There is a history of thinking that photographs provide a special kind of access to the objects depicted in them, beyond the access that would be provided by a painting or drawing. What is included in the photograph does not depend on the photographer’s beliefs about what is in front of the camera. This feature leads Kendall Walton to argue that photographs literally allow us to see the objects which appear in them. Current generative algorithms produce images in response to (...) users’ text prompts. Depending on the parameters, the output can resemble specific people or things which are named in the prompt. This resemblance does not depend on the user’s beliefs, so generated images are in this sense like photographs. Given this parallel, how should we think about AI-generated images? (shrink)

In this article, the concept of system of symbolic 2-plithogenic linear equations and its solutions are introduced and studied. The Cramer's rule was applied to solve the system of symbolic 2-plithogenic linear equations. Also, provided enough examples for each case to enhance understanding.

A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize these arguments to symbolic 2-plithogenic structure. We introduce the structure of clean and nil-clean symbolic (...) 2-plithogenic rings and some of its elementary properties are presented. Also, we have found the equivalence between classical clean(nil-clean) ring R and the corresponding symbolic 2-plithogenic ring 2-SPR. (shrink)

We formalize what it means to have permission to say something. We adapt the dynamic logic of permission by van der Meyden (J Log Comput 6(3):465–479, 1996 ) to the case where atomic actions are public truthful announcements. We also add a notion of obligation. Our logic is an extension of the logic of public announcements introduced by Plaza ( 1989 ) with dynamic modal operators for permission and for obligation. We axiomatize the logic and show that it is decidable.

We show how in the hierarchies${F_\alpha }$of Fieldian truth sets, and Herzberger’s${H_\alpha }$revision sequence starting from any hypothesis for${F_0}$ that essentially each${H_\alpha }$ carries within it a history of the whole prior revision process.As applications we provide a precise representation for, and a calculation of the length of, possiblepath independent determinateness hierarchiesof Field’s construction with a binary conditional operator. We demonstrate the existence of generalized liar sentences, that can be considered as diagonalizing past the determinateness hierarchies definable in Field’s recent (...) models. The ‘defectiveness’ of such diagonal sentences necessarily cannot be classified by any of the determinateness predicates of the model. They are ‘ineffable liars’. We may consider them a response to the claim of Field that ‘the conditional can be used to show that the theory is not subject to “revenge problems”.’. (shrink)

Davidson’s explanation of first‐person authority in utterance of sentences of the form ‘I V that p’ derives first‐person authority from the requirements of interpretation of speech. His account is committed to the view that utterance sentences are truth‐bearers, that believing that p is a matter of holding true an utterance sentence, and that a speaker’s knowledge of what he means gives him knowledge of what belief he expresses by his utterance. These claims are here faulted. His explanation of first‐person authority (...) by reference to the requirements of interpretability is committed to the view that all understanding involves interpretation. This is argued to be a misconception of understanding and of speaker’s meaning. Davidson’s account involves acceptance of the cognitive assumption that normally when a person Vs that p, he knows that he does. This assumption is challenged. Throughout, Davidson’s conception is compared and contrasted with Wittgenstein’s. (shrink)

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

We look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta’s theory of truth over arithmetic using \emph{fully varied revision} sequences yields a complete \Pi13 set of integers; (iii) the set of \emph{stably categorical} sentences using their revision operator ψ is similarly \Pi13 and which (...) is complete in Gödel’s universe of constructible sets L; (iv) give an alternative account of a theory of truth—realistic variance that simplifies full variance, whilst at the same time arriving at Kripkean fixed points. (shrink)

1. The Tractatus doctrine of saying and showing In a letter to Russell dated 19.4.1919, written shortly after he had finished the Tractatus, Wittgenstein told Russell that the main contention of the book, to which all else, including the account of logic, is subsidiary, ‘is the theory of what can be expressed (gesagt) by prop[osition]s -- i.e. by language -- (and, which comes to the same, what can be thought) and what cannot be expressed by prop[osition]s, but only shown (gezeigt); (...) which I believe is the cardinal problem of philosophy’ (CL 68). This was emphasized in both preface and conclusion of the book. The preface observes that the whole sense of the book can be summed up in the following words: ‘what can be said at all can be said clearly, and what we cannot talk about we must pass over in silence’ (TLP p.3). The conclusion of the book (TLP 7) simply repeats this. The preceding three remarks, however, are noteworthy. They make three claims. First, ‘There are, indeed, things that cannot be put into words. They make themselves manifest. They are what is mystical’ (TLP 6.522). This reiterates the leitmotif of the book, namely that there are things that cannot, by the very nature of representation, be said. But though they cannot be said, they are shown by features of the relevant system of representation. Secondly, the correct method in philosophy would really be to say nothing except what can be said, i.e. empirical propositions that have nothing to do with philosophy, and then, when someone wanted to say something metaphysical, to demonstrate to him that he had failed to give meaning to certain signs in his propositions (TLP 6.53). This method, of course, is not the method that has been followed throughout the book, which consists almost exclusively of modal assertions concerning what must, can or cannot be thus and so in reality, in language and in the relation between language and reality.. (shrink)

1. First person authority: the received explanation Over a wide range of psychological attributes, a mature speaker seems to enjoy a defeasible form of authority on how things are with him. The received explanation of this is epistemic, and rests upon a cognitive assumption. The speaker’s word is a authoritative because when things are thus-and-so with him, then normally he knows that they are. This is held to be because the speaker has direct and privileged access to the contents of (...) his consciousness by means of introspection, conceived as a faculty of inner sense. Like perceptual knowledge, introspective knowledge is held to be direct and non-evidential. Accordingly, the first-person utterances ‘I have a pain’, ‘I believe that p’, ‘I intend to V’ are taken to be descriptions of what is evident to inner sense. Many classical thinkers held such subjective knowledge to be not only immediate, but also infallible and indubitable. The challenge to the received conceptions came from Wittgenstein. He denied the cognitive assumption, arguing that it cannot be said of me at all (except perhaps as a joke) that I know that I am in pain. For what is that supposed to mean — except perhaps that I am in pain?1 If it makes no sense to say that one knows that one is in pain, then the epistemic explanation is a non-starter, since it explains the special authoritative status of a person’s avowal of pain by reference to the putative fact that the subject of pain knows, normally knows, or cannot but know, that he is in pain when he is. It is important to note that Wittgenstein did not mechanically generalize the case of pain across the whole domain of firstperson utterances. The case of pain constitutes only one pole of a range of such utterances. Avowals and averrals of belief and intention approximate the other pole, and require independent analysis and grammatical description. (shrink)

How should a liberal state treat its citizens who subscribe to religion and enjoy its component goods? This thesis explores the possibility of reconciling religion and justice. It argues for (1) a proper understanding of religion and the kind of good it constitutes; (2) the possibility of a liberal theory of justice which takes fully into account the claims of believers; and (3) an arrangement of social institutions which protects the engagement of citizens with faith with the goods of religion. (...) There have been several recent liberal approaches to the question which promise to accommodate the claims of believers in societies characterized by pluralism. They aim at the coexistence of citizens with faith with other citizens who are either non-adherents or even opposed to religion. However, so this thesis argues, these approaches are not successful. In particular, they fail to establish more than a mere doctrine of non-discrimination against believers. As a result, these liberal frameworks fail to address the central question of how liberal justice ought to treat religious goods. In reaction, some theorists of religion have claimed that there is a deep incompatibility between liberalism and a proper understanding of what a life devoted to religion is. In contrast, this thesis proposes a novel approach which starts from a unified view of religion, and proceeds to develop a liberal framework to accommodate the claims of believers. It argues that whilst non-discrimination is obviously necessary and fundamental, a more ambitious, proper understanding of religious goods and religious needs can contribute to a more coherent liberal strategy towards citizens with faith. It could also help motivate social policies and institutions to treat believers and non-believers in a just and fair manner. (shrink)

The criminal law presently distinguishes between actions and omissions, and only rarely proscribes failures to avert consequences that it would be an offense to bring about. Why? In recent years it has been persuasively argued by both Glover and Bennett that, celeris paribus, omissions to prevent a harm are just as culpable as are actions which bring that harm about. On the other hand, and acknowledging that hitherto “lawyers have not been very successful in finding a rationale for it,” Tony (...) Honoré has sought to defend the law's differential treatment. He proposes a “distinct-duties theory” that in addition to the general duties we owe to everyone, we also owe distinct duties to a more limited collection of people and associations, specified by features of our relationship with them. Where a distinct duty holds, breach by omission may well be no better than breach by positive action. But absent a distinct duty, omissions, per Honoré, are less culpable. They are mere failures to intervene and improve or rectify things, whereas actions are positive interventions which make things worse. And, thus, the law has good reason to differentiate between them. (shrink)

And in what sense can one speak of the hermeneutics of original argument? In The Hermeneutics of Original Argument, P. Christopher Smith explores these questions in building upon Heidegger's hermeneutical thought.

We consider notions of truth and logical validity defined in various recent constructions of Hartry Field. We try to explicate his notion of determinate truth by clarifying the path-dependent hierarchies of his determinateness operator.

In response to criticisms of the use of the Ideological Surround Model to analyze Tolerance of Ambiguity, emphasis is placed on how the methodologies of this model operate from Christian pacifist assumptions. This model seeks to promote social scientific methodologies that will allow competing perspectives to obtain increasing clarity on points of conflict.

The Secret Doctrine comprises a virtual encyclopaedia of the "anciently universal wisdom-tradition" -- scarcely an issue of consequence in the broad range of human experience is left untouched. As part of the Secret Doctrine Centenary project, this 441-page Index provides ready access to the vast quantity of material from many cultures set forth in the SD's original two volumes published in 1888. Due to the topics covered, it is as much an index of ideas as it is of subjects, works, (...) persons, and proper names. To aid the reader, major subject entries are cross-referenced; foreign terms are identified by language and, where possible, given in both their 1888 spelling(s) and as modernly transliterated, often with one or two word definitions. Subentries are arranged alphabetically. Cited works and authors, whose titles or names are not given in the SD are placed in brackets for convenient identification. Also included is an Appendix of foreign phrases with translation and source reference -- all helping to make this Index an invaluable reference tool for students of The Secret Doctrine. (shrink)

I. Beyond Utilitarianism In the summer of 1982, I published an article called “Missiles and Morals,” in which I argued on utilitarian grounds that nuclear deterrence in its present form is not morally justifiable. The argument of “Missiles and Morals” compared the most likely sort of nuclear war to develop under nuclear deterrence with the most likely sort of nuclear war to develop under American unilateral nuclear disaramament. For a variety of reasons, I claimed diat the number of casualties in (...) a two-sided nuclear war developing under DET would be at least fifteen times greater than the number of casualties in a one-sided nuclear attack developing under UND. If one assumes that human lives lost or saved is the principal criterion by which nuclear weapons policies should be measured, it follows that DET is morally superior to UND on utilitarian grounds only if the chance of a two-sided nuclear war under DET is more than fifteen times less dian the chance of a one-sided nuclear attack under UND. Since I did not believe that the chance of nuclear war under deterrence is fifteen times less than the chance of nuclear war under unilateral nuclear disarmament, I inferred diat utilitaranism failed to justify DET. Indeed, on utilitarian grounds, DET stood condemned. (shrink)

One of the gains to be reckoned from the study of nomenclature in the sepulchral inscriptions of the early empire is the gradual abandonment of attempts to distinguish between slave and freeborn on the basis of personal name or cognomen alone, especially when this is of Latin derivation. Nevertheless, one still finds personal cognomina in undated inscriptions adduced as sole evidence for the origin or status of individuals below senatorial rank. Thus in a standard work on freedmen in the early (...) empire, recently reprinted, names such as Agilis, Amandus, Auctus, Communis, Donatus, Faustus, Felix, etc., are said to be commonly servile, but others such as Aquila, Bassus, Capito, Cams, Celer, Crescens, etc., are taken as ingenuous. The criteria used in making such a distinction are subjective and arbitrary and the statistics based on them are largely valueless. It is the purpose of this note to consider briefly on this question the evidence of the personal nomenclature of the Imperial slaves and freedmen. In this group, the Familia Caesaris, no problem of status arises, and the fact that the majority of their inscriptions can be dated, at least approximately, makes it possible to trace the chronological development of the use of cognomina ingenua by one important group of servile origin from the first to the early third century A.D. Moreover, such a development is useful evidence for change in the social structure of the early empire. (shrink)

1. Belief and mental statesDavidson holds that intentional verbs occurring in the form ‘A Vs that p’ signify propositional attitudes. These are, he claims, mental states, and dispositions. Davidson does not conceive of himself as introducing a special technical sense of the common intentional verbs. He insists that ‘the mental states in question are beliefs, desires, intentions, and so on, as ordinarily conceived'. Consequently he contends that believing that p is a mental state, disposition or dispositional state. These ontological claims (...) about the nature of belief inform his account of the logical form of belief sentences. I shall address the question of whether believing that p can justly be deemed a mental state, a disposition or dispositional state. Subsequently I shall examine Davidson's account of the logical form of belief sentences.Our concept of a mental state, like so many of the concepts which philosophers treat as categorial, is none too sharply defined. It has a respectable use, which can be described. But, like other such general psychological terms, e.g. ‘mental process’, ‘mental activity’, far from being the ‘hardest of the hard’ - a sharply circumscribed categorial term akin to a variable in a well-constructed formal system — it has blurred boundaries and is elastic. Like all our ordinary psychological concepts, it evolved in order to meet everyday needs. As Wittgenstein observed, ‘The concepts of psychology are just everyday concepts. They are not concepts newly fashioned by science for its own purposes, as are the concepts of physics and chemistry.’Although our ordinary concepts can be replaced by technical ones for specialized purposes, they cannot be abused without generating conceptual confusion and incoherence. If the expression ‘mental state’ is being employed in its ordinary sense, then it is wrong to hold that believing that p is to be in any mental state. If it is being employed in a special technical sense, then those who employ it thus owe us an account of what it means and how it is to be used. This Davidson and the many other philosophers who subscribe to the view that believing is a mental state have not done. Until such an account is forthcoming, one may presume that they think of themselves as deploying our ordinary concept of a mental state. And if so, I shall argue, they are misusing it. (shrink)

Th e con fusion a nd b arren ness o f psycho logy is no t to be e xplain ed b y calling it a “yo ung science”; its state is not comparable with that of physics, for instance, in its beginnings. (Rather with that of certain branches of mathematics. Set theory.) For in psychology there are experimental methods and conceptual confusion. (As in the oth er case, con cep tual co nfusion and m ethod s of pro of.) (...) The existence of the experimental method makes us think we have the means of solving the problems that trouble us; though problem and method pass one another by. (PI p. 232). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Kennedy Institute of Ethics Journal 10.1 (2000) 103-108 [Access article in PDF] Letters "Small Sacrifices" in Stem Cell Research Madam: I agree with Professors McGee and Caplan (in their article "The Ethics and Politics of Small Sacrifices in Stem Cell Research," KIEJ, June 1999) that the question of the nature and status of the source of stem cells must be addressed. However, in their eagerness to convince us of (...) the smallness of the sacrifices, I think the authors use some unfortunate rhetorical devices and move much too quickly over some necessary distinctions.The rhetorical display is unfortunate if the article is intended to be a fair and rational development of an argument--e.g., those who hold a position in opposition to the authors do not argue they "inveigh." The section on the political area of the controversy seems particularly dismissive of other's positions.However, I will focus on just two areas where I think a more nuanced consideration would make the question of the moral legitimacy of the "small sacrifices" of embryos less obvious than the authors' rhetoric would suggest.First, they claim that opponents of such research assume some sort of "super status" for an embryo. The rights generally conceded to born human beings may not be as "weak" as they characterize. But even considering only the "negative right against unwarranted violence," I think the authors misdescribe the situation. Contrary to their assertion, I do not know when "adults and even children are... forced to give life... in the defense or at least interest of the community's highest ideals and most pressing interests" (p. 153). Could they be speaking of capital punishment, justified in the name of protecting the community? But then why mention children?It is true that not everyone can be guaranteed every means to preserving and enhancing life. But this limitation on positive rights is not a "forced giving." Adults may be compelled to risk life--e.g. in a draft for the sake of a war. But, again, the more or less justifiable imposition of a risk is not the same as selecting out one particular individual or class to be directly killed. Neither adults nor born children are compelled to be killed for the sake of organ "donation," even if a greater number might be saved. If one grants equivalent status to the embryo (as the authors seem to do here for the sake of argument), opponents do not have to claim a "super status" for embryos, just the ordinary human right not to be killed even for "compassionate" motives.A second area where I think the authors move too quickly is in their impoverished definition of the essential humanity of the early embryo as exhaustively represented by the physical structure of its DNA. The authors seem to recognize [End Page 103] that, ordinarily, there is more to personhood than sheer physical structure. For example, they mention memories and habits (p. 154). They could also speak of relationships, attitudes, and the like. Since an early embryo has no such components of personality as we experience it, the authors hold that its identity could only be contained in its DNA. Since this DNA is preserved, even spread far and wide, by the use of stem cells, it almost seems as if we are doing the early embryo a favor by breaking it up.However, just because the embryo does not have any conscious memories or other attributes of character or personality, that does not mean its identity is constituted only by its physical structure described statically. The early embryo is not just a bundle of discrete structures, and its DNA is not just an inert lump made up of certain smaller lumps. Both the embryo and its DNA are active. Thus the identity of even an early embryo includes both its current processes and the innate potential for further activity and development. Although lacking a conscious will, the early embryo is already in a sense an agent, already doing things--growing, changing, and heading toward something that... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:,178 HISTORY OF PHILOSOPHY in accord with Thomas on certain important points, but his own theology is more in the spirit of Plato and Augustine. Professor Kristeller's vast learning is at the service of admirably balanced conclusions. Not everyone will agree with all his interpretations; Ficino perhaps did not imagine himself to be "constructing a system of philosophy" (p. 96) since the very title of his work, Theologia platonica, (...) suggests that he continues, with new materials, the labor of mediaeval theolo#ans. And Ficino's doctrine of the continuity of the supernatural life of the soul in this world and the next (p. 120) seems to be completely in accord with Thomas. But the author's very careful scholarly method and sound general conclusions are beyond criticism. Two hitherto unpublished Latin texts are printed in critical edition at the end of the French lecture, the Opus aureum in Thomistas by Baptists Mantuanus, which is anti-Thomas, and the Opusculum ad Laurentium Medicem on beatitude, by Vincentius Bandellus, which is pro-Thomas. Like Professor Kristeller's fine lecture, these new texts are a permanent contribution to scholarship. PAUL J. W. MILLER University of Colorado The Anatomy of Leviathan. By F. S. McNeilly. (New York: St. Martin's Press, 1968. Pp. 264. $8.50) The one thing about which Hobbes's commentators have agreed is the absence of any significant process of development in the several statements of his philosophic views. This has been most evident in their willingness to use the various texts as a common repository from which evidence for their interpretations could be drawn with little regard for its specific textual origin. Notoriously, no consensus has emerged from such endeavors and McNeilly believes this method of interpreting Hobbes far too indiscriminate. He contends that careful examination of the differing expressions and contexts of apparently recurrent arguments will show, in many cases, not the same argument repeated several times, but several different arguments. And these, properly discriminated, reveal a definite pattern of development culminating, in Leviathan, with a political theory substantially different from that of the earlier works. While the political theory of the Elements of Law and De Cive consists of a series of predictions founded on the known psychological tendencies of men, the theory of Leviathan, MeNeilly contends, is independent of any particular concept of human nature. Rather it is a "formal system of necessarily true propositions" (p. 213) constituting "a systematic analysis of value systems generally" (p. 245). Excepting two introductory chapters, the whole of McNeilly's argument is given over to substantiating this radical thesis, his point of departure being Hobbes's allegedly shifting views on method which are taken to vary somewhat inconsistently in the earlier works among self evidence, conventionalist and hypothetico-deductive theories and combinations of these. By contrast, in Leviathan, McNeilly argues, Hobbes expounds a conventionalist view with "clarity and persistence" (pp. 84-85). When this BOOK REVIEWS 479 conventionalism is combined with the adoption of mathematics as the paradigm of sound science, it leads Hobbes to the view that pohtical theory can be constructed as a formal system of necessary propositions because he believes that mathematics is about the world and extends this mistake to formal systems generally. These methodological commitments then, render any concept of human nature irrelevant to political theory. McNeilly's task in the second main section of the book is to show that in contrast to the earlier works, and contrary to all appearances, the Leviathan's account of human nature is completely neutral with regard to any possible set of motives and hence, wholly formal. Specifically he argues that materialism and mechanism play no active role in Hobbes's account of the passions and that the psychological egoism characteristic of the Elements and the fourth part of De Corpore is abandoned. (Throughout it is assumed that De Corpore was substantially complete before Leviathan was composed; this may not be true of the fourth part, as McNeilly recognizes, but he is undeterred.) The formal account of the passions in Leviathan then is formally compatible with either egoistic or nonegoistic interpretations of human motivation. Similarly, it is argued that Hobbes gives up his pessimism about men as... (shrink)

During the first years of the post-war era, many French scientists travelled in the United States. As they looked for a reference to be used in rebuilding their own scientific landscape, their diaries say as much about the rise of the American biomedical complex as they do about their perception of research in the country. In order to illustrate how the French biologists adopted, competed with, or challenged the American model and how transatlantic exchanges played a critical role in the (...) molecularization of the life sciences, this paper presents three trajectories of laboratories. These include the services respectively led by P. Lepine and J. Monod at the Pasteur Institute, and G. Schapira's biochemical research unit at the Hopital des Enfants Malades. The three studies document the massive transatlantic circulation of materials, techniques, instruments, and people during the scientific reconstruction. The reconstruction however produced highly differentiated characters each operating in his own niche: the biotechnological inventor, the neo-clinician, and the fundamental biologist. The comparison situates the rise of molecular biology within the context of a rapidly expanding biomedical research system. It will help in understanding how, in contrast to the American situation, a logic of ''demedicalization'' became in France a means for developing biology at the molecular level. (shrink)

Suppose a computer prints out the following little "poem": The shooting of the hunters she heardBut to pity it moved her not. What can we say about the meaning of this "poem"? We can say that it is ambiguous. It could mean: She heard the hunters shooting at animals, people, etc., but she had no pity for the victims. . . . She heard the hunters being shot but did not pity them. . . . She heard the hunters shooting (...) at someone or something and she heard the hunters being shot but did not pity either. An author could use the above word sequence to convey either , , or . But since we cannot treat the text produced by the computer as anyone's use of the words in question, it would not make sense to decide among its linguistically possible readings, just as it would not make sense to choose among the linguistically possible readings of an ambiguous sentence if it is considered in abstraction from its use by a speaker on a particular occasion. For example, it would not make sense to say of the sentence "He saw the man carrying the suitcase" that it just means "He saw the man who is carrying the suitcase" if we know that and in which what ways the sentence is ambiguous. If someone did say this, we would be inclined to think either that he does not know that the sentence is ambiguous or that he is talking not about the sentence but about an utterance of that sentence by a speaker on some occasion. Hence all we can do in interpreting the computer "poem" is to specify the set of its linguistically possible readings, namely, {, , }. But it would not make sense to select , for example, and say, "That is what the computer poem means, not , nor ." P. D. Juhl is an assistant professor of German at Princeton University. The present essay, in a different form, will appear in his forthcoming book, The Nature of Literary Interpretation. See also: "Against Theory" by Steven Knapp and Walter Benn Michaels in Vol. 8, No. 4. (shrink)

P S Wilson; Interests, Values and Educational Language, Journal of Philosophy of Education, Volume 10, Issue 1, 30 May 2006, Pages 147–166, https://doi.org/10.1.

Old philosophical problems never die, but they can be reinterpreted. In this paper, I offer a reinterpretation of the problem of reconciling divine omniscience and human free will. Classical discussions of this problem concentrate on the nature of God and the concept of free will. The present discussion will focus attention on the concept of knowledge, drawing on developments in epistemology that resulted from the posing of a certain problem by Edmund Gettier in 1963.

In its original form Dirac's equations have been expressed by use of the γ-matrices γμ, μ=0, 1, 2, 3. They are elements of the matrix algebra M 4 (ℂ). As emphasized by Hestenes several times, the γ-matrices are merely a (faithful) matrix representation of an orthonormal basis of the orthogonal spaceℝ 1,3, generating the real Clifford algebra Cl 1,3 . This orthonormal basis is also denoted by γμ, μ=0, 1, 2, 3. The use of the matrix algebra M 4 (ℂ) (...) to represent Cl 1,3 has some unsatisfactory aspects. The γ-matrices contain imaginary numbers as entries whereas Cl 1,3 is real. Moreover, as a matrix algebra Cl 1,3 is M 2 (ℍ) but only a part of M 4 (ℂ). For that reason we investigate in this paper several forms of Dirac's equations in terms of M 2 (ℍ) instead of M 4 (ℂ). In Section1 we survey Dirac's equations describing the interaction of matter with electromagnetic, electroweak, and strong fields. Section2 deals with electromagnetic/weak interactions employing M 2 (ℍ). Finally, in Section3 we deal with Dirac's equations for strong interactions between quarks. In contrast to su(2) ⊕ u(1), the Lie algebra su(3) is not isomorphic to any subalgebra of Cl 1,3 . Therefore we do not give a description of strong interactions by use of M 2 (ℍ). Instead of such an approach we describe these interactions using the space of quadruples of bivector fields in Cl 1,3 . The thus obtained description has remarkable formal resemblance to the original Dirac equations using wave functions with values in the linear spaceℂ 4. (shrink)

Beschouwing over de problemen waarvoor de psycholoog zich, gezien de complexiteit van de mens, geplaatst ziet.