The qualitative theory of nomic truth approximation, presented in Kuipers in his, in which ‘the truth’ concerns the distinction between nomic, e.g. physical, possibilities and impossibilities, rests on a very restrictive assumption, viz. that theories always claim to characterize the boundary between nomic possibilities and impossibilities. Fully recognizing two different functions of theories, viz. excluding and representing, this paper drops this assumption by conceiving theories in development as tuples of postulates and models, where the postulates claim to exclude nomic impossibilities (...) and the models claim to represent nomic possibilities. Revising theories becomes then a matter of adding or revising models and/or postulates in the light of increasing evidence, captured by a special kind of theories, viz. ‘data-theories’. Under the assumption that the data-theory is true, achieving empirical progress in this way provides good reasons for the abductive conclusion that truth approximation has been achieved as well. Here, the notions of truth approximation and empirical progress are formally direct generalizations of the earlier ones. However, truth approximation is now explicitly defined in terms of increasing truth-content and decreasing falsity-content of theories, whereas empirical progress is defined in terms of lasting increased accepted and decreased rejected content in the light of increasing evidence. These definitions are strongly inspired by a paper of Gustavo Cevolani, Vincenzo Crupi and Roberto Festa, viz., “Verisimilitude and belief change for conjunctive theories” :183–222, 2011). (shrink)

This article outlines the work of a group of US mathematicians called the American Postulate Theorists and their influence on Tarski's work in the 1930s that was to be foundational for model theory. The American Postulate Theorists were influenced by the European foundational work of the period around 1900, such as that of Peano and Hilbert. In the period roughly from 1900???1940, they developed an indigenous American approach to foundational investigations. This made use of interpretations of precisely formulated (...) axiomatic theories to prove such metatheoretic properties as independence, consistency, categoricity and, in some cases, completeness of axiom sets. This approach to foundations was in many respects similar to that later taken by Tarski, who frequently cites the work of American Postulate Theorists. Their work served as paradigm examples of the theories and concepts investigated in model theory. The article also examines the possibility of a more specific impetus to Tarski's model theoretic investigation, arising from his having studied in 1927???1929 a paper by C. H. Langford proving completeness for various axiom sets for linear orders. This used the method of elimination of quantifiers. The article concludes with an examination of one example of Langford's methods to indicate how their correct formulation seems to call for model-theoretic concepts. (shrink)

Das Buch enthält die Einführung in die Lektüre sowie den Textkommentar zu den der Analyse der Grundsätze der Modalität gewidmeten "Postulaten des empirischen Denkens überhaupt". Untersucht wird Kants gesamte Theorie der Modalbegriffe (Möglichkeit - Unmöglichkeit, Dasein - Nichtsein, Notwendigkeit - Zufälligkeit) seit Mitte der 1750er Jahre bis zur Kritik der reinen Vernunft. Die Postulate sind nach Kant nicht objektiv, sondern subjektiv-synthetisch: Der Gegenstand der Erfahrung, welcher zunächst anhand der objektiv-synthetischen Funktionen der Quantität, Qualität und Relation bestimmt wird, lässt sich (...) nun in seinem Verhältnis zum setzenden Subjekt betrachten. Die Postulate thematisieren jedoch nicht - hier liegt die konstitutive Charakteristik dieser synthetischen Urteile a priori - das Subjekt selbst, sondern das Objekt als solches und die Objektivität überhaupt. Wie diese Untersuchung zeigt, antwortet Kant erst hier - nicht in den viel diskutierten Deduktionskapiteln oder in den anderen Grundsatzkapiteln - auf die Frage "Was ist ein Objekt?" und bezieht zugleich Stellung gegenüber anderen philosophischen Theorien der Objektivität des 18. Jahrhunderts: Rationalismus, Empirismus, Idealismus, Skeptizismus. (shrink)

We present a quantum mechanical analysis of Bell’s approach to quantum foundations based on his hidden-variable model. We claim and try to justify that the Bell model contradicts to the Heinsenberg’s uncertainty and Bohr’s complementarity principles. The aim of this note is to point to the physical seed of the aforementioned principles. This is the Bohr’s quantum postulate: the existence of indivisible quantum of action given by the Planck constant h. By contradicting these basic principles of QM, Bell’s model (...) implies rejection of this postulate as well. Thus, this hidden-variable model contradicts not only the QM-formalism, but also the fundamental feature of the quantum world discovered by Planck. (shrink)

A detailed list of postulates is formulated in an algebraic setting. These postulates are sufficient to entail the standard time evolution governed by the Schrödinger or Dirac equation. They are also necessary in a strong sense: Dropping any one of the postulates allows for other types of time evolution, as is demonstrated with examples. Some philosophical remarks hint on possible further investigations.

The aim of interpretation is to capture the past in the future: to capture, not to recapture, first, because the iterative prefix suggests that meaning, which was once manifest, must now be found again. But the postulated author dispenses with this assumption. Literary texts are produced by very complicated actions, while the significance of even our simplest acts is often far from clear. Parts of the meaning of a text may become clear only because of developments occurring long after its (...) composition. And though the fact that an author means something may be equivalent to the fact that a writer could have meant it, this is not to say that the writer did, on whatever level, actually mean it.Alexander Nehamas, professor of philosophy at the University of Pittsburgh, has written articles on ancient Greek philosophy, literary theory, Nietzsche and Thomas Mann. (shrink)

In the paper I analyze two features of the genre of the pedagogical. First is a particular usage of “should” statements where one can identify an effect of erasing present normative behavior, while that which is postulated is turned into an unattainable ideal, or a value. Second, I analyze “presumptive tautologies” in the discourse of aims of education. I focus on negative dimensions of these two features and, using theoretical insights from Laclau and Rancière, I connect them to the work (...) of negativity in political ontology so that the relation between the pedagogical and the political can thus be re-articulated. (shrink)

Articles by two American mathematicians, E. V. Huntington and Oswald Veblen, are discussed as examples of a movement in foundational research in the period 1900-1930 called American postulate theory. This movement also included E. H. Moore, R. L. Moore, C. H. Langford, H. M. Sheffer, C. J. Keyser, and others. The articles discussed exemplify American postulate theorists' standards for axiomatizations of mathematical theories, and their investigations of such axiomatizations with respect to metatheoretic properties such as independence, completeness, and (...) consistency. (shrink)

Michael Oakeshott provides the best articulation of the widespread view that the moral foundations of the modern state limit it to the defense and maintenance of a system of formal rules governing individuals and non-state enterprises. While this understanding of the proper relation between individual and state has been challenged by liberals of a more Rawlsian persuasion, these criticisms have persuaded few to change their minds, as they rest upon assumptions that are plainly incompatible with the view under consideration. I (...) argue that, rightly understood, central and attractive features of Oakeshott’s own conception of understanding, philosophy, individuality, and education lead to significantly different conclusions than those embraced by Oakeshott himself. The “morality of individuality” upon which Oakeshott rests his strict restrictions on the use of state power requires that we be open to the use of that power to guarantee that all receive the education postulated by individuality. (shrink)

The postulates of rational preference suggested by Von Neumann and Morgenstern have been defended as descriptive or empirical generalizations and as normative principles. It is argued that the postulates are inaccurate empirical generalizations and unacceptable normative principles.

If K is an index of relative voting power for simple voting games, the bicameral postulate requires that the distribution of K -power within a voting assembly, as measured by the ratios of the powers of the voters, be independent of whether the assembly is viewed as a separate legislature or as one chamber of a bicameral system, provided that there are no voters common to both chambers. We argue that a reasonable index – if it is to be (...) used as a tool for analysing abstract, ‘uninhabited’ decision rules – should satisfy this postulate. We show that, among known indices, only the Banzhaf measure does so. Moreover, the Shapley–Shubik, Deegan–Packel and Johnston indices sometimes witness a reversal under these circumstances, with voter x ‘less powerful’ than y when measured in the simple voting game G1 , but ‘more powerful’ than y when G1 is ‘bicamerally joined’ with a second chamber G2 . Thus these three indices violate a weaker, and correspondingly more compelling, form of the bicameral postulate. It is also shown that these indices are not always co-monotonic with the Banzhaf index and that as a result they infringe another intuitively plausible condition – the price monotonicity condition. We discuss implications of these findings, in light of recent work showing that only the Shapley–Shubik index, among known measures, satisfies another compelling principle known as the bloc postulate. We also propose a distinction between two separate aspects of voting power: power as share in a fixed purse (P-power) and power as influence (I-power). (shrink)

This paper explores an analogy between two approaches to teleology in nature and two theories of authorship. I argue that Spinoza’s attempt (as Kant criticizes it in the Third Critique) to explain all natural unity, and explain away apparent teleological unity, in terms of inhering in the same subject (God) or proceeding causally from God’s essence mirrors the view Proust lays out in the essay “Gustave Moreau” that the features of a work of art are unified in virtue of occurring (...) together in, and proceeding from the laws of, the artist’s inner soul. Meanwhile, the strategy Kant favors for understanding interdependent natural systems like organisms—provisionally considering them as purposively designed—resembles the one Alexander Nehamas recommends in “The Postulated Author” (1981) for interpreting a work of art: imagining the agent who could have intended all its features. I propose that this analogy sheds light on the unity of the two parts of the Third Critique by pointing to the similarity between interpreting beautiful objects and interpreting nature. (shrink)

The pessimistic induction and the problem of underdetermination in the philosophy of science have a rich history. In their recent incarnation as the problem of unconceived alternatives, most fully articulated by Kyle Stanford (2010) in Exceeding Our Grasp, the induction is more specific and underdetermination is construed more epistemically than is typical…The problem is not that there are empirically equivalent alternatives, that is, alternative between which no empirical evidence could ever distinguish. The problem is that multiple radically different alternative that (...) are empirically inequivalent might be equally well-confirmed by current evidence, and we might fail to even conceive one or more of those alternatives… In “Of German Tanks and Scientific Theories: Estimating the Number of Unconceived Alternatives,” Burkay Ozturk (2016) challenges Stanford on a distinct front. By applying a method of statistical estimation to scientific alternatives, Ozturk argues that the possibility space within which the alternatives are located allows for probable knowledge. The particular frequentist estimation method Ozturk employs requires that we assume the alternative pool is finite, which seems to be both false and wildly implausible. At first glance. I argue in this comment that Ozturk’s postulate of finitude is actually defensible in circumstances that might actually hold for ordinary scientific contexts. (shrink)

The device of setting forth an argument in the form of a postulate set, while not unknown to jurisprudence, is nevertheless sufficiently novel to justify a brief account of the process. At one time human thought took axioms and postulates for avowals of unalterable truth, but the nineteenth century made common the practice of speculating with alternative presuppositional systems, so that deeper insight into the nature of this scientific device revealed it as merely a method among many for clarifying (...) and fecundating thought. (shrink)

In this study we shall analyze the postulate set into its various elements. In order to carry out our analysis, it is advisable to have before us a typical set.We take the set of five postulates for Boolean Algebras given by H. M. Sheffer in Trans. Am. Math Soc. 14, p. 482 ff.

Whereas several commentators have held that Kant’s argument for the postulate of private right fails insofar as it begs the question, I argue here that this criticism misses the mark. Critics have...

It was Heine who cynically suggested that Kant introduced the postulates of practical reason to comfort his manservant Lampe. Kant's view of morality is teleological, in that it sees obedience to the moral law as, at the same time, the fulfilment of human perfection. The legislation of the moral law which man himself creates is the true expression of man's autonomy and superiority over the sensuous bounds nature has set him. It is in such legislation that he begins to realise (...) his transcendentally free nature and fulfil himself as a distinctively human person. The law of duty is thus known, practically, as supremely authoritative. An intelligible ethical theory can certainly be extracted from the Kantian metaphysical context. Indeed, his doctrine is so complex that a number of alternative methods of demythologisation present themselves, depending largely upon the interests of the interpreter. (shrink)

The process of rationally revising beliefs in the light of new information is a topic of great importance and long-standing interest in artificial intelligence. Moreover, significant progress has been made in understanding the philosophical, logical, and computational foundations of belief revision. However, very little research has been reported with respect to the revision of other mental states, most notably propositional attitudes such as desires and intentions. In this paper, we present a first attempt to formulate a general framework for understanding (...) the revision of mental states. We develop an abstract belief-desire-intention model of agents, and introduce a notion of rationality for this model. We then present a series of formal postulates characterizing the processes of adding beliefs, desires, and intentions, updating costs and values, and removing beliefs, desires, and intentions. We also investigate the computational complexity of several problems involving the abstract model and comment on algorithms for revision. (shrink)

Although the subjective expected utility (SEU) theory is more than 60 years old, it was recently discovered by Hartmann (Econometrica 88(1):203–205, 2020, https://doi.org/10.3982/ECTA17428) that one of the original seven postulates is redundant, i.e., it is implied by the other six postulates. In this brief communication, we show that this redundant axiom is the only one that is implied by the other axioms, thereby establishing that the remaining six postulates form an independent axiomatic system. This result further streamlines the preference assumptions (...) underlying the SEU theory. (shrink)

It is widely claimed that the second Critique’s argument for the postulate of immortality is relevantly different from the first Critique’s argument for the postulate. It is also widely claimed that after the second Critique, Kant distances himself from its particular version of the argument, and even the postulate altogether. It is the purpose of this article to challenge these claims, arguing instead that (a) there is overwhelming textual evidence showing that Kant did not abandon the (...) class='Hi'>postulate; (b) the second Critique does not contain a substantially different argument for the postulate than how it is argued for in the first Critique; and (c) the philosophical objections levied against the second Critique’s argument, including its putative substitution of holiness for virtue, become moot once its argument is better understood. (shrink)

A reproducibility principle is formulated and adopted as the guiding criterion for the acceptance of an experimental procedure as a simultaneous measurement of several observables. It is pointed out that this criterion can be applied to classical as well as quantum physics, and that it incorporates compatible as well as incompatible observables. The concept of fuzzy probability measure is presented as a possible mathematical tool for the description of statistical processes involving measurements of incompatible observables.

This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the 17th-century studies (...) on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the 18th century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz’s essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Leibniz editions, most of them are transcribed from Leibniz’s manuscripts written in Hannover, and published here for the first time. The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments. (shrink)

Kant's noncognitive argument based on practical reason claims that moral considerations alone suffice to justify the idea of personal immortality as a postulate. Some recent objections are considered here that have charged him with overstepping his own distinction between phenomenon and noumenon. After examining the arguments, Kant is exonerated of having violated his own principles. More troubling, however, is the peculiarity involved in postulating an infinite progression toward a goal whose attainment, by hypothesis, would undermine the very foundations of (...) morality (which for Kant always requires the agonistic condition of struggling to improve one's lower nature). It is argued that this paradox necessitates a reexamination of some tacit cultural presuppositions underlying Kant's conception of the soul. Finally, an examination is made of the thought of Kitarō Nishida, whose Zen Buddhist–inspired dialectic of the basho (logical "place") provides an alternative perspective from which to reconsider the postulate of immortality. Nishida, like Kant, rigorously maintains the phenomenonnoumenon distinction, yet his examination of ethics leads him to postulate an eventual sublation of the "soul" principle. It is concluded that Kant's postulate of immortality, while plausible enough on its own terms, is limited by a Western cultural bias and therefore fails in the end to be compelling. (shrink)

Sufficient texts show that for aristotle the universal notion expresses the same real thing as the particular, Though in a different way. His grounds for a universal so conceived are twofold. First, In every sensible thing there is a basic formal principle that, Though individual, Brings each instance into formal identity with all the other instances. Secondly, In human intellectual cognition there is an active principle that raises knowledge above the status of photographing or registering or cataloguing, And actualizes what (...) was only potential in the real thing. In knowing sensible things universally, The human intellect is able to grasp the concrete thing as characterized by a formal nature, Thereby knowing it in a way that holds equally for all other instances. Though patently incomplete, This conception of the universal is free from internal contradictions. It provides a framework for fruitful discussion, And remains a challenge. (shrink)

Most philosophers of science nowadays hold a network or postulational view of the meaning of theoretical words. However, there are many nuances to this view, and after explicitly separating them, we show what we take to be wrong with each one. While we reject the postulational view we do not defend its traditional alternatives either; rather we show the pointlessness of insisting on a single source for the meaning of theoretical words. We also point out the shortcomings of Carnap's newest (...) meaning criterion which depends upon a network view. But, again, we suggest not only that this new rendition of the criterion is faulty but also that there is something misguided about any search at all for such a criterion. (shrink)

A theory of magnitudes involves criteria for their equivalence, comparison and addition. In this article we examine these aspects from an abstract viewpoint, by focusing on the so-called De Zolt’s postulate in the theory of equivalence of plane polygons (“If a polygon is divided into polygonal parts in any given way, then the union of all but one of these parts is not equivalent to the given polygon”). We formulate an abstract version of this postulate and derive it (...) from some selected principles for magnitudes. We also formulate and derive an abstract version of Euclid’s Common Notion 5 (“The whole is greater than the part”), and analyze its logical relation to the former proposition. These results prove to be relevant for the clarification of some key conceptual aspects of Hilbert’s proof of De Zolt’s postulate, in his classicalFoundations of Geometry(1899). Furthermore, our abstract treatment of this central proposition provides interesting insights for the development of a well-behaved theory ofcompatiblemagnitudes. (shrink)

Erwin Panofsky developed the postulate of clarification to explain the mental habit common to Gothic architecture and Western medieval scholasticism, but the postulate is equally applicable to the commentary tradition of Song-dynasty China. The commentary on the Book of Changes authored by Cheng Yi (1033–1107) provides a good example of how the Confucians of the Song dynasty took their concern for clarity to a recognizably medieval extreme. By looking at how Cheng Yi understands and foregrounds the clarity of (...) the Book of Changes, we can begin to see both what was medieval about Song-dynasty China and why the medieval method continues to be viable for interpreters of the Book of Changes. (shrink)

In this article I analyse the correlation between the direct and the mediated in activity, consciousness and personality. Cultural-historical psychology, attitude theory and activity theory were solving the tasks of overcoming the ‘postulate of directness’, which led to the ‘postulate of mediation’. None of these postulates shows in its entirety the path of human psychological development and the work of human consciousness. The direct and the mediated are examined in this article as equally necessary conditions for the development (...) of the human psyche. A lot of attention is paid to the nature of the initial, primary spontaneity of a child as an indispensable condition for mastering culture. The direct is the necessary condition for the development of culture, and the mediated is the mechanism of this development. (shrink)

The projection postulate, which prescribes “collapse of the state vector” upon measurement, is not an essential part of quantum mechanics. Rather it is only an optional discarding of certain branches of the state vector that are expected to be irrelevant for the purpose at hand. However, its use is hazardous, and there are examples of repeated measurements for which the conventional application of the projection postulate leads to incorrect results.

If we take the state function of quantum mechanics to describe belief states, arguments by Stairs and Friedman-Putnam show that the projection postulate may be justified as a kind of minimal change. But if the state function takes on a physical interpretation, it provides no more than what I call a fortuitous approximation of physical measurement processes, that is, an unsystematic form of approximation which should not be taken to correspond to some one univocal "measurement process" in nature. This (...) fact suggests that the projection postulate does not provide a proper locus for interpretive investigation. Readers will also find section 3's analysis of fortuitous approximations of independent interest and presented without the perils of quantum mechanics. (shrink)

The author's approach to philosophy is strongly influenced by contemporary axiomatics. His central thesis is that each of us should try to clarify the postulates which are implicit in our thinking. In this way philosophic communication can be facilitated, and differences resolved.--R. B.

In this paper I argue that Kant would have endorsed Clifford’s principle. The paper is divided into four sections. In the first, I review Kant’s argument for the practical postulates. In the second, I discuss a traditional objection to the style of argument Kant employs. In the third, I explain how Kant would respond to this objection and how this renders the practical postulates consistent with Clifford’s principle. In the fourth, I introduce positive grounds for thinking that Kant would have (...) endorsed this principle. (shrink)

I consider how procedural postulationism might be combined with the view that postulational possibility should itself be open to expansion.