The concept of the subject, of what Hegel calls absolute negativity, already appears early in the logic of being.1 Absolute negativity, negation of the negation, occurs throughout the logic as identity in difference understood as self-identification under different descriptions. First, the subject refers to itself merely under an incomplete description. Secondly, it refers to something other than itself under a second description which is logically required by the first. (For example, the description of being in general requires some (...) determinate description of being in particular). But this second description is dialectically excluded by the assumption that the first description is complete. Thirdly, the subject negates its negation of the other. It discovers itself in the other, under the other description, and thus comes to refer to itself less incompletely. This is Hegel in the analytic mode. (shrink)

Reading Hegel‘s Science of Logic - Irfan Ajvazi.

I propose a new reading of Hegel’s discussion of modality in the ‘Actuality’ chapter of the Science of Logic. On this reading, the main purpose of the chapter is a critical engagement with Spinoza’s modal metaphysics. Hegel first reconstructs a rationalist line of thought — corresponding to the cosmological argument for the existence of God — that ultimately leads to Spinozist necessitarianism. He then presents a reductio argument against necessitarianism, contending that as a consequence of necessitarianism, no adequate (...) explanatory accounts of facts about finite reality can be given. (shrink)

Parmenides plays an important role in the first section of Hegel’s Science of Logic due to his definition of being as a pure thought-determination. This article investigates, first, how Hegel conceives the Parmenidean being. Secondly, by discussing Hegel's logical analysis of pure being and pure nothing, it aims to show why and how such conception of being, according to Hegel, provides a crucial insight into the function of the understanding.

This article challenges the prevailing interpretations of Hegel's account of the concept "contradiction" in the Science of Logic by arguing that it is concerned with the principle of Hegel's method rather than with the classical law of non-contradiction. I first consider Hegel's Doctrine of Essence in view of Kant's discussion of the concepts of reflection in the first Critique. On this basis, I examine Hegel's account of the logical principles based on the concepts "identity," "opposition," and "contradiction." Finally, (...) I point out how the principle Hegel derives from the concept of contradiction actually informs his own method. (shrink)

Review for a non-academic audience of Huaping Lu-Adler, _Kant and the Science of Logic_.

Axel Honneth reconstructs Hegel’s social and political philosophy on the basis of the concept of recognition. For Honneth, recognition is a constitutive relation between individuals that is in principle symmetrical. By conceiving recognition through symmetry, Honneth effectively bans the inclusion of power within recognitive relation. He thus regards the relations of power as cases of non-recognition or misrecognition. In this paper, I develop an alternative theory of the constitutive relation between individuals for Hegel, one that is based on the asymmetrical (...) relation of power. To this aim, I focus on the chapter of “determinations of reflection” in the Science of Logic. Through a close analysis of Hegel’s Logic, I argue that the most fundamental form of relation between individuals is the relation of opposition, that individuals are solely constituted in and through the relation of opposition, and that the relation of opposition is essentially asymmetrical. Together, these claims establish... (shrink)

This paper contributes to explaining the rise of logical empiricism in mid-twentieth century (North) America and to a better understanding of American philosophy of science before the dominance of logical empiricism. We show that, contrary to a number of existing histories, philosophy of science was already a distinct subfield of philosophy, one with its own approaches and issues, even before logical empiricists arrived in America. It was a form of speculative philosophy with a concern for speculative metaphysics, normative (...) issues relating to science and society and issues which later were associated with logical empiricist philosophy of science, issues such as confirmation, scientific explanation, reductionism and laws of nature. Further, philosophy of science was not primarily pragmatist in orientation. We also show, with the help of our historical characterization, that a recent account of the emergence of analytic philosophy applies to the rise of logical empiricism. It has been argued that the emergence of American analytic philosophy is partly explained by analytic philosophers’ use of key institutions, including of journals, to marginalize speculative philosophy and promote analytic philosophy. We argue that this use of institutions included the marginalization of speculative and value-laden philosophy of science and the promotion of logical empiricism. (shrink)

I outline the theoretical framework of, and three research programs within American speculative philosophy of science during the period 1900-1931. One program applies verificationism to research in psychology, one investigates the methodology of research programs, and one analyses scientific explanation and other scientific concepts. The primary sources for my outline are works by Morris Raphael Cohen, Grace Andrus de Laguna, Theodore de Laguna, Edgar Arthur Singer Jr., Harold Robert Smart, and Marie Collins Swabey. I also use my outline to (...) provide a partial comparison of American speculative philosophy of science and 1930s logical positivism. My comparison suggests that logical positivism was a proposal for substantially narrowing down and winding back American philosophy of science and was based on positions that were already problematized in the American context. -/- . (shrink)

A critical discussion of Lu-Adler's chapter on Kant's mature view of pure general logic. I sketch an alternative interpretation of its formality on which Kant would hold no deduction is possible of this logic's laws.

In this study, the aim is to view on the ‘Being, Nothing and Becoming’ that takes place at the beginning of ‘The Doctrine of Being’ which is the first book of Hegel’s Science of Logic. Even if the main issue is the ‘Being, Nothing and Becoming’, it is considered within a holistic view. İt is the important to carry out the aim of this study that some questions are need to be asked and answered in order to make (...) real having a holistic view considered. These questions: (1) Why does The Science of Logic start with ‘Being’?, (2) What is ‘being’?, (3) What does to happen the ‘nothing’ from ‘being’ mean? How does it happen?, (4) What is ‘nothing’?, (5) What does to happen the ‘becoming’ from ‘being’ and ‘nothing’ mean? How does it happen?, (6) What is becoming? In the study, it is aimed that to proceed with the answers of these questions. The other part of the study is to view on a deep comprehension which provides to answer the questions mentioned above. At this point, it benefits from explanations on understanding, dialectic and speculation taken place at 79.-82. paragraphs of Logic which is the first book of Hegel’s Encyclopedia. At this context, an aim occurs to ask and answer some questions like: (a) What is ‘understanding’?, (b) What is ‘dialectic’?, (c) What is ‘speculation’? In conclusion, the final aim is to explain why Hegel’s proceeds with these like this way –not like another way– and how is to proceed with these like this way. (shrink)

Filozofia analityczna po logicyzmie Fregego i atomizmie logicznym Russella odziedziczyła szereg założeń związanych z istnieniem rodzajowej dziedziny bytów indywidualnych, których tożsamość i elementarne określenia już mamy zdefiniowane. Te „indywidua” istnieją tylko w idealnych „światach możliwych” i nie są niczym innym jak zbiorami posiadającymi strukturę bądź czystymi zbiorami matematycznymi. W przeciwieństwie do takich czysto abstrakcyjnych modeli, Hegel analizuje rolę pojęciowych rozróżnień i odpowiednich brakujących inferencji w rzeczywistym świecie. Tutaj wszystkie obiekty są przestrzennie i czasowo skończone. Nawet jeśli rzeczywiste rzeczy poruszają się (...) zgodnie z pewnymi formami, są tylko momentami w całościowym procesie. Wszelako, formy te nie są przedmiotami bezpośredniej, empirycznej obserwacji, lecz zakładają udane i powtarzalne działania i akty mowy. W rezultacie żadna semantyka odnoszącej się do świata referencji nie może obyć się bez kategorii Heglowskich, które wykraczają daleko poza narzędzia opartej wyłącznie na relacjach logiki matematycznej. (shrink)

The purpose of this article is to present an evidence-supported curriculum covering the fundamentals of logic, reasoning, and argumentation skills to address the emphasized basic knowledge, skills, and abilities required to be scientifically literate, which will prepare the public to understand and engage with science meaningfully. An analytic-synthetic approach toward understanding the notion of public is taken using a theoretical biomimetics framework that identifies naturally occurring objects or phenomena that descriptively captures the essence of a construct to facilitate (...) creative problem-solving. In the present case, the problem being solved is how to reconcile what is meant by public, how it ought to be interpreted, determining the diverse levels of confidence in science that exist, and various understandings of science all with one another. The results demonstrate there is an inherent denotative-connotative inconsistency in the traditional notion of public that can be explicated through the concept of a fractal allowing for comprehension of the relationship between public confidence in, and understanding of, science. (shrink)

The present study defines the function of the foundation of science in early modern Dutch philosophy, from the first introduction of Cartesian philosophy in Utrecht University by Henricus Regius to the acceptance of Newtonian physics by Willem Jacob ‘s Gravesande. My main claim is that a foundation of science was required because the conceptual premises of new ways in thinking had to be justified not only as alternatives to the established philosophical paradigms or as an answer to the (...) “sceptical crisis” signalled by Richard Popkin, but also in order to be introduced in the academia. This being my general thesis, different kinds of foundation of scientific knowledge are analysed in the light of the specific problems philosophers had to face. To this end, foundational theories are analysed in the light of 1) the overall aim of their philosophy, 2) the relations of disciplines they thought out, 3) what they regarded as scientific knowledge. Through this analysis, I assess that the foundation of science was carried out by metaphysical, logical and theological arguments, which fitted the needs of answering the didactical and introductory requirements of new paradigms, assessed the reliability of new methodology in leading us to grasp the truth, and provided philosophy with its conceptual apparatus. Finally, I demonstrate that a philosophy of science as a reflection on the principles, methods, concepts and application of modern science emerged in the Dutch Republic. (shrink)

Just started a new book. The aim is to establish a science of knowledge in the same way that we have a science of physics or a science of materials. This might appear as an overly ambitious, possibly arrogant, objective, but bear with me. On the day I am beginning to write it–June 7th, 2020–, I think I am in possession of a few things that will help me to achieve this objective. Again, bear with me. My (...) aim is well reflected in the title I chose (just now) for this book: Knowledge & Logic: Towards a science of knowledge. Its most important feature is that I shall take logic to be to knowledge science as calculus is to physics or to materials science. I do not intend to reclaim knowledge from the bosom of philosophy, in which, known as epistemology its erudite discussion has hardly progressed since Plato first defined it as true belief with logos. With only a few adjustments, it will actually provide me with the right, science-bound start. More recently, knowledge has been reclaimed by the field of BA, a reclaim that has opened the box of Pandora: Among the evils, and perhaps at the head of the list, is an overly lay, essentially naive, notion of knowledge. But the very idea that one can have something like “knowledge (management) software” puts us on the right track. (shrink)

Volume 27, Issue 6, December 2019, Page 1256-1260.

We present a theory of human artistic experience and the neural mechanisms that mediate it. Any theory of art has to ideally have three components. The logic of art: whether there are universal rules or principles; The evolutionary rationale: why did these rules evolve and why do they have the form that they do; What is the brain circuitry involved? Our paper begins with a quest for artistic universals and proposes a list of ‘Eight laws of artistic experience’ -- (...) a set of heuristics that artists either consciously or unconsciously deploy to optimally titillate the visual areas of the brain. One of these principles is a psychological phenomenon called the peak shift effect: If a rat is rewarded for discriminating a rectangle from a square, it will respond even more vigorously to a rectangle that is longer and skinnier that the prototype. We suggest that this principle explains not only caricatures, but many other aspects of art. Example: An evocative sketch of a female nude may be one which selectively accentuates those feminine form-attributes that allow one to discriminate it from a male figure; a Boucher, a Van Gogh, or a Monet may be a caricature in ‘colour space’ rather than form space. Even abstract art may employ ‘supernormal’ stimuli to excite form areas in the brain more strongly than natural stimuli. Second, we suggest that grouping is a very basic principle. The different extrastriate visual areas may have evolved specifically to extract correlations in different domains , and discovering and linking multiple features into unitary clusters -- objects -- is facilitated and reinforced by direct connections from these areas to limbic structures. In general, when object-like entities are partially discerned at any stage in the visual hierarchy, messages are sent back to earlier stages to alert them to certain locations or features in order to look for additional evidence for the object . Finally, given constraints on allocation of attentional resources, art is most appealing if it produces heightened activity in a single dimension rather than redundant activation of multiple modules. This idea may help explain the effectiveness of outline drawings and sketches, the savant syndrome in autists, and the sudden emergence of artistic talent in fronto-temporal dementia. In addition to these three basic principles we propose five others, constituting a total of ‘eight laws of aesthetic experience’. (shrink)

This paper challenges the first Gettier counterexample to the tripartite account of knowledge. Noting that 'the man who will get the job' is a description and invoking Donnellan's distinction between their 'referential' and 'attributive' uses, I argue that Smith does not actually believe that the man who will get the job has ten coins in his pocket. Smith's ignorance about who will get the job shows that the belief cannot be understood referentially, his ignorance of the coins in his pocket (...) shows that it cannot be understood attributively. An explanation for why Smith appeared to have justified true belief is given by distinguishing between 'belief' and 'belief in truth'. Smith believes the sentence 'the man who will get the job has ten coins in his pocket' to be true (he mistakenly believes that Jones will get the job, of whom he knows that he has ten coins in his pocket) (hence his 'belief'), the sentence is true (hence 'truth'), and he has sufficient reason to assent to it (hence his 'justification'). But he does not believe the proposition expressed. Hence he does not know it either. (shrink)

How were reliable predictions made before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? The book examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. Also included are the problem of induction before Hume, design (...) arguments for the existence of God, and theories on how to evaluate scientific and historical hypotheses. It is explained how Pascal and Fermat's work on chance arose out of legal thought on aleatory contracts. The book interprets pre-Pascalian unquantified probability in a generally objective Bayesian or logical probabilist sense. (shrink)

This work in metaphysics adheres to the critical demands of Immanuel Kant for what Kant would call a science of metaphysics, in that it consits strictly of a priori principles that, while from pure reason, can help make sense of our phenomenal world (Kant's criterion for objective validity). The work has an Appendix quoting Kant's most relevant remarks with regard to a science, and offers parallel quotes from David Hume's "Treatise of Human Nature". The work advances the explanation (...) of a causal process that accounts for the origination of the universals: space, time, mass (or substance), and mind (or consciousness), and it necessitates the existence of God as Absolute Being and Absolute Mind. Hegel's 'Science of Logic' is quoted wherein Hegel makes an analogous claim. The causal process is defined with both a definite beginning and a definite end and agreement can be found with the statement found in the book of Revelation, final chapter: "I am the Alpha and the Omega, the first and the last, the beginning and the end." The statement suggests a movement that is not in conflict with the science, and seems to reflect Hegel's own thoughts. The science does not conflict with, but it further finds agreement with the science of big bang cosmology, but it goes further in necessitating a 'singularity' at the beginning of time. The causal process defined has a Formative Phase and a Creative Phase, with the former preceding the big bang and the latter following after the big bang. (shrink)

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are (...) given. Specifically, a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)

The identity theory’s rise to prominence in analytic philosophy of mind during the late 1950s and early 1960s is widely seen as a watershed in the development of physicalism, in the sense that whereas logical behaviourism proposed analytic and a priori ascertainable identities between the meanings of mental and physical-behavioural concepts, the identity theory proposed synthetic and a posteriori knowable identities between mental and physical properties. While this watershed does exist, the standard account of it is misleading, as it is (...) founded in erroneous intensional misreadings of the logical positivists’—especially Carnap’s—extensional notions of translation and meaning, as well as misinterpretations of the positivists’ shift from the strong thesis of translation-physicalism to the weaker and more liberal notion of reduction-physicalism that occurred in the Unity of Science programme. After setting the historical record straight, the essay traces the first truly modern identity theory to Schlick’s pre-positivist views circa 1920 and goes on to explore its further development in Feigl, arguing that the fundamental difference between the Schlick-Feigl identity theory and the more familiar and influential Place-Smart-Armstrong identity theory has resurfaced in the deep and seemingly unbridgeable gulf in contemporary philosophy of consciousness between inflationary mentalism and deflationary physicalism. (shrink)

This paper reconstructs the American reception of logical positivism in the early 1930s. I argue that Moritz Schlick (who had visiting positions at Stanford and Berkeley between 1929 and 1932) and Herbert Feigl (who visited Harvard in the 1930-31 academic year) played a crucial role in promoting the *Wissenschaftliche Weltauffassung*, years before members of the Vienna Circle, the Berlin Group, and the Lvov-Warsaw school would seek refuge in the United States. Building on archive material from the Wiener Kreis Archiv, the (...) Harvard University Archives, and the Herbert Feigl Papers, as well as a large number of publications in American philosophy journals from the early 1930s, I reconstruct the subtle transformation of the American philosophical landscape in the years immediately preceding the European exodus. I argue that (1) American philosophical discussions about meaning and significance and (2) internal dynamics in the Vienna Circle between 1929 and 1931 significantly impacted the way in which US philosophers came to perceive logical positivism. (shrink)

Frege claims that the laws of logic are characterized by their “generality,” but it is hard to see how this could identify a special feature of those laws. I argue that we must understand this talk of generality in normative terms, but that what Frege says provides a normative demarcation of the logical laws only once we connect it with his thinking about truth and science. He means to be identifying the laws of logic as those that (...) appear in every one of the scientific systems whose construction is the ultimate aim of science, and in which all truths have a place. Though an account of logic in terms of scientific systems might seem hopelessly antiquated, I argue that it is not: a basically Fregean account of the nature of logic still looks quite promising. (shrink)

Putnam, Hilary FPhilosophy of logic. Harper Essays in Philosophy. Harper Torchbooks, No. TB 1544. Harper & Row, Publishers, New York-London, 1971. v+76 pp. The author of this book has made highly regarded contributions to mathematics, to philosophy of logic and to philosophy of science, and in this book he brings his ideas in these three areas to bear on the traditional philosophic problem of materialism versus (objective) idealism. The book assumes that contemporary science (mathematical and physical) (...) is largely correct as far as it goes, or at least that it is rational to believe in it. The main thesis of the book is that consistent acceptance of contemporary science requires the acceptance of some sort of Platonistic idealism affirming the existence of abstract, non-temporal, non-material, non-mental entities (numbers,scientific laws, mathematical formulas, etc.). The author is thus in direct opposition to the extreme materialism which had dominated philosophy of science in the first three quarters of this century. the book can be especially recommended to the scientifically literate, general reader whose acquaintance with these areas is limited to the earlier literature of when it had been assumed that empiricistic materialism was the only philosophy compatible with a scientific outlook. To this group the book presents an eye-opening challenge fulfilling the author’s intention of “shaking up preconceptions and stimulating further discussion”. (shrink)

This essay takes logic and ethics in broad senses: logic as the science of evidence; ethics as the science justice. One of its main conclusions is that neither science can be fruitfully pursued without the virtues fostered by the other: logic is pointless without fairness and compassion; ethics is pointless without rigor and objectivity. The logician urging us to be dispassionate is in resonance and harmony with the ethicist urging us to be compassionate.

The title of the present paper might arouse some curiosity among the minds of the readers. The very first question that arises in this respect is whether India produced any logic in the real sense of the term as has been used in the West. This paper is centered only on the three systems of Indian philosophy namely Nyāya, Buddhism and Jainism. We have been talking of Indian philosophy, Indian religion, Indian culture and Indian spirituality, but not that which (...) are of more fundamental concepts for any branch of knowledge whether it is social sciences or humanities. No aspect of human life and the universe has been left unexamined by Indian philosophers, and this leads to a totality of vision in both philosophical and psychological fields. In this paper we will discuss the main thinkers, sources and main concepts related to Indian Logic. (shrink)

Philosophers of logic are particularly interested in understanding the aims, epistemology, and methodology of logic. This raises the question of how the philosophy of logic should go about these enquires. According to the practice-based approach, the most reliable method we have to investigate the methodology and epistemology of a research field is by considering in detail the activities of its practitioners. This holds just as true for logic as it does for the recognised empirical and abstract (...) sciences. If we wish to systematically understand the aims and epistemology of logic, we are best placed achieving this by looking at what logicians do, rather than reflecting upon the nature of logic itself. In this entry, we outline the motivations for a practice-based approach towards the philosophy of logic and highlight its advantages over more “top-down” approaches, which attempt to infer conclusions about the nature of logic and its methodology on the basis of traditional assumptions about knowledge, metaphysics, or logic itself. We end by addressing several prominent concerns raised against the practice-based approach. (shrink)

In the *Science of Logic*, Hegel states unequivocally that the category of “life” is a strictly logical, or pure, form of thinking. His treatment of actual life – i.e., that which empirically constitutes nature – arises first in his *Philosophy of Nature* when the logic is applied under the conditions of space and time. Nevertheless, many commentators find Hegel’s development of this category as a purely logical one especially difficult to accept. Indeed, they find this development only (...) comprehensible as long as one simultaneously assumes that Hegel breaks his promise to let the logic do the leading. However, if Hegel were to in fact allow the logical development to be led by biological analogies at this point, problems would ensue. Not only would it contradict his own speculative method, which should secure the necessity of the categories, but it would also endanger the ontological generality of the category of life itself. Beyond undermining his method and the logical integrity of the category, however, I will argue that such a reading makes the transition to the next category of “cognition” unintelligible and problematic. My aim in the first part of this paper is to argue how logical life can be read as a pure category. I then argue in the second part how my reconstruction makes the transition to cognition intelligible without resorting to profane or supernatural interpretations. (shrink)

The science of logic has occupied an important role in Islamic history. Especially when al-Gazali 505-1111 has come and claimed that who learned Islamic sciences, without learning the Logic we cannot trust in his knowledge. From this time The science of logic has been flourished and quietly began to include in many sciences even Tefsir and Fiqh. After that, Al-razzi 606/1210 has established a big school in Islamic philosophy in general and in logic in (...) particular. al-Khonaji 646/1248 one of his important students. Who moved from Iran to Egypt and became Qadi al-Qudat (Chief Islamic justice). He has improved The science of logic by his books; like Keshf al-Asrar. In the sixth/twelfth one of his books has been spread in Muslim world and became the first step for who wanted to learn Logic. Beside that we have a lot of scholars has made commentaries on this book. In this article we focused on (Metn al-Jumal) by al-Konaji with his spreading in the Sixth. Seventh h.centuries. (shrink)

The Logic of Analogy is a study of the valid logical forms of qualitative and quantitative analogical argument, and the rules pertaining to them. It investigates equally valid conflicting arguments, statistics-based arguments and their utility in science, arguments from precedent used in law-making or law-application, and examines subsumption in analogical terms. Included for purposes of illustration is a large section on Talmudic use of analogical reasoning.

The monopolistic tendency of modern science in asserting itself as the exclusive interpreter of the human psyche or mind through its psychology does so while negating the most crucial dimension that makes it a complete psychology, the metaphysical order as is found across the world in all times and places. The reductionistic turn of modern Western psychology away from its metaphysical roots has deformed the original “science of the soul” rendering it null and void. That spirituality and metaphysics (...) have been marginalized and deemed irrelevant in modern science was assumed to be the logical course of progress. Ironically, however, their fundamental absence is the reason contemporary psychology is in disarray. Numerous individuals may see this as preposterous and think that to suggest this is to turn back the clock to the dark ages of knowledge. However, if psychology is returned to its origin in metaphysics, sacred science, and spiritual principles, it can again become worthy of being called a “science of the soul.” This interview with Islamic philosopher, Seyyed Hossein Nasr, on the discipline of psychology explores the original meaning of the “science of the soul” as it is understood across the diverse cultures of the world. (shrink)

A review essay on Peacocke's book A Study of Concepts. Raises questions about the role of the concept of finding an inference primitively compelling and questions of detail about the basic framework, its application to the systematicity of thought, the response to potential objections in the chapters on the metaphysics of concepts and naturalism, and the treatment of the concept of belief.

In this inaugural lecture I offer, against the background of a discussion of knowledge representation and its tools, an overview of my research in the philosophy of science. I defend a relational model-theoretic realism as being the appropriate meta-stance most congruent with the model-theoretic view of science as a form of human engagement with the world. Making use of logics with preferential semantics within a model-theoretic paradigm, I give an account of science as process and product. I (...) demonstrate the power of the full-blown employment of this paradigm in the philosophy of science by discussing the main applications of model-theoretic realism to traditional problems in the philosophy of science. I discuss my views of the nature of logic and of its role in the philosophy of science today. I also specifically offer a brief discussion on the future of cognitive philosophy in South Africa. My conclusion is a general look at the nature of philosophical inquiry and its significance for philosophers today. South African Journal of Philosophy Vol. 25 (4) 2006: pp. 275-289. (shrink)

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

Peirce considered his esthetics to be one of a trio of normative sciences. Ostensibly, the sciences of logic, ethics and esthetics, would study the traditional norms of truth, goodness and beauty. Logic was normative in the sense that it studied how people ought to reason, if truth is to be the result. Similarly, ethics is the study of how we ought to conduct ourselves, if good is to happen. At the same time, Peirce seems to have difficulty fitting (...) the study of the beautiful into this sort of normative framework. As Peirce says, esthetics was handicapped by its definition as a theory of beauty. Instead, Peirce sees esthetics as bound up with a study of ends. Peirce argues that ends are essential to normative behavior, understood as the deliberate pursuit of a purpose, the latter serving to direct and correct the behavior. Ends may be ideals, ideas, standards, or goals. In this regard, the study of esthetics is bound up with what ought to be pursued. The key problem of the normative sciences is to discover which ends ought to be pursued. In Peirce’s formative accounts, he seems to waver between assigning this task to ethics at times and esthetics otherwise. In some places, he argues that ethics defines the ends to be pursued and studies the summum bonum. On the other hand, esthetics is claimed to be the study of ideals, that which is objectively admirable, and the conditions of attractive and repulsive ideas. To that extent, Peirce claims in a number of places that the ethically good rests on a notion of the esthetically good, the morally good being a species of the esthetically good. Although Peirce notes his neglect of the study of esthetics, he does provide a preliminary study of ends, which prove to be instructive in getting a sense of what he counts as admirable to pursue. I argue that besides this positive esthetics, which identifies ends and the conditions which makes them worthy of pursuit, he also suggests a negative esthetics, one that is does not work backwards from the ideal to the means to achieve it, but sees ends as something that evolves forward as human endeavor attempts to correct those pursuits that have led to error and misdirection. Peirce’s negative esthetics is modelled after the way in which he accounts for the ability of science to self-correct away from errant hypotheses to ones less subject to error, converging toward the truth. In the same way, the pursuit of ends is a matter of converging toward the right end through self-correction. (shrink)

This is a presentation about the impacts of Logic and Theory of Computation. It starts by some explanations about Theory of Computation and its relations with the other subjects in science. Then we have some explanations about paradoxes and some historical points. In continuation, we present some of the most important paradoxes. Forthcoming, Five subjects around the relations between Logic and Theory of computation is introduced. Finally, we present a new approach to solve P vs NP problem (...) via Paradoxes (Presentation 6/20/2022 In Persian, Online seminar of The Iranian Association for Logic (IAL) . (shrink)

Proposition are the material of our reasoning. Proposition are the basic building blocks of the world/thought. Proposition have intense relation with the world. World is a series of atomic facts and these facts are valued by the proposition although sentences explain the world of reality but can’t have any truth values, only proposition have truth values to describe the world in terms of assertions. Propositions are truth value bearers, the only quality of proposition is truth & falsity, that they are (...) either true or false. Proposition mirrors the world and explains how world is arranged in an orderly manner. It scans the world(object) and are composed of atomic facts experienced and can be analyzed into propositions. Propositions are the basic units of logic. The truth (affirm) and falsity (nego) are the qualities of the propositions and universality (generality) and Particularity are the quantities of the propositions. There are propositions which are neither true nor false, they are called Pseudo-Propositions and their quality are ipso-facto i.e meaningless. Propositions are used in computers with the modifications brought by the modern logicians in the form of statements or logical sentences. The truth table of the logical gates and binary operations (1,s or 0,s are due to the revolution of the modern logic or mathematical logic. It is a fact that proposition cannot change the word but it shows the relation between the object and of the word. Objectives: The objectives of this research is to explore the importance and need of propositions in logic. It also shows the analysis of propositions and how a philosopher thoughts in terms of propositions or concepts. In this research problem it is shown that propositions had been described in many ways by most of the philosophers and logicians from Aristotle to contemporary philosophers. It also analysis the contribution of the philosophers towards proposition and its relation to the world of reality. This research also describes the definition and nature of proposition. (shrink)

P.F. Strawson contributed to many philosophical domains, including the philosophy of language, the history of philosophy, metaphysics, moral philosophy and philosophical methodology. Most of his contributions in these areas have influenced contemporary debates, either because his views are still defended or because they are still considered worthy of detailed responses. His views on the philosophy of logic have been only rarely discussed, however. My aim in this paper is threefold. First, I provide a systematic account of Strawson’s philosophy of (...) logic. I argue that Strawson is an important predecessor of logical expressivism, a contemporary position in the philosophy of logic most notably defended by Robert Brandom. My main focus is on Strawson’s largely-neglected 1982 paper ‘Logical Form and Logical Constants’, which contains his most mature ideas on the topic. Second, while Strawson’s position is of historical and independent philosophical interest, I argue that he leaves many points unclear. Finally, I propose several clarifications of Strawson’s position. (shrink)

This piece explores the meaning of the following quote from Charles Peirce (1902), ". . . the main reason logic is unsettled is that thirteen different opinions are current as to the true aim of the science. Now this is not a logical difficulty, but an ethical difficulty; for ethics is the science of aims. Secondly, it is true that ethics has been, and always must be, a theatre of discussion for the reason that its study consists (...) in the gradual development of a distinct recognition of a satisfactory aim. It is a science of subtleties, no doubt; but it is not logic, but the development of the ideal, which really creates and resolves the problems of ethics.". (shrink)

The clamour for scientific reasoning in philosophy is born out of a belief that scientific reasoning is infallible and universal. This paper argues that while scientific reasoning is infallible, it is so only with regard to the objects of knowledge in science. And because objects of knowledge are not the same across disciplines, claims that scientific reasoning is universal in its application are patently misplaced. -/- The belief in the universality of scientific reasoning has its genesis in what may (...) be called the ‘same genre argument’. If all objects of knowledge have a common essential and characteristic quality they can be put in a common basket and so belong to a common set. So far so good. The problem with this thesis arises when it is assumed that all objects of knowledge there can be (in this universe and beyond, if there is a beyond) are elements of that common universal set. If they are, they share an essential quality with and so belong to the same genre as material objects in our material universe. This essential quality is the material nature (mass and/or energy) of all matter in the phenomenal world, a quality that gives matter (a) objective reality and (b) makes it a percept. Scientific method is geared to studying percepts through a percept-perceiver one-to-one relationship. -/- If all objects of knowledge, however, are not material objects, they will neither be percepts nor show up as objective realities to perceiver/scientific observers and on their scientific tools. There are such objects. What was mere speculation once can be scientifically proven today. Only, the approach to the proof must be different. -/- There is a category of objects that are not material in nature; but they are objects of knowledge. These are called wholes. Examples of wholes are (i) God of Abrahamic religions; (ii) the Self/Brahman of the Upanishads; (iii) the universe in entirety. Every whole is characterized by dimensions. Dimensions are not objective realities because they are not material objects. Because they are not objective realities they are not objectively verifiable. Hence they will always elude science and scientific reasoning. That does not mean that they don’t exist. The universe is a whole. Its dimensions are space and time. Neither is objectively real; yet both are realities. -/- The paper concludes by considering the dynamics of logical progression from premise (axiom) to theorem. If the premise is wrong there can be no knowledge, no matter how powerful the logical apparatus that is used. (shrink)

Before remarking on “The New Science of the Mind”, I first offer some comments on philosophy and its relationship to contemporary psychological research as exemplified in the works of Searle (S),Wittgenstein (W), Hacker (H) et al. It will help to see my reviews of PNC (Philosophy in a New Century), TLP, PI, OC, Making the Social World (MSW) and other books by and about these geniuses, who provide a clear description of higher order behavior, not found in psychology nor (...) philosophy, that I will refer to as the WS framework. -/- As with so many philosophy books, we might stop with the title. As the quotes and comments above and in my other reviews and the books they cover indicate, there are compelling reasons for regarding the problems we face in describing the psychology of higher order thought as conceptual and not scientific. This ought to be crystal clear to all, but science envy and almost complete oblivion to WSH etc. is a la mode! But as H notes above, the issues discussed here are all about language games and have nothing to do with science. In fact, as usual, if one translates into plain English there is very little of interest here, and certainly nothing not said before and better by WS etc. countless times since the 30’s (see e.g., The Blue and Brown Books from 1933-35). It is not surprising that he makes no significant references to any of the above books or persons (the only reference to S is an article from 1958!), though in my view they are at the top of the list of the major figures in descriptive psychology. -/- On p119 he tells us that the key to all this is to figure out how “…a personal level cognitive process can belong to a representational subject. This is the task of the second half of the book.” But W did this 80 years ago and since we have the beautifully clear explanations of WSH, H&M etc., there is no point to torturing oneself with the rather aimless and opaque prose that veers off at the end into Sartre, Heidegger, Husserl, and Frege, with a dash of postmodernist word salad for good measure. A valiant effort on an interesting topic, but ultimately exhausting and fruitless. -/- 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)

This article discusses a relation between the formal science of logical semantics and some monotheistic, polytheistic and Trinitarian Christian notions. This relation appears in the use of the existential quantifier and of logical-modal notions when some monotheistic and polytheistic concepts and, principally, the concept of Trinity Dogma are analyzed. Thus, some presupposed modal notions will appear in some monotheistic propositions, such as the notion of “logically necessary”. From this, it will be shown how the term “God” is a polysemic (...) term and is often treated as both subject and predicate. This will make it clear that there is no plausible intellectual justification for believing that the term “God” can only be used as a name and never as a predicate, and vice versa. After that analysis, I will show that the conjunction of the “Trinity Dogma” with some type of “monotheistic position” would necessarily imply some class of absurdity and/or semantic “oddity”. (shrink)

We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and completeness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems. -/- .

A brief but rigorous description of the logical structure of mathematical truth.