation of the label ‘analytic philosophy’, it is argued, ought to function as a call to more imaginative methodological-theoretical engagement across the traditional division between continental and analytic approaches. (shrink)

With Hegel’s metaphysics attracting renewed attention, it is time to address a long-standing criticism: Scholars from Marx to Popper and Habermas have worried that Hegel’s metaphysics has anti-individualist and authoritarian implications, which are particularly pronounced in his Philosophy of History, since Hegel identifies historical progress with reason imposing itself on individuals. Rather than proposing an alternative non-metaphysical conception of reason, as Pippin or Brandom have done, this article argues that critics are broadly right in their metaphysical reading of Hegel’s (...) central concepts. However, they are mistaken about what Hegel’s approach entails, when one examines the specific types of states discussed by the philosopher in his Philosophy of History. Even on a traditional metaphysical reading, Hegel is not only non-authoritarian; he also makes a powerful argument concerning freedom, whereupon the freest society involves collective oversight and the shaping of social structures so as to ensure that they benefit everybody. (shrink)

Developments in the realm of formal sciences and math foundations during the twentieth century were marked by important methodological advances. Such new approaches partialy owe their appearance to the abandonment of the previous paradigm. To identify how this transition occured, in this essay we observe some aspects regarding the works of Gödel and Tarski, who, under a certain interpretations, restructure epistemological bases of math's formalisms. It'll be argued that the theoretical variabilities produced in abstract sciences upon weakening previous (...) viewpoints forced to abandon some of the components of hegemonic programs. (shrink)

This article is devoted to the philosophical study of the conditions under which knowledge can become a component or tool of education. The presentation of the contribution of epistemology to human development and education is based on addressing issues such as the nature of knowledge, sources of knowledge, theories, and criteria of truth. We proceed from the idea that knowledge is a condition of education. Particular attention is paid to the issue of distinguishing between such types of knowledge as 'knowing (...) how’ and ‘knowing that'. Educational practices open a common foundation that unites the life world of people, types of sociality, and hermeneutical practices. The epistemological approach to the question of the essence of knowledge assumes that knowledge meets three requirements, namely, knowledge must be objective, subjective, and evidentiary. Epistemology includes subjectivity as the basis of human existence in the natural world and the world with others. Intersubjectivity is considered a criterion for the reliability of knowledge about the world, which allows asserting the relationship of the objective with the subjective. (shrink)

Gila Sher interviewed by Chen Bo: -/- I. Academic Background and Earlier Research: 1. Sher’s early years. 2. Intellectual influence: Kant, Quine, and Tarski. 3. Origin and main Ideas of The Bounds of Logic. 4. Branching quantifiers and IF logic. 5. Preparation for the next step. -/- II. Foundational Holism and a Post-Quinean Model of Knowledge: 1. General characterization of foundational holism. 2. Circularity, infinite regress, and philosophical arguments. 3. Comparing foundational holism and foundherentism. 4. A post-Quinean model of knowledge. (...) 5. Intellect and figuring out. 6. Comparing foundational holism with Quine’s holism. 7. Evaluation of Quine’s Philosophy -/- III. Substantive Theory of Truth and Relevant Issues: 1. Outline of Sher’s substantive theory of truth. 2. Criticism of deflationism and treatment of the Liar. 3. Comparing Sher’s substantive theory of truth with Tarski’s theory of truth. -/- IV. A New Philosophy of Logic and Comparison with Other Theories: 1. Foundational account of logic. 2. Standard of logicality, set theory and logic. 3. Psychologism, Hanna’s and Maddy’s conceptions of logic. 4. Quine’s theses about the revisability of logic. -/- V. Epilogue. (shrink)

It is often said that ‘every logical truth is obvious’ (Quine 1970: 82), that the ‘axioms and rules of logic are true in an obvious way’ (Murawski 2014: 87), or that ‘logic is a theory of the obvious’ (Sher 1999: 207). In this chapter, I set out to test empirically how the idea that logic is obvious is reflected in the scholarly work of logicians and philosophers of logic. My approach is data-driven. That is to say, I propose that systematically (...) searching for patterns of usage in databases of scholarly works, such as JSTOR, can provide new insights into the ways in which the idea that logic is obvious is reflected in logical and philosophical practice, i.e., in the arguments that logicians and philosophers of logic actually make in their published work. (shrink)

I discuss the quantum mechanical theory of consciousness and freewill offered by Stapp (1993, 1995, 2000, 2004). First I show that decoherence-based arguments do not work against this theory. Then discuss a number of problems with the theory: Stapp's separate accounts of consciousness and freewill are incompatible, the interpretations of QM they are tied to are questionable, the Zeno effect could not enable freewill as he suggests because weakness of will would then be ubiquitous, and the holism of measurement in (...) QM is not a good explanation of the unity of consciousness for essentially the same reason that local interactions may seem incapable of accounting for it. (shrink)

Crime is a serious social problem, but its causes are not exclusively social. There is growing consensus that explaining and preventing it requires interdisciplinary research efforts. Indeed, the landscape of contemporary criminology includes a variety of theoretical models that incorporate psychological, biological and sociological factors. These multi-disciplinary approaches, however, have yet to radically advance scientific understandings of crime and shed light on how to manage it. In this paper, using conceptual tools on offer in the philosophy of science in (...) combination with theoretical work represented in this special volume of Psychology, Crime and Law, I provide some perspective on why explanatory progress in criminology has remained elusive and evaluate some positive proposals for attaining it. -/- . (shrink)