In this chapter we will argue, firstly, that Bacon’s engages in a pecu-liar form of mathematization of nature that develops a quali-quantitative methodology of measurement. Secondly, we will show that medicine is one of the disciplines where that dual way of measurement is practiced. In the first section of the chapter, we will expose the ontology involved in the Baconian proposal of measurement of nature. The second section will address the place that mixed mathematics occupies in Bacon’s scheme (...) of scientific branches and will suggest that a proper advancement of medicine can generate a new branch of mixed mathematics. The next section will reconstruct Bacon’s approach to measurement and expose its quali-quantitative import. In the last section, we will show some examples of medicine in which this quali-quantitative measurement is applied. (shrink)

Given the sharp distinction that follows from Hume’s Fork, the proper epistemic status of propositions of mixed mathematics seems to be a mystery. On the one hand, mathematical propositions concern the relation of ideas. They are intuitive and demonstratively certain. On the other hand, propositions of mixed mathematics, such as in Hume’s own example, the law of conservation of momentum, are also matter of fact propositions. They concern causal relations between species of objects, and, in this (...) sense, they are not intuitive or demonstratively certain, but probable or provable. In this article, I argue that the epistemic status of propositions of mixed mathematics is that of matters of fact. I wish to show that their epistemic status is not a mystery. The reason for this is that the propositions of mixed mathematics are dependent on the Uniformity Principle, unlike the propositions of pure mathematics. (shrink)

I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the ‘that’) with causal principles from geometry (...) (the ‘why’). My argument shows that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the ‘why’ in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience. (shrink)

Accounts of Hobbes’s ‘system’ of sciences oscillate between two extremes. On one extreme, the system is portrayed as wholly axiomtic-deductive, with statecraft being deduced in an unbroken chain from the principles of logic and first philosophy. On the other, it is portrayed as rife with conceptual cracks and fissures, with Hobbes’s statements about its deductive structure amounting to mere window-dressing. This paper argues that a middle way is found by conceiving of Hobbes’s _Elements of Philosophy_ on the model of a (...) mixed-mathematical science, not the model provided by Euclid’s _Elements of Geometry_. I suggest that Hobbes is a test case for understanding early-modern system-construction more generally, as inspired by the structure of the applied mathematical sciences. This approach has the additional virtue of bolstering, in a novel way, the thesis that the transformation of philosophy in the long seventeenth century was heavily indebted to mathematics, a thesis that has increasingly come under attack in recent years. (shrink)

Plastic waste is a significant environmental problem for almost all countries; therefore, protecting the environment from the problem is crucial. The most sensible solution to these problems is substituting the natural aggregates with substantial plastic waste in various building materials. This study aimed to optimise the mixed design ratio of cement brick containing plastic waste as aggregate replacement. Plastic cement brick mixtures were prepared by the incorporation of four different types of plastic waste such as polyethylene terephthalate (PET), high-density (...) polyethylene, low-density polyethylene and polypropylene into cement bricks with different cement contents (150, 300 and 450 g) and plastic replacement percentages (0, 3 and 6%). Compressive strength and water absorption of the plastic cement bricks were analysed using a statistical model through the response surface methodology. It revealed the optimum cement brick mixed design is C3-1% PET with the compressive strength of 27.50 MPa and water absorption of 1.16%. The optimised plastic cement brick also satisfied the general ASTM C62-17 requirements for building bricks despite the higher porosity observed by the scanning electron microscopy. The results from Fourier transform infrared spectroscopy analysis also showed that the addition of the plastic waste into cement brick was unlikely to modify the chemical compound within the cement brick mixtures. Thus, the proposed mathematical model can predict the required hardened properties of plastic cement bricks and could lead to greater utilisation of plastic waste in building materials. (shrink)

The concept of similarity has had a rather mixed reputation in philosophy and the sciences. On the one hand, philosophers such as Goodman and Quine emphasized the „logically repugnant“ and „insidious“ character of the concept of similarity that allegedly renders it inaccessible for a proper logical analysis. On the other hand, a philosopher such as Carnap assigned a central role to similarity in his constitutional theory. Moreover, the importance and perhaps even indispensibility of the concept of similarity for many (...) empirical sciences can hardly be denied. The aim of this paper is to show that Quine’s and Goodman’s harsh verdicts about this notion are mistaken. The concept of similarity is susceptible to a precise logico-mathematical analysis through which its place in the conceptual landscape of modern mathematical theories such as order theory, topology, and graph theory becomes visible. Thereby it can be shown that a quasi-analysis of a similarity structure S can be conceived of as a sheaf (etale space) over S. (shrink)

I show that the mathematical description of opponent-colors theory is identical to the mathematical description of two-state quantum systems in a mixed state. Based on the dual-aspect theory of phenomenal consciousness, which suggests that one or more physical entities in our universe have phenomenal aspects that are dual to their physical aspects and therefore predicts an exact correspondence between a system’s phenomenal states and the objective states of its underlying physical substrate, I hypothesize that color sensations are phenomenal dual (...) aspects of two-state quantum systems in a mixed state. Since nothing in this hypothesis suggests that what brings about the phenomenal experience that is dual to two-state quantum systems is the two-dimensionality of these systems, it is natural to generalize this hypothesis and suggest that other types of phenomenal experience (e.g., taste, odor, sound) are phenomenal dual aspects of quantum systems of higher dimensionalities. Finally, I propose that the two-state quantum systems that give rise to color in the brain are two-state ion-channels. (shrink)

I show that the mathematical description of opponent-colors theory is identical to the mathematical description of two-state quantum systems in a mixed state. Following the principles of dual-aspect theory of phenomenal consciousness, which predicts an exact correspondence between a system’s phenomenal states and the objective states of its underlying physical substrate, I suggest that color sensations are phenomenal dual aspects of two-state quantum systems in a mixed state. Since nothing in this hypothesis suggests that what brings about the (...) phenomenal experience that is dual to two-state quantum systems is the two-dimensionality of these systems, it is natural to generalize this hypothesis and suggest that other types of phenomenal experience (e.g., taste, odor, sound) are phenomenal dual aspects of quantum systems of higher dimensionalities. Finally, I propose that the two-state quantum systems that give rise to color in the brain are two-state ion-channels. (shrink)

The Western Philippines University – College of Education’s Project MATHEMATICS (Mathematics Enhanced Mentoring, Assistance, and Training to In-need and Challenged Students) was implemented as part of the Adopt-a-School Program to address the mathematical needs of Laura Vicuña Center – Palawan youths. To evaluate the extent of the project implementation, the study assessed its impact through the feedback gathered from the clients served. It specifically described the quality of project implementation, determined the attainment of project objectives, and enumerated client (...) feedback. A concurrent triangulation mixed-method research design was used with 32 clientele samples selected purposively. The study utilized a survey, problem set test, and focus-grouped interview to obtain data pertinent to the study’s objectives. The findings revealed an aspirational quality of the implemented project, improved mathematical performance, and the client’s desire for ongoing mentoring. The implications and limitations of the study are discussed, along with recommendations for future extension projects, monitoring and evaluation, and re-planning activities. (shrink)

This study aimed to trace the 2015 to 2019 MAME graduates in the College of Teacher Education for Graduate Studies of the University of Northern Philippines in terms of their personal profile, their work-related profile before and after taking their master’s degree, reasons of taking up the program, competency level before and after taking the program, appraisal of the most useful courses offered in the program, evaluation on the contribution of the program to their personal and professional growth and assessment (...) on the features of the program and suggestions of how to improve the program. The researcher utilized mixed method of research. The subjects were the MAME graduates, and a questionnaire and open-ended questions were sent to them thru various online flat forms. Based on the findings of the study, the following conclusions are derived: pursuing graduate studies chooses no sex, civil status or age as long as there is a will to improve one's self; students have math- related educational background and finished the program within the prescribed number of years; having master’s degree could contribute greatly in landing a permanent teaching job in public schools; professional and personal growth and development is the strongest drive to pursue advance education; the program offers subjects that are useful which enhanced the teaching competencies of the graduates and consequently contribute to the holistic development of the graduates; and that there are areas needing improvement in the MAME program. (shrink)

With the growing emphasis on early mathematics education, it is imperative to explore the preparedness of early years mathematics pre-service teachers in relation to content knowledge, beliefs, and dispositions. Therefore, this mixed-methods study explored Lebanese pre-service teachers’ mathematics dispositions and efficacy beliefs in the context of a mathematics methods course. The sample comprised of 11 pre-service teachers who completed a survey prior to and after completing the methods course. Additionally, they each participated in a semi-structured (...) interview shortly after beginning the course. Results revealed pre-service teachers had the most positive beliefs with regards to how mathematics is learned, the nature and usefulness of mathematics, and personal teaching efficacy. Following the course, statistically significant differences were observed with regards to how mathematics is learned, personal teaching efficacy beliefs, and general teaching efficacy beliefs. Practical implications include the importance of subject-specific mathematics methods courses for teachers of younger children, as well as supporting the development of pre-service teachers’ conceptual mathematical understanding prior to entering the profession. (shrink)

With the growing emphasis on early mathematics education, it is imperative to explore the preparedness of early years mathematics pre-service teachers in relation to content knowledge, beliefs, and dispositions. Therefore, this mixed-methods study explored Lebanese pre-service teachers’ mathematics dispositions and efficacy beliefs in the context of a mathematics methods course. The sample comprised of 11 pre-service teachers who completed a survey prior to and after completing the methods course. Additionally, they each participated in a semi-structured (...) interview shortly after beginning the course. Results revealed pre-service teachers had the most positive beliefs with regards to how mathematics is learned, the nature and usefulness of mathematics, and personal teaching efficacy. Following the course, statistically significant differences were observed with regards to how mathematics is learned, personal teaching efficacy beliefs, and general teaching efficacy beliefs. Practical implications include the importance of subject-specific mathematics methods courses for teachers of younger children, as well as supporting the development of pre-service teachers’ conceptual mathematical understanding prior to entering the profession. (shrink)

This paper examines Hobbes’s criticisms of Robert Boyle’s air-pump experiments in light of Hobbes’s account in _De Corpore_ and _De Homine_ of the relationship of natural philosophy to geometry. I argue that Hobbes’s criticisms rely upon his understanding of what counts as “true physics.” Instead of seeing Hobbes as defending natural philosophy as “a causal enterprise … [that] as such, secured total and irrevocable assent,” 1 I argue that, in his disagreement with Boyle, Hobbes relied upon his understanding of natural (...) philosophy as a mixed mathematical science. In a mixed mathematical science one can mix facts from experience with causal principles borrowed from geometry. Hobbes’s harsh criticisms of Boyle’s philosophy, especially in the _Dialogus Physicus, sive De natura aeris_, should thus be understood as Hobbes advancing his view of the proper relationship of natural philosophy to geometry in terms of mixing principles from geometry with facts from experience. Understood in this light, Hobbes need not be taken to reject or diminish the importance of experiment/experience; nor should Hobbes’s criticisms in _Dialogus Physicus_ be understood as rejecting experimenting as ignoble and not befitting a philosopher. Instead, Hobbes’s viewpoint is that experiment/experience must be understood within its proper place – it establishes the ‘that’ for a mixed mathematical science explanation. (shrink)

For an Aristotelian observer, the halo is a puzzling phenomenon since it is apparently sublunary, and yet perfectly circular. This paper studies Aristotle's explanation of the halo in Meteorology III 2-3 as an optical illusion, as opposed to a substantial thing (like a cloud), as was thought by his predecessors and even many successors. Aristotle's explanation follows the method of explanation of the Posterior Analytics for "subordinate" or "mixed" mathematical-physical sciences. The accompanying diagram described by Aristotle is one of (...) the earliest lettered geometrical diagrams, in particular of a terrestrial phenomenon, and versions of it can still be found in modern textbooks on meteorological optics. (shrink)

The subject of this essay-based dissertation is Hume’s natural philosophy. The dissertation consists of four separate essays and an introduction. These essays do not only treat Hume’s views on the topic of natural philosophy, but his views are placed into a broader context of history of philosophy and science, physics in particular. The introductory section outlines the historical context, shows how the individual essays are connected, expounds what kind of research methodology has been used, and encapsulates the research contributions of (...) the essays. The first essay treats Newton’s experimentalist methodology in gravity research and its relation to Hume’s causal philosophy. It is argued that Hume does not see the relation of cause and effect as being founded on a priori reasoning, similar to the way in which Newton criticized non-empirical hypotheses about the causal properties of gravity. Contrary to Hume’s rules of causation, the universal law does not include a reference either to contiguity or succession, but Hume accepts it in interpreting the force and the law of gravity instrumentally. The second article considers Newtonian and non-Newtonian elements in Hume more broadly. He is sympathetic to many prominently Newtonian themes in natural philosophy, such as experimentalism, critique of hypotheses, inductive proof, and the critique of Leibnizian principles of sufficient reason and intelligibility. However, Hume is not a Newtonian philosopher in many respects: his conceptions regarding space and time, the vacuum, the specifics of causation, the status of mechanism, and the reality of forces differ markedly from Newton’s related conceptions. The third article focuses on Hume’s Fork and the proper epistemic status of propositions of mixed mathematics. It is shown that the epistemic status of propositions of mixed mathematics, such as those concerning laws of nature, is that of matters of fact. The reason for this is that the propositions of mixed mathematics are dependent on the Uniformity Principle. The fourth article analyzes Einstein’s acknowledgement of Hume regarding special relativity. The views of the scientist and the philosopher are juxtaposed, and it is argued that there are two common points to be found in their writings, namely an empiricist theory of ideas and concepts and a relationist ontology regarding space and time. (shrink)

The paper delineates a new approach to truth that falls under the category of “Pluralism within the bounds of correspondence”, and illustrates it with respect to mathematical truth. Mathematical truth, like all other truths, is based on correspondence, but the route of mathematical correspondence differs from other routes of correspondence in (i) connecting mathematical truths to a special aspect of reality, namely, its formal aspect, and (ii) doing so in a complex, indirect way, rather than in a simple and direct (...) way. The underlying idea is that an intricate mind is capable of creating intricate routes from language to reality, and this enables it to apply correspondence principles in areas for which correspondence is traditionally thought to be problematic. (shrink)

Elementary preservice teachers (EPTs) substantially impact the quality of mathematics education, and their subject preference and problem-solving performance are essential indicators of their readiness to teach. The study described EPTs’ subject preference and problem-solving performance. Through a sequential explanatory research design, the quantitative inquiry involved 125 random samples, while the qualitative inquiry was participated by 30 non-random samples. Data were obtained by using an online survey and conferencing. Quantitative data were analyzed through descriptive statistics and analysis of variance, whereas (...) qualitative data were themed accordingly. The EPTs displayed unsatisfactory problem-solving performance and preferred to handle subjects other than math. Besides, the analysis found no significant performance differences with the EPTs’ subject preferences. Further, the EPTs who preferred to teach mathematics expressed their confidence in mathematics. Meanwhile, the EPTs who preferred other subjects displayed math avoidance. The study revealed an alarming result indicating that the EPTs are unprepared for teaching. As agents in cultivating the nation’s mathematics education status, these EPTs must be equipped with fundamental content knowledge. It is suggested that educational decision-makers take measures to address the issues identified concerning EPTs’ readiness to teach mathematics successfully. (shrink)

Truth pluralists say that truth-bearers in different “discourses”, “domains”, “domains of discourse”, or “domains of inquiry” are apt to be true in different ways – for instance, that mathematical discourse or ethical discourse is apt to be true in a different way to ordinary descriptive or scientific discourse. Moreover, the notion of a “domain” is often explicitly employed in formulating pluralist theories of truth. Consequently, the notion of a “domain” is attracting increasing attention, both critical and constructive. I argue that (...) this is a red herring. First, I identify the theoretical role for which pluralists appeal to domains, which is to answer what I call the “Individuation Problem”: saying what determines the way in which a particular truth-bearer is apt to be true. Second, I argue that pluralists need not appeal to domains for this purpose. I thus conclude that, despite the usual way of glossing the view, there is no role for the notion of a “domain” to play in the pluralist’s theory of truth. I argue that this defuses the “Problem of Mixed Atomics” and allows the pluralist to sidestep potentially intractable disputes about the nature of domains. (shrink)

The study determined the problem-solving performance and skills of prospective elementary teachers (PETs) in the Northern Philippines. Specifically, it defined the PETs’ level of problem-solving performance in number sense, measurement, geometry, algebra, and probability; significant predictors of their problem-solving performance in terms of sex, socio-economic status, parents’ educational attainment, high school graduated from and subject preference; and their problem-solving skills. The PETs’ problem-solving performance was determined by a problem set consisting of word problems with number sense, measurement, geometry, algebra, and (...) probability. A mixed-method research design was employed. Senior PETs purposively served as a sample where they mostly preferred to teach other subjects than mathematics. PETs who preferred math performed satisfactorily, while prospective teachers who opted for other subjects performed unsatisfactorily. The PETs’ unsatisfactory output indicates the need for remediation to advance the mathematical material skills and enrich the problem-solving abilities of these primary schools' potential teachers. Besides, results showed that subject preference strongly affected and predicted the problem-solving success of the PETs. PETs who preferred to teach mathematics performed significantly better than their counterparts; hence, mathematics as a field of specialization in the Bachelor of Elementary Education program may be considered by teacher education institutions. Further, most PETs displayed lack of problem-solving skills; thus, a Problem-Solving course is recommended for them. (shrink)

Various changes and advances have taken place in the ways of teaching and learning. With the encountered global pandemic crisis, flexible learning has been practiced particularly in state universities and colleges. This study sought to determine the level of procedural fluency in College Algebra as well as the difficulties and interventions applied by tertiary students of Cotabato State University (CSU) in the flexible learning set-up. The period covered by the study was during the first semester of the school year 2021-2022. (...) The respondents were a sample of 30 first-year mathematics major students of CSU. It used mixed methods; the quantitative approach was utilized to know the students’ knowledge of procedures in solving mathematical problems while the qualitative approach was utilized to explore the difficulties of the students in learning mathematics as well as the coping strategies that can serve as basis for mathematics intervention program. The findings revealed that most of the respondents have a low level of procedural fluency in College Algebra, particularly emerging in the understanding the problem, devising a strategy, and solving steps while inept in the problem-solving checking process. On the part of new normal learning, difficulties were experienced such as poor knowledge of the prerequisite skills and unstable internet connection. As part of their interventions, facing the encountered problems, practicing repeatedly, and watching online video tutorials were applied. Based on the findings of the study, it is concluded that the first-year students have low level of procedural fluency in College Algebra problem-solving particularly in the Polya’s principles of understanding the problem, devising a plan, carrying out the plan, and checking the answer. Because of the learning challenges encountered by the students, it is recommended to develop step-by-step video tutorials that can address their problem-solving difficulties and supplement their learning in the flexible mode of delivery. (shrink)

My aim in this chapter is to extend the Realist account of the foundations of linguistics offered by Postal, Katz and others. I first argue against the idea that naive Platonism can capture the necessary requirements on what I call a ‘mixed realist’ view of linguistics, which takes aspects of Platonism, Nominalism and Mentalism into consideration. I then advocate three desiderata for an appropriate ‘mixed realist’ account of linguistic ontology and foundations, namely (1) linguistic creativity and infinity, (2) (...) linguistics as a theory of types (and not tokens) and (3) independence but structural respect between language and the linguistic competence thereof. My own brand of mixed realism, what I call ante rem realism, is defended along the lines of an ante rem or non-eliminative structuralism, the likes of which has been offered for mathematics by Resnik (1997) and Shapiro (1997). In other words, grammars describe a mind-independent (but not necessarily unconnected) linguistic reality in terms of linguistic patterns or structures also known as natural languages. I further amend this picture to allow for the possibility of a naturalistic account of language acquisition and evolution by arguing against a particular view of the type-token distinction. (shrink)

My goal in this paper is, to tentatively sketch and try defend some observations regarding the ontological dignity of object references, as they may be used from within in a formalized language. -/- Hence I try to explore, what properties objects are presupposed to have, in order to enter the universe of discourse of an interpreted formalized language. -/- First I review Frege′s analysis of the logical structure of truth value definite sentences of scientific colloquial language, to draw suggestions from (...) his saturated vs. unsaturated sentence components paradigm. -/- Next try investigate, in how far reference to non pure math objects might allow for a role as argument of a truth value function. Object kinds to be considered are: common sense objects, technical objects, humanities object kinds (social, psychical, ...), objects of art, ... , be they abstract, concrete, or in this respect mixed objects. -/- Then have a comment on the just referenced label abstract objects. -/- Next try to get an idea wrt the ontological significance of the fact, that pure math objects and functions in some important classical cases can be uniquely defined by means of categorical theories. Here, in the course of my argument, I have a little corollary wrt the standard model of first order Peano arithmetic, reducing the epistemological significance of the existence of the non standard models. -/- Next, wrt a special concept of a formalized empirical theory, I care for whether the impure math objects and mixed objects described here, and complying best with truth value function mapping, are also reliable candidates for the ontological commitment of such theories: and discuss an alternative, which reduces the ontological significance of the universe of discourse of the theories intended models. -/- In the end I sum up what is - from my point of view - the status quo, according to my respective findings. (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)

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory (...) to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives. (shrink)

This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents (...) some theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well. (shrink)

What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition that accounts for the time-asymmetry of the universe. The natural choice is given not by a wave function but by a density matrix. I begin by classifying quantum theories into two types: theories with a fundamental wave function and theories with (...) a fundamental density matrix. The Past Hypothesis is compatible with infinitely many initial wave functions, none of which seems to be particularly natural. However, once we turn to density matrices, the Past Hypothesis provides a natural choice---the normalized projection onto the Past Hypothesis subspace in the Hilbert space. Nevertheless, the two types of theories can be empirically equivalent. To provide a concrete understanding of the empirical equivalence, I provide a novel subsystem analysis in the context of Bohmian theories. Given the empirical equivalence, it seems empirically underdetermined whether the universe is in a pure state or a mixed state. Finally, I discuss some theoretical payoffs of the density-matrix theories and present some open problems for future research. (Bibliographic note: the thesis was submitted for the Master of Science in mathematics at Rutgers University.). (shrink)

What is the proper metaphysics of quantum mechanics? In this dissertation, I approach the question from three different but related angles. First, I suggest that the quantum state can be understood intrinsically as relations holding among regions in ordinary space-time, from which we can recover the wave function uniquely up to an equivalence class (by representation and uniqueness theorems). The intrinsic account eliminates certain conventional elements (e.g. overall phase) in the representation of the quantum state. It also dispenses with first-order (...) quantification over mathematical objects, which goes some way towards making the quantum world safe for a nominalistic metaphysics suggested in Field (1980, 2016). Second, I argue that the fundamental space of the quantum world is the low-dimensional physical space and not the high-dimensional space isomorphic to the ``configuration space.'' My arguments are based on considerations about dynamics, empirical adequacy, and symmetries of the quantum mechanics. Third, I show that, when we consider quantum mechanics in a time-asymmetric universe (with a large entropy gradient), we obtain new theoretical and conceptual possibilities. In such a model, we can use the low-entropy boundary condition known as the Past Hypothesis (Albert, 2000) to pin down a natural initial quantum state of the universe. However, the universal quantum state is not a pure state but a mixed state, represented by a density matrix that is the normalized projection onto the Past Hypothesis subspace. This particular choice has interesting consequences for Humean supervenience, statistical mechanical probabilities, and theoretical unity. (shrink)

We look into the ontology of quantum theory as distinct from that of the classical theory in the sciences. Theories carry with them their own ontology while the metaphysics may remain the same in the background. We follow a broadly Kantian tradition, distinguishing between the noumenal and phenomenal realities where the former is independent of our perception while the latter is assembled from the former by means of fragmentary bits of interpretation. Theories do not tell us how the noumenal world (...) is constituted but are conceptual constructs applying to models generated in the phenomenal world within limited contexts. -/- The ontology of quantum theory principally rests on the view that entities in the world are pervasively correlated with one another not by means of probabilities as in the case of the classical theory, but by means of probability amplitudes involving finely tuned phases characterising the oscillatory behaviour of quantum mechanical states. -/- The amplitude-dependent correlations (quantum entanglement) exist over and above the classical ones expressed in terms of probabilities. While the classical correlations are essentially local in nature, quantum correlations are shared globally in the process of environment-induced decoherence. The decoherence is an effectively random process that removes local correlations in the course of global sharing of entanglement—the removal being especially manifest in the case of systems that appear as classical ones. It is this aspect of the decoherence process that makes the so-called measurement postulate (one relating to wave function collapse) cohere with the rest of the principles of quantum theory where the latter implies a Schrodinger type time evolution of quantum mechanical systems. -/- The mathematical basis of the quantum correlations consists of the description of pure states of a system in terms of vectors in a linear vector space (a mixed state appears as an admixture of pure states with some probability distribution associated with it) and, in addition, the description of (pure) states of composite systems as vectors in the product space arising from the component sub-systems. -/- The crucial aspect of the decoherence process, of significance in the context of the apparent incompatibility of the measurement postulate with the unitary Schrodinger evolution, relates to the fact that it is almost instantaneous in the case of a classical object (one that is nevertheless amenable to a quantum description). Indeed, the decoherence time is, in all likelihood, of the order of the Planck scale, being driven by field fluctuations in the Planck regime. This points to factors of an unknown nature determining the finest details of the decoherence process since Planck scale physics remains an obscure terrain. -/- In other words, quantum theory is, to all intents and purposes, in the need of a radical revision, in keeping with the fact that all theories are defeasible and need revision as our domains of experience expand and get realigned in a complex manner. The context within which quantum theory (and quantum field theory too) is defined is set precisely by the Planck scale, across which a novel theoretical framework is likely to emerge. However, as in the case of theory revisions in general, that emerging theory will stand in an asymmetric relation of incommensurability with the present-day quantum theory, where the concepts of the latter will be comprehensible in terms of those of the former, but the converse will not hold. (shrink)

This research article was championed as a way of providing discourses pertaining to the concept of "Critical Realism (CR)" approach, which is amongst many othe forms of competing postmodern philosophical concepts for the engagement of dialogical discourses in the area of established econonetric methodologies for effective policy prescription in the economic science discipline. On the the whole, there is no doubt surrounding the value of empirical endeavours in econometrics to address real world economic problems, but equally so, the heavy weighted (...) use and reliance on mathematical contents as a way of justifying its scientific base seemed to be loosing traction of the intended focus of economics when it comes to confronting real world problems in the domain of social interaction. In this vein, the construction of mixed methods discourse(s), which favour that of CR philosophy is hereby suggested in this article as a way forward in confronting with issues raised by critics of mainstream economics and other professionals in the postmodern era. (shrink)

Time has puzzled scientists. Some see it as just a tool and a unit of measurement, while others consider time to be a real thing and needs to be measured. There are also those who believe that time is an ancient thing that arose with the creation of the universe and the Earth, running parallel to life in them, and counting every movement, event, or speed in them. While some see it as an essential part and a major component of (...) the virtual relationship that includes life and place, there are also those who see time as a metaphysical thing that only appeared and developed in human consciousness and then mixed with the physics of life. Is duration measured by movement, or is movement measured by duration or time? Here began the dilemma of this research: How did time transform from a concept that reads and measures the flow of time forward, that is, the flow of time, according to Isaac Newton, into a physical measuring tool that calculates the movement, speed, and state of things? Then the concept turned into a tool that calculates the speed of light and tells the story of the origin and development of the universe. Scientists will not agree on a clear, direct, and frank interpretation of the concept of time, but people generally agree that time can be divided into past, present, and future. This division, according to this research, has gradually developed in human consciousness since the manifestations of knowledge appeared in the human mind and began to take its first steps. In the wondrous land where the sun rises repeatedly, the moon also rises, planets and stars appear, trees grow, rivers and seas overflow, storms and rain intensify, light appears and then darkness, and creatures wake up and sleep, mysteriously and repeatedly, until all these phenomena have become Appearances are measurable, with the development of human consciousness. In this brief research paper, we will discuss what is called “the present,” and the validity of its existence in the real time in which we live, and where its place is in human consciousness, and why scientists let it tamper with mathematical, physical, and social matter, and transformed it from a mere thing that does not exist, to a rest stop, which sometimes takes a long time., between the past and the future. (shrink)

In this essay, we consider the formal and ontological implications of one specific and intensely contested dialectical context from which Deleuze’s thinking about structural ideal genesis visibly arises. This is the formal/ontological dualism between the principles, ἀρχαί, of the One (ἕν) and the Indefinite/Unlimited Dyad (ἀόριστος δυάς), which is arguably the culminating achievement of the later Plato’s development of a mathematical dialectic.3 Following commentators including Lautman, Oskar Becker, and Kenneth M. Sayre, we argue that the duality of the One and (...) the Indefinite Dyad provides, in the later Plato, a unitary theoretical formalism accounting, by means of an iterated mixing without synthesis, for the structural origin and genesis of both supersensible Ideas and the sensible particulars which participate in them. As these commentators also argue, this duality furthermore provides a maximally general answer to the problem of temporal becoming that runs through Plato’s corpus: that of the relationship of the flux of sensory experiences to the fixity and order of what is thinkable in itself. Additionally, it provides a basis for understanding some of the famously puzzling claims about forms, numbers, and the principled genesis of both attributed to Plato by Aristotle in the Metaphysics, and plausibly underlies the late Plato’s deep considerations of the structural paradoxes of temporal change and becoming in the Parmenides, the Sophist, and the Philebus. After extracting this structure of duality and developing some of its formal, ontological, and metalogical features, we consider some of its specific implications for a thinking of time and ideality that follows Deleuze in a formally unitary genetic understanding of structural difference. These implications of Plato’s duality include not only those of the constitution of specific theoretical domains and problematics, but also implicate the reflexive problematic of the ideal determinants of the form of a unitary theory as such. We argue that the consequences of the underlying duality on the level of content are ultimately such as to raise, on the level of form, the broader reflexive problem of the basis for its own formal or meta-theoretical employment. We conclude by arguing for the decisive and substantive presence of a proper “Platonism” of the Idea in Deleuze, and weighing the potential for a substantive recuperation of Plato’s duality in the context of a dialectical affirmation of what Deleuze recognizes as the “only” ontological proposition that has ever been uttered. This is the proposition of the univocity of Being, whereby “being is said in the same sense, everywhere and always,” but is said (both problematically and decisively) of difference itself. (shrink)

In a series of formal studies and less formal applications, Hong and Page offer a ‘diversity trumps ability’ result on the basis of a computational experiment accompanied by a mathematical theorem as explanatory background (Hong & Page 2004, 2009; Page 2007, 2011). “[W]e find that a random collection of agents drawn from a large set of limited-ability agents typically outperforms a collection of the very best agents from that same set” (2004, p. 16386). The result has been extremely influential as (...) an epistemic justification for diversity policy initiatives. Here we show that the ‘diversity trumps ability’ result is tied to the particular random landscape used in Hong and Page’s simulation. We argue against interpreting results on that random landscape in terms of ‘ability’ or ‘expertise.’ These concepts are better modeled on smother and more realistic landscapes, but keeping other parameters the same those are landscapes on which it is groups of the best performing that do better. Smoother landscapes seem to vindicate both the concept and the value of expertise. Change in other parameters, however, also vindicates diversity. With an increase in the pool of available heuristics, diverse groups again do better. Group dynamics makes a difference as well; simultaneous ‘tournament’ deliberation in a group in place of the ‘relay’ deliberation in Hong and Page’s original model further emphasizes an advantage for diversity. ‘Tournament’ 2 dynamics particularly shows the advantage of mixed groups that include both experts and non-experts. As a whole, our modeling results suggest that relative to problem characteristics and conceptual resources, the wisdom of crowds and the wisdom of the few each have a place. We regard ours as a step toward attempting to calibrate their relative virtues in different modelled contexts of intellectual exploration. (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)

The investigation into logical form and structure of natural sciences and mathematics covers a significant part of contemporary philosophy. In contrast to this, the metatheory of normative theories is a slowly developing research area in spite of its great predecessors, such as Aristotle, who discovered the sui generis character of practical logic, or Hume, who posed the “is-ought” problem. The intrinsic reason for this situation lies in the complex nature of practical logic. The metatheory of normative educational philosophy and (...) theory inherits all the difficulties inherent in the general metatheory but has also significantly contributed to its advancement. In particular, the discussion on its mixed normative-descriptive character and complex composition has remained an important part of research in educational philosophy and theory. The two points seem to be indisputable. First, the content of educational philosophy and theory is a complex one, connecting different disciplines. Second, these disciplines are integrated within the logical form of practical inference or means-end reasoning. On the other hand, the character of consequence relation in this field, although generally recognized as specific, represents an unresolved prob- lem, a solution of which requires a sophisticated logical theory and promises to influence the self- understanding of educational philosophy and theory. (shrink)

The post-conflict societies of Bosnia and Kosovo continue to be plagued by the deleterious effects of ethno-nationalism and ethnic enclaves. Unfortunately, this mix impedes both democracy and peace building within these Balkan countries. One way to promote such building is for these enclaves to collapse, thereby allowing multiethnic societies to develop. This essay proposes that enclaves be dealt with physically by ridding them of those evocative objects that help to create and maintain enclaves. By getting physical in this way, however, (...) we find ourselves in a dilemma, caught on the horns of legality and expediency. Yet there is a promising path between the horns that involves civic design. This essay offers a physicalist theory of managing these impediments to democracy and peace building, beginning with four hypotheses, followed by an abstraction and mathematization in the form of a matrix, a dilemma arising from these hypotheses, and possible solutions. (shrink)

►JOHN CORCORAN AND IDRIS SAMAWI HAMID, Two-method errors: having it both ways. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: [email protected] Philosophy, Colorado State University, Fort Collins, CO 80523-1781 USA E-mail: [email protected] Where two methods produce similar results, mixing the two sometimes creates errors we call two-method errors, TMEs: in style, syntax, semantics, pragmatics, implicature, logic, or action. This lecture analyzes examples found in technical and in non-technical contexts. One can say “Abe knows whether Ben draws” in two other (...) ways: ‘Abe knows whether or not Ben draws’ or ‘Abe knows whether Ben draws or not’. But a stylistic TME occurs in ‘Abe knows whether or not Ben draws or not’. One can say “Abe knows how Ben looks” using ‘Abe knows what Ben looks like’. But syntactical TMEs are in ‘Abe knows what Ben looks’ and in ‘Abe knows how Ben looks like’. One can deny that Abe knows Ben by prefixing ‘It isn’t that’ or by interpolating ‘doesn’t’. But a pragmatic TME occurs in trying to deny that Abe knows Ben by using ‘It isn’t that Abe doesn’t know Ben’. There are several standard ways of defining truth using sequences. Quine’s discussions in the 1970 first printing of Philosophy of logic [3] and in previous lectures were vitiated by mixing two [1, p. 98]. The logical TME in [3], which eluded Quine’s colleagues, was corrected in the 1978 sixth printing [2]. But Quine never explicitly acknowledged, described, or even mentioned the error. This lecture presents and analyses two-method errors in the logic literature. [1] JOHN CORCORAN, Review of Quine’s 1970 Philosophy of Logic. In Philosophy of Science, vol. 39 (1972), pp. 97–99. [2] JOHN CORCORAN, Review of sixth printing of Quine’s 1970 Philosophy of Logic. In Mathematical Reviews MR0469684 (1979): 57 #9465. [3] WILLARD VAN ORMAN QUINE, Philosophy of logic, Harvard, 1970/1986. (shrink)

In this paper, the performance of inverted pendulum have been Investigated using robust control theory. The robust controllers used in this paper are H∞ Loop Shaping Design Using Glover McFarlane Method and mixed H∞ Loop Shaping Controllers. The mathematical model of Inverted Pendulum, a DC motor, Cart and Cart driving mechanism have been done successfully. Comparison of an inverted pendulum with H∞ Loop Shaping Design Using Glover McFarlane Method and H∞ Loop Shaping Controllers for a control target deviation of (...) an angle from vertical of the inverted pendulum using two input signals (step and impulse). The simulation result shows that the inverted pendulum with mixed H∞ Loop Shaping Controller to have a small rise time, settling time and percentage overshoot in the step response and having a good response in the impulse response too. Finally the inverted pendulum with mixed H∞ Loop Shaping Controller shows the best performance in the overall simulation result. (shrink)

Quantum theory brought an irreducible lawlessness in physics. This is accompanied by lack of specification of state of a system. We can not measure states even though they ever existed. We can measure only transition from one state into another. We deduce this lack of determination of state mathematically, and thus provide formalism for maximum precision of determination of mixed states. However, the results thus obtained show consistency with Heisenberg's uncertainty relations.

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 and behavior, 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 Wittgenstein, arguably the greatest intuitive psychologist of all time, has laid it before us long ago, beginning with the Blue and Brown Books in the early 1930’s. Language is programmed in our genes and is involved in nearly all our social behavior. Philosophy in the strict sense (i.e., academic philosophy), is as Wittgenstein showed us, the study of the way language is used (language games) and I regard it as the descriptive psychology of higher order thought (i.e., pretty much everything involving language which is often called System 2 or slow thinking). However, as I hope I have shown in my writings over the last decade, nonlinguistic behavior or System 1 or fast thinking is also described with language and this leads to endless confusion which I have tried to clarify here and which is summarized in the tables that I present. 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 with critical reviews of the writings of a wide variety of behavioral scientists (i.e., everyone). The first group of articles attempt to give some insight into how we behave that is reasonably free of theoretical delusions. In the next three groups I comment on three of the principal delusions preventing a sustainable world— technology, religion and politics (cooperative groups). People believe that society can be saved by them, so I provide some suggestions in the rest of the book as to why this is unlikely via short articles and reviews of recent books by well-known writers. (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)

This collection of articles was written over the last 10 years and edited to bring them up to date (2017). The copyright page has the date of the 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., 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. The first group of articles attempts to give some insight into how we behave that is reasonably free of the theoretical delusions that are universal. In the next group, I show how these insights apply by reviewing some books in philosophy and psychology. Next I review books on science and religion and finally provide reviews and articles showing how understanding of both science and philosophy gives insight into the tragic delusions destroying the world. People believe that society can be saved by science, religion and politics, so I provide some suggestions as to why this is unlikely via short articles and reviews of recent books by well-known writers. 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. 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 ii 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 and behavior, 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. iii 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 (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 futures. Many of the articles describe the ‘digital delusions’, which confuse the language games of System 2 with the automatisms of System 1, 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. Also for ‘reduction’ of 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 (and cannot be made clear) what the ‘results’ mean. Reductionist metaphysics is a joke, but most scientists and philosophers lack the appropriate sense of humor. Other digital delusions are that 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. Hi-tech enthusiasts hugely underestimate the problems iv resulting from unrestrained motherhood, and of course it is neither profitable nor politically correct (and now with third world supremacism dominant, not even possible) to be honest about it. The last section describes various versions of the ‘altruism delusion’ that we are selected for cooperation, and that the euphonious ideals of Democracy, Diversity and Equality 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 it. 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. 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 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 (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). Many accept the delusion that we are selected for cooperation with people generally (group selection or altruism) and not just our immediate relatives (kin selection or inclusive fitness), so I spend some time in the essays of the last section demolishing this fantasy. One thing rarely mentioned by the group selectionists is the fact that, even were ‘group selection’ possible, selfishness is at least as likely (probably far more likely in most contexts) to be group selected for as altruism. Just try to find examples of true altruism in nature –the fact that we can’t (which we know is not possible if we understand evolution) tells us that its apparent presence in humans is an artefact of modern life concealing the facts, and that it can no more be selected for than the tendency to suicide (which in fact it is). One does not really need science or mathematics to grasp this – it is crushingly obvious that an v organism cannot be selected for behavior that decreases the frequency of its own genes in the next generation. One might also benefit from considering a phenomenon never (in my experience) mentioned by group selectionists -- cancer. No group has as much in common as the (originally) genetically identical cells in our own bodies-a 100 trillion cell clone-- but we are all born with thousands and perhaps millions of cells that have already taken the first step on the path to cancer and generate millions to billions of cancer cells in our life. If we did not die of other things first, we (and perhaps all multicellular organisms) would all die of cancer. Only a massive and hugely complex mechanism built into our genome that represses or derepresses trillions of genes in trillions of cells, and kills and creates billions of cells a second, keeps the majority of us alive long enough to reproduce. One might take this to imply that a just, democratic and enduring society for any kind of entity on any planet in any universe is only a dream, and that no being or power could make it otherwise. It is not only ‘the laws’ of physics that are universal and inescapable, or perhaps we should say that inclusive fitness is a law of physics. The great mystic Osho said that the separation of God and Heaven from Earth and Humankind was the most evil idea that ever entered the Human mind. In the 20th century an even more evil notion arose—that humans are born with rights, rather than having to earn privileges. Thus, every day the population increases by 200,000, who must be provided with resources to grow and space to live, and who soon produce another 200,000 etc. And one almost never hears it noted that what they receive must be taken from those already alive. Their lives diminish those already here in both major obvious and countless subtle ways. Every new baby destroys the earth from the moment of conception. There cannot be human rights without human wrongs. It cannot be more obvious, but one will never see the streets full of protesters against motherhood. 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 4 billion more ca. 2100 will collapse industrial civilization and bring about starvation, disease, violence and war on a staggering scale. The earth loses about 2% of it’s topsoil every year, so as it nears 2100, most of it’s 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 vi nightmare of crime and poverty. China will continue to overwhelm America and the world, as long as it maintains the dictatorship which limits selfishness. 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. 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. The popular notions supported by the Democratic Party and Third World Supremacists are that Democracy, Diversity, Equality and Social Justice will produce a Utopia in America and the world, but it is clear as crystal that they unavoidably foster selfishness and divisiveness and are producing collapse. Hence my concluding essay “Suicide by Democracy”. The most basic facts, almost never mentioned, are that there are not enough resources in America or the world to lift a significant percentage of the poor out of poverty and keep them there. Even the attempt to do this is already bankrupting America and destroying the world. The earth’s capacity to produce food decreases daily, as does our genetic quality. And now, as always, by far the greatest enemy of the poor is other poor and not the rich. -/- My writings are available 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)

This collection of articles and reviews 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 and dictatorship appears inevitable. -/- Since philosophy proper is essentially the same as the descriptive psychology of higher order thought (behavior), and 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 and behavior, 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. -/- Although I separate the book into sections on philosophy and psychology, religion, biology, the ‘hard sciences’ and politics/sociology/economics, 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 problems 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. -/- I hope that these essays will help to separate the philosophical issues of language use from the scientific factual issues, and in some small way hinder the collapse of civilization, or at least make it clear why it is doomed. -/- Those wishing to read my other writings may see Talking Monkeys 2nd ed (2019), The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle 2nd ed (2019), Suicide by Democracy 3rd ed (2019), The Logical Stucture of Human Behavior (2019) and Suicidal Utopian Delusions in the 21st Century 4th ed (2019) . (shrink)

This article focuses on the criticisms of current approaches in educational research methodology. Itsummarizes rationales for mixed methods and argues that the mixing quantitative paradigm andqualitative paradigm is problematic due to practical and philosophical arguments. It is alsoindicated that the current rise of mixed methods work has increased problems with quantitativeand qualitative methods. In this article we offer a different symbolic system, with differentlogical form for describing educational phenomena based on the philosophical assumptions andnew mathematical reasoning: para-quantitativism. Para-quantitative (...) theory is an approachwhich has been developed in respect to close relationship between paradigm and method, using apostpositivist transcendental realism as a philosophical beginning of the research methodology,taking Operational Logic System or Fuzzy Logic System (OLS/FLS) as logic of scientificresearch in education. (shrink)

Latest Sermon from the Church of Fundamentalist Naturalism by Pastor Hofstadter. Like his much more famous (or infamous for its relentless philosophical errors) work Godel, Escher, Bach, it has a superficial plausibility but if one understands that this is rampant scientism which mixes real scientific issues with philosophical ones (i.e., the only real issues are what language games we ought to play) then almost all its interest disappears. I provide a framework for analysis based in evolutionary psychology and the work (...) of Wittgenstein (since updated 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)

A variety of philosophical positions have been proposed and developed to motivate, justify, and guide mixed methods research. This chapter provides a brief overview of the main positions in the debate over the philosophical foundations of mixed methods research. It shows that ‘philosophical foundations’ means differently while different positions provide ‘philosophical foundations’ in different senses. It also highlights the significance of the collaboration between researchers and philosophers in the examination of the philosophical foundations of mixed methods research.

The term 'covert mixed quotation' describes cases in which linguistic material is interpreted in the manner of mixed quotation — that is, used in addition to being mentioned — despite the superficial absence of any commonly recognized conventional devices indicating quotation. After developing a novel theory of mixed quotation, I show that positing covert mixed quotation allows us to give simple and unified treatments of a number of puzzling semantic phenomena, including the projective behavior of conventional (...) implicature items embedded in indirect speech reports and propositional attitude ascriptions, so-called 'c-monsters,' metalinguistic negation, metalinguistic negotiation, and 'in a sense' constructions. (shrink)

There is a major debate as to whether there are non-causal mathematical explanations of physical facts that show how the facts under question arise from a degree of mathematical necessity considered stronger than that of contingent causal laws. We focus on Marc Lange’s account of distinctively mathematical explanations to argue that purported mathematical explanations are essentially causal explanations in disguise and are no different from ordinary applications of mathematics. This is because these explanations work not by appealing to what (...) the world must be like as a matter of mathematical necessity but by appealing to various contingent causal facts. (shrink)

Notwithstanding diverse opinions and debates about mixing methods, mixed methods research (MMR) is increasingly being used in sport and exercise psychology. In this paper, we describe MMR trends within leading sport and exercise psychology journals and explore critical realism as a possible underpinning framework for conducting MMR. Our meta-study of recent empirical mixed methods studies published in 2017–2019 indicates that eight (36%) of the 22 MMR studies explicitly stated a paradigmatic position (five drew on pragmatism, two switched paradigms (...) between qualitative and quantitative elements of the study, and one was situated in relativist-interpretivism). The remaining 14 (64%) studies did not report their underpinning research philosophical assumptions. Evaluating the merits and limitations of these positions against critical realist assumptions suggests that several paradigmatic disagreements are potentially reconcilable. These include (a) maintaining that ontological and epistemological concerns are important for methodological integrity of a mixed methods study; (b) switching between paradigms in the same study is problematic; and (c) refuting the qualitative-quantitative incommensurability thesis, therefore allowing mixed methods research without compromising philosophical coherence. From a critical realist position, we suggest that both quantitative and qualitative designs are justifiable in a mixed methods study because (1) they help corroborate, refine, or refute plausible explanations of phenomena (epistemological), but (2) with different methodologies utilised to perform different tasks in the same research design related to different psycho-social system features (ontological). We call for a collaborative engagement by researchers across paradigmatic positions to work towards the advancement of methodological pluralism in our research community. (shrink)

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

It has proved challenging to account for the dual role that a directly quoted part of a 'that'-clause plays in so-called mixed quotation. The Davidsonian account, elaborated by Cappelen and Lepore, handles many cases well; but it fails to accommodate a crucial feature of mixed quotation: that the part enclosed in quotation marks is used to specify not what the quoter says when she utters it, but what the quoted speaker says when she utters it. Here I show (...) how the Davidsonian can do better. The proposal rests on the idea that mixed quotation involves deferred demonstration: a mixed quotati on specifies what the subject says partly by demonstrating the quoter's utterance of the unquoted part and partly by deferred-demonstrating the subject's utterance of the quotation-marked part. (shrink)