We introduce an abstract framework for general rough set theory from a mereological perspective and consider possible concepts of ’a priori’ granules and granulation in the same. The framework is ideal for relaxing many of the relatively superfluous set-theoretic axioms and for improving the semantics of many relation based, cover-based and dialectical rough set theories. This is a relatively simplified presentation of a section in three different recent research papers by the present author.

The acquisition and evolution of speech production, discourse and communication can be negatively impacted by brain malformations. We describe, for the first time, a case of developmental dynamic dysphasia (DDD) in a right-handed adolescent boy (subject D) with cortical malformations involving language-eloquent regions (inferior frontal gyrus) in both the left and the right hemispheres. Language evaluation revealed a markedly reduced verbal output affecting phonemic and semantic fluency, phrase and sentence generation and verbal communication in everyday life. Auditory comprehension, repetition, naming, (...) reading and spelling were relatively preserved, but executive function was impaired. Multimodal neuroimaging showed a malformed cerebral cortex with atypical configuration and placement of white matter tracts bilaterally and abnormal callosal fibers. Dichotic listening showed right hemisphere dominance for language and functional magnetic resonance imaging (fMRI) additionally revealed dissociated hemispheric language representation with right frontal activation for phonology and bilateral dominance for semantic processing. Moreover, subject D also had congenital mirror movements (CMM), defined as involuntary movements of one side of the body that mirror intentional movements of the other side. Transcranial magnetic stimulation and fMRI during voluntary unimanual (left and right) hand movements showed bilateral motor cortex recruitment and tractography revealed a lack of decussation of bilateral corticospinal tracts. Genetic testing aimed to detect mutations that disrupt the development of commissural tracts correlating with CMM (e.g., Germline DCC mutations) was negative. Overall, our findings suggest that DDD in subject D resulted from the underdevelopment of the left inferior frontal gyrus with limited capacity for plastic reorganization by its homologous counterpart in the right hemisphere. Corpus callosum anomalies probably contributed to hinder interhemispheric connectivity necessary to compensate language and communication deficits after left frontal involvement. (shrink)

Hans Reichenbach introduced two seemingly separate sets of distinctions in his epistemology at different times. One is between the axioms of coordination and the axioms of connections. The other distinction is between the context of discovery and the context of justification. The status and nature of each of these distinctions have been subject-matter of an ongoing debate among philosophers of science. Thus, there is a significant amount of works considering both distinctions separately. However, the relevance of Reichenbach's two distinctions to (...) each other does not seem to have enjoyed the same amount of interest so far. This is what I would like to consider in this paper. In other words, I am concerned with the question: what kind of relationship is there between his two distinctions, if there is any? (shrink)

This paper considers the question whether the notion of the relative apriori, central to Michael Friedman’s transcendentalist programme for philosophy of science, is available also to philosophers who reject appeals to a synthetic a priori. After tracing the rediscovery of the relative a priori and delineating its potential, the question is considered whether Friedman’s arguments against Quinean naturalism and Carnap’s attenuated logicism tell against a conception of philosophy as scientific metatheory that combines logical and empirical inquiries. (...) Finding an opening here it is argued that this conception can also help itself to the notion of a relative a priori which, it is agreed, is central to historically informed theorising about science. (shrink)

This paper is a sequel to my 'Theological Misinterpretations of Current Physical Cosmology' (Foundations of Physics [1996], 26 (4); revised in Philo [1998], 1 (1)). There I argued that the Big Bang models of (classical) general relativity theory, as well as the original 1948 versions of the steady state cosmology, are each logically incompatible with the time-honored theological doctrine that perpetual divine creation ('creatio continuans') is required in each of these two theorized worlds. Furthermore, I challenged the perennial theological doctrine (...) that there must be a divine creative cause (as distinct from a transformative one) for the very existence of the world, a ratio essendi. This doctrine is the theistic reply to the question: 'Why is there something, rather than just nothing?' I begin my present paper by arguing against the response by the contemporary Oxford theist Richard Swinburne and by Leibniz to what is, in effect, my counter-question: 'But why should there be just nothing, rather than something?' Their response takes the form of claiming that the a priori probability of there being just nothing, vis-à-vis the existence of alternative states, is maximal, because the non-existence of the world is conceptually the simplest. On the basis of an analysis of the role of simplicity in scientific explanations, I show that this response is multiply flawed, and thus provides no basis for their three contentions that (i) if there is a world at all, then its 'normal', natural, spontaneous state is one of utter nothingness or total non-existence, so that (ii) the very existence of matter, energy and living beings constitutes a deviation from the allegedly 'normal', spontaneous state of 'nothingness', and (iii) that deviation must thus have a suitably potent (external) divine cause. Related defects turn out to vitiate the medieval Kalam Argument for the existence of God, as espoused by William Craig. Next I argue against the contention by such theists as Richard Swinburne and Philip L. Quinn that (i) the specific content of the scientifically most fundamental laws of nature, including the constants they contain, requires supra-scientific explanation, and (ii) a satisfactory explanation is provided by the hypothesis that the God of theism willed them to be exactly what they are. Furthermore, I contend that the theistic teleological gloss on the 'Anthropic Principle' is incoherent and explanatorily unavailing. Finally, I offer an array of considerations against Swinburne's attempt to show, via Bayes's theorem, that the existence of God is more probable than not. (shrink)

The aim of this paper is to show that a comprehensive account of the role of representations in science should reconsider some neglected theses of the classical philosophy of science proposed in the first decades of the 20th century. More precisely, it is argued that the accounts of Helmholtz and Hertz may be taken as prototypes of representational accounts in which structure preservation plays an essential role. Following Reichenbach, structure-preserving representations provide a useful device for formulating an up-to-date version of (...) a (relativized) Kantian a priori. An essential feature of modern scientific representations is their mathematical character. That is, representations can be conceived as (partially) structure-preserving maps or functions. This observation suggests an interesting but neglected perspective on the history and philosophy of this concept, namely, that structure-preserving representations are closely related to a priori elements of scientific knowledge. Reichenbach’s early theory of a relativized constitutive but non-apodictic a priori component of scientific knowledge provides a further elaboration of Kantian aspects of scientific representation. To cope with the dynamic aspects of the evolution of scientific knowledge, Cassirer proposed a re-interpretation of the concept of representation that conceived of a particular representation as only one phase in a continuous process determined by pragmatic considerations. Pragmatic aspects of representations are further elaborated in the classical account of C.I. Lewis and the more modern of Hasok Chang. (shrink)

This paper is the forerunner of an extensive logical analysis of the relativity idea, in which an axiomatic structure based upon the principles of topology is developed. It is meant to expose the manner in which relativity stretches from the pole of pure conception to that of factual observation, from the a priori to the a posteriori. We take pains to show, in connection with special relativity, precisely which elements are postulational and which are verifiable empirically. Our attempt can (...) be somewhat naively characterized as an effort to show how misguided it is to "derive" relativity from such experimental facts as the Michelson-Morley experiment--as so many textbooks profess to do. (shrink)

This study aims, first, to delimit the seemingly synonymous concepts of “phenomenon” and “appearance” and second, to trace the functions of each in Kant’s philosophy and the phenomenological tradition. The analy­sis is based on Immanuel Kant’s Critique of Pure Reason and the central works of Edmund Husserl and Eugen Fink. Kant does not explicitly distinguish the two terms and only speaks about phenomena when he deals with the categorial application of reason. With Husserl, appearance is linked with the area of (...) the natural attitude while the phenomenon is absolute. Fink’s position is interesting in that it differs from the views of the main representatives of transcendental philosophy, Kant and Husserl. According to Fink, appearing is the foundation of the fact that what exists is and that appearing is being. Fink takes a different approach to the meanings of appearance as opposing the thing in itself which possesses true but unknowable being and appearance as taking place in the “relative” sphere of the natural attitude : with Fink, appearance turns out to be the condition of the existence of objects. Appearance, understood through the prism of the human being which perceives something as Vorschein, implies an inherently open world. Following Fink, I analyse these provisions and examine, first, light as the metaphysical source of cognition, second, the human being as a special kind of being, third, the pre-Socratic treatment of being and, fourth, the formation of a distinct phenomenological idiom. I come to the conclusion that the metaphysical-ontological method of phenomenological analysis of appearance proposed by Fink affords a new insight into the a priori principle and the nature of Kant’s “thing in itself” and proposes a new grounding of Husserl’s thesis which questions Kant’s agnosticism. (shrink)

Arguably, one of the most exciting recent advances in moral philosophy is the ongoing scientific naturalization of normative ethics and metaethics, in particular moral psychology. A relatively neglected area in these improvements that is centrally important for developing a scientifically based naturalistic metaethics concerns the nature and acquisition of successful moral agency. In this paper I lay out two examples of how empirically based findings help us to understand and explain some cases of successful moral agency. These are research in (...) moral internalization and aggression management. Using these examples, I sketch some lessons for investigating successful moral learning and moral action. My proposal reflects a common theme in scientifically based philosophy generally: the shift from the armchair methods of analyzing concepts and finding a priori foundations, the enterprise of first philosophy, to an effort to study the phenomena themselves, using empirical findings and theories to answer philosophical questions about these phenomena, an endeavor recently characterized as second philosophy. (shrink)

The Theory of Relativity and A Priori Knowledge will hereafter be cited as "RAK. " The German edition is out of print. 2 H. Reichenbach, The Philosophy of ...

The capacity to engage in systems thinking is often viewed as being a product of being able to understand complex systems due to one's facility in mastering systems theories, methods, and being able to adeptly reason. Relatively little attention is paid in the systems literature to the processes of learning from experience and creating knowledge as a direct consequence of individuals engaging systems thinking itself over time. In fact, the potential efficacy of systems thinking to improve performance normally seen as (...) only contingent on a priori knowledge, rather than knowledge created via learning from experience. Such newly create knowledge often results from engaging in modeling efforts and systemic forms of inquiry. This article proposes a model for creating new knowledge by coupling systems modeling with a pragmatic approach to knowledge-creation. This approach is based on a foundation of the pragmatic concepts first proposed by the American philosopher/scientist Charles Sanders Peirce over a century ago. This model offers systems practitioners a framework to engage in knowledge-intensive systems thinking (KIST) for addressing complex problematic issues. (shrink)

After a chapter which is an introduction to and summary of the rest of the book, chapter 2 begins by criticizing various attempts to do away with theories, such as the Reichenbach-Salmon conception of theoretical truth in terms of observational consequences, and the Ramsey strategy of replacing first-order theoretical sentences by second-order nontheoretical ones; it then argues against hypothetico-deductivist theories of confirmation on the grounds that they are unable to handle the relevance of evidence to theory, whether or not other (...) formal constraints or even nonformal ones such as simplicity and explanatory power are added to those theories; it ends with an exposition of the Reichenbach-Carnap conventionalist thesis that the confirmation of hypotheses with evidence presupposes analytic principles connecting hypothetical and empirical concepts. Chapter 3 criticizes Bayesian theories of confirmation on such grounds as that the a priori arguments for Bayesian restrictions on beliefs are insufficient; that the Bayesian explanations of notions like variety of evidence, ad hocness, and simplicity are inadequate; and that they cannot account, without drastic revisions, for the relevance of evidence to theory, especially old evidence to new theory. Chapter 4 is an unsympathetic account of historically oriented philosophies of science; Lakatos’s notion of progressive research programs and Laudan’s theory of problem-solving effectiveness are found to be insufficiently precise and dubbed examples of "new fuzziness", while the Sneed-Stegmüller dynamics of theories is regarded as "a paradigm of misplaced rigor" ; and all three are criticized as unable to explicate the concept of evidential relevance. Chapter 5 is a formal and informal elaboration of the basic idea in Glymour’s account of theory and evidence, namely that confirmation or support is a three-term relation among evidence, hypothesis, and theory, so that evidence confirms an hypothesis only relative to a theory, and such that evidence e confirms hypothesis h relative to T if T with e implies, but T without e does not imply, an instance of h, and T with e does not imply a comparable hypothesis h’ different from h; the most interesting part of this chapter is a series of discussions showing how such an idea makes sense of the "methodological truisms" that it is possible selectively to test certain parts of a theory but not others, that a theory is supported better by a greater variety of evidence, that redundant or physically meaningless quantities are an undesirable feature of theories, that there are no inviolable rules, that a "white shoe" does not confirm "all ravens are black," that a theory is more useful and better supported than the set of its observational consequences, and that the hypothetico-deductive method often works. Since Glymour claims no originality for the conception of this general account, but only for its description, he plausibly thinks it necessary to apply it to some important historical cases of actual science; he does so in the next chapter by discussing at some length the structure and merits of Ptolemaic and Copernican astronomy, of Newton’s universal gravitation, of nineteenth century atomism, of Freud’s Rat Man, and of general relativity. For example, he argues convincingly that Copernicanism was better supported by the evidence available even before the telescope because it alone, and not the Ptolemaic theory, can determine some planetary properties which are presupposed by both theories, can test and confirm some common hypotheses, and can be confirmed in an essential rather than incidental manner; and though Glymour admits that the Copernicans tended to argue in terms of explanatory rather than confirmatory superiority, he sketches an interesting account of the relation between explanation and confirmation which strengthens his case. He also analyzes the text at the beginning of book 3 of Newton’s Principia and compiles a reconstruction of the intricate details of the inferential structure of the argument to universal gravitation; his impressive reconstruction clearly shows that Newton’s method is neither the inductivist one he himself thought he was following, nor the one attributed to him by Pierre Duhem, but rather one in accordance with Glymour’s so-called "bootstrap strategy" of repeatedly using the evidence from Kepler’s second and third laws, from lunar data, and from falling bodies, together with the theory consisting of the second and third laws of motion, to arrive at increasingly general instances of the principle of universal gravitation. Glymour’s account of arguments for and against the atomic theory from Thomson to Cannizzaro is his longest historical example, but he himself admits that this illustration of the bootstrap strategy is "certainly not the neatest", and rather "diffuse, and perhaps disconnected". Chapter 7 is a detailed application of the same principles to the technique known among social scientists as "causal modeling"; since such "causal models" are essentially systems of algebraic equations, Glymour’s account shows indirectly that the bootstrap strategy is applicable to any scientific theory presented as a set of algebraic equations; this, of course is not surprising, since the formal considerations with which Glymour begins the exposition of his theory in chapter 5 involve systems of algebraic equations. Chapter 8 is an attempt to apply Glymour’s theory of evidence to the very common scientific practice of curve-fitting, where one measures values of two or more quantities and then infers a functional relationship; Glymour argues that simpler polynomials are preferred because they are tested more frequently and more severely by the data and because they are more informative; but then he criticizes his own explanation and concludes that "the bootstrap procedures of chapter 5 do not seem to help the problem much more than a whit" ; this is admirably honest, but if one wants an additional logical or methodological rationale, then one would perhaps have to go to the meta-level and say that Glymour is here testing his own theory, and he is more interested in a further illustration of the bootstrap methodology even with a failed test, than he is to claim universal or exclusive validity for it. In chapter 9 Glymour uses his bootstrap theory of confirmation to criticize geometrical conventionalism; he considers the alternative theories of space or space-time proposed by conventionalists to show the radical undetermination of geometries by evidence, for example, a non-Euclidean geometry with no universal force instead of Newtonian gravitation with Euclidean geometry; he argues that such alternatives are simply not as well tested as the originals and that their equivalence to the originals is questionable. The last chapter is a brief discussion of further problems worthy of future investigation. (shrink)

The prevailing interpretation of Augustine’s theory of divine illumination suggests that illumination provides the human mind with the content of our a priori concepts. While there is strong textual evidence to support this view, I contend it offers an incomplete picture of the work illumination does in Augustine’s epistemology. Based on an analysis of Augustine’s solution to the paradox of language acquisition in De magistro, I argue illumination also supplies the mind with the content of all our empirical concepts. (...) In this text, Augustine calls our attention to the problem that learning the meaning of words by even the simplest of means—through direct acquaintance (i.e., by having an object pointed out to us and labeled with a name)—turns out to require a relatively sophisticated grasp of the word’s usage in the first place, one that depends on illumination to provide the content of all our universal concepts. (shrink)

A thumbnail sketch of the philosophical thinking about the a priori would surely include that it has been dominated by two major approaches: the Kantian absolute conception of it and the Millian-Quinean absolute rejection of it (section 2). Yet, one can find in the literature claims about the existence of a ›functional a priori‹, a ›relative a priori‹, a ›relativised a priori‹ and suchlike. They are all meant to carve a space between the two extremes. (...) An important thought behind the search for a middle ground is that the supposed coincidence between the constitutive and the unrevisable is wrong. The entitlement to accept a principle as being constitutive of experience prior to any empirical justification of it is compatible with an entitlement to revise or abandon such a principle on empirical grounds. If a priori principles are meant to be independent of experience, how should this claim of independence be understood so that room is left for the possibility that a principle is both independent of experience and revisable on empirical grounds (section 3)? A straightforward and natural way to approach this issue is to think of constitutive principles along the lines of Poincaréan conventions, which can be seen as delineating a new sense of the a priori – the conventional a priori principles. These are substantive principles that are constitutive of theoretical frameworks – in the sense that they define (or constitute) the object of knowledge – without being either synthetic a priori or empirical generalisations. Still, their negation is conceivable and they are revisable on empirical grounds (section 4). (shrink)

Kant's original version of transcendental philosophy took both Euclidean geometry and the Newtonian laws of motion to be synthetic a priori constitutive principles—which, from Kant's point of view, function as necessary presuppositions for applying our fundamental concepts of space, time, matter, and motion to our sensible experience of the natural world. Although Kant had very good reasons to view the principles in question as having such a constitutively a priori role, we now know, in the wake of Einstein's (...) work, that they are not in fact a priori in the stronger sense of being fixed necessary conditions for all human experience in general, eternally valid once and for all. And it is for precisely this reason that Kant's original version of transcendental philosophy must now be either rejected entirely or radically reconceived. Most philosophy of science since Einstein has taken the former route: the dominant view in logical empiricism, for example, was that the Kantian synthetic a priori had to be rejected once and for all in the light of the general theory of relativity. (shrink)

An influential strand in philosophy of science claims that scientific paradigms can be understood as relativized a priori frameworks. Here, Kant’s constitutive a priori principles are no longer held to establish conditions of possibility for knowledge which are unchanging and universally true, but are restricted only to a given scientific domain. Yet it is unclear how exactly a relativized a priori can be construed as both stable and dynamical, establishing foundations for current scientific claims while simultaneously making (...) intelligible the transition to a subsequent framework. In this article, I show that important resources for this problem have been overlooked in Kant’s theory of reflective judgement in the third Critique. I argue that Kant accorded the task of formulating new scientific laws to reflective judgement, which is charged with forming new ‘universals’ that guide the experience of nature. I show that this is the very task attributed to the relativized a priori: the constitution of a given conceptual framework, not of the conditions for object-reference as such. I conclude that Kant’s considered conception of science encompasses the operations of both reflective and determining judgement. Relativizations of the a priori should follow Kant’s lead. (shrink)

This paper is a defence of the view that action explanation deploys (relatively) a priori principles. The argument is that this is so because action explanation succeeds, Not just through revealing regularity, But through exhibiting the presence of an expected and privileged pattern. Its job is to 'normalise' action, Not just 'regularise' it.

This paper explores the problems that are raised by a certain traditional sceptical paradox. The conclusion will be that the most challenging problem raised by this paradox does not primarily concern the justification of beliefs; it concerns the justification of belief-forming practices. This conclusion is supported by showing that if we can solve the sceptical problem for belief-forming practices, then it will be a relatively straightforward matter to solve the problem that concerns the justification of beliefs.

At the outset of this discussion, I undertook to present an argument from design which would follow Swinburne's example in making use of a priori judgments, while avoiding some of the objections which have been posed in response to his treatment of these issues. So we need to ask: how does this approach to the question of design compare with Swinburne's?Swinburne argues that a chaotic world is a priori more likely than an ordered world: this consideration provides one (...) central reason, on his account, for giving an explanation of some sort for the world's regularity. The other central argument he advances for this claim is the argument from analogy (in terms of the coins) which we noted earlier. The approach I have taken offers an alternative route to this same conclusion. In particular, it substitutes the simpler a priori judgments recorded in (i) and (ii) for the rather difficult and contentious claim that chaos is a priori more likely than order. In place of this claim, I have offered the judgment that order, or recurrence, is more likely given the activity of a common source or common kind of source than otherwise: this proposal does not commit us to a view either way on the question of whether order is a priori likely per se. Moreover, in place of Swinburne's analogical argument, I have offered an a priori approach, with the advantages I have noted.Given that recurrence is to be explained, we might ask: why offer an explanation in terms of design? On this point, Swinburne argues, for instance, that no other explanation of temporal regularity is even possible a priori. Again, the a priori principles which I have used, in (iv) and (v), may be less ambitious, but at the same time more persuasive. In support of this same idea, Swinburne also cites various ideas to do with the predictive power of the idea of design. I have tried to bring out the role of this sort of consideration in terms of my principle (v). Principle (iv) has no place in Swinburne's account, in view of his reliance on the principle of simplicity as a measure of prior probability.Lastly, we may ask: if we are to cite a designer, are there reasons for attributing to this agent more powers than are needed for the production of the effect to be explained? On this point, Swinburne cites the principle of simplicity. Again, my approach avoids what has proved to be a relatively controversial judgment about the nature of a priori probabilities, offering in place of the principle of simplicity the less ambitious principle recorded in (iii). At this point, I have moreover inverted the logical sequence of Swinburne's argument: it seems to me that, in the ways I have indicated, it is helpful to consider the extent of the powers of the source of recurrence before addressing the question of design.In these various ways, I hope I have made good my undertaking to present an argument which avoids some of the controversy surrounding the particular measures of a priori probability which figure in Swinburne's argument. Moreover, I hope that this approach provides an indication of how a priori judgments may function in a relatively unproblematic way within an argument from design, in so far as (i)–(v) are all rather modest proposals. In sum, the argument I have presented is distinguished by its explicit use of the a priori judgments recorded in (i)–(v), by its attempt to buttress in this fashion analogical forms of argument, and by the logical role it gives to the idea that the source of regularity possesses more powers than are required for the production of this effect.Lastly, we might ask: how persuasive is this argument? Of course, the cogency of the idea of design depends upon the balance of debate in other areas of the philosophy of religion, especially upon our ability to provide some account of the existence of evil. In this paper, I have been concerned to argue simply that recurrence by kind provides evidence for design: I have not addressed the question of whether other features of the world provide good evidence against the idea of (benevolent) design. However, if we confine our attention to this one phenomenon, there is it seems to me good evidence for the idea of design, (i) and (ii) suggest that recurrence surely calls for some explanation; (iii), together with the existence in nature of statistical irregularities, suggests that whatever provides this explanation could have brought about other effects besides; and design seems the only clear explanation of why this effect should have been brought about, if (as I have argued) analogies drawn from vegetable and animal reproduction fail, and if we cannot explain the effect satisfactorily by reference to the conditions of observation. Moreover, I have argued that there are reasons for supposing that the probability a priori of design is relatively high in relation to the probability a priori of any rival hypothesis of equivalent predictive power. In brief, this is because the design hypothesis (unlike the hypothesis of theism) can cite an agent of relatively indeterminate power in order to account for the phenomenon to be explained. In this regard, it is less ‘precisely defined’ than any rival hypothesis of equivalent predictive power. If all of this is so, then as philosophers from early times have supposed, temporal regularity provides the basis for a powerful argument in favour of design. It remains true, of course, that its import can be judged in full only when we have taken into account the relevance of other phenomena, many of which are apparently less favourable to the idea of design. (shrink)

ABSTRACT: It is a familiar story that Kant’s defence of our synthetic a priori cognition in the Critique of Pure Reason suffered sharp criticism throughout the extended philosophical revolutions that established analytic philosophy, the pragmatist tradition, and the phenomenological tradition as dominant philosophical movements in the first half of the twentieth century. One of the most important positive adaptations of Kant’s outlook, however, was the combined analytic and pragmatist conceptions of the a priori that were developed by the (...) American philosophers C. I. Lewis (1883–1964) and Wilfrid Sellars (1912–1989), most notably in Lewis’s 1929 classic, Mind and the World Order, followed by Sellars’ critical reworking of Lewis’s outlook in ‘Is There a Synthetic A Priori?’ (1953) and other mid-century articles. Both Lewis and Sellars defended central aspects of Kant’s analysis of our a priori knowledge of mind-independent physical objects and necessary causal connections. But both also radically transformed Kant’s view by defending the idea that there are alternative a priori conceptual frameworks that are subject to an ongoing process of reassessment and replacement on overall pragmatic and explanatory grounds. Furthermore, while Sellars’ answer to his question, ‘Is There a Synthetic A Priori?’ thus represented a partial endorsement of Lewis’s pragmatic relativization of the a priori, I argue that Sellars’ account of meaning diverged from Lewis in ways that constituted a significant improvement upon the previous ‘analytic’ defenses of the a priori, not only in Lewis but in general. This arguably has implications for wider disputes concerning the nature and possibility of a priori knowledge in non-formal domains. (shrink)

The principle of mass additivity states that the mass of a composite object is the sum of the masses of its elementary components. Mass additivity is true in Newtonian mechanics but false in special relativity. Physicists have explained why mass additivity is true in Newtonian mechanics by reducing it to Newton’s microphysical laws. This reductive explanation does not fit well with deducibility theories of reductive explanation such as the modern Nagelian theory of reduction, and the a priori entailment theory (...) of reduction that is prominent in the philosophy of mind. Nonetheless, I argue that a reconstruction of the explanation that incorporates distinctively philosophical concepts in fact fits both theories. I discuss the implications of this result for both theories and for the reductive explanation of consciousness. (shrink)

This book originally appeared in 1920 under the title Relativitätstheorie und Erkenntnis Apriori and was the first of Reichenbach's numerous writings on the philosophical problems of relativity theory, space, and time. In this book the author attempted to show how Kant's theory of the a priori, especially concerning the concept of the a priori as "constituting the concept of [the] object" in question, comes into irrevocable conflict with certain facts of both the General and Special theories of relativity; (...) and that, therefore, we must amend Kant's treatment of the role of the a priori in knowledge accordingly. The translator, Maria Reichenbach, has provided a long and useful introduction, placing the work in the context of Reichenbach's philosophical career and activities, and providing background material on the author himself. This is the second of a continuing series of works by Reichenbach to appear under the California Press imprint.—P. J. M. (shrink)

In this book, David Stump traces alternative conceptions of the a priori in the philosophy of science and defends a unique position in the current debates over conceptual change and the constitutive elements in science. Stump emphasizes the unique epistemological status of the constitutive elements of scientific theories, constitutive elements being the necessary preconditions that must be assumed in order to conduct a particular scientific inquiry. These constitutive elements, such as logic, mathematics, and even some fundamental laws of nature, (...) were once taken to be a priori knowledge but can change, thus leading to a dynamic or relative a priori. Stump critically examines developments in thinking about constitutive elements in science as a priori knowledge, from Kant’s fixed and absolute a priori to Quine’s holistic empiricism. By examining the relationship between conceptual change and the epistemological status of constitutive elements in science, Stump puts forward an argument that scientific revolutions can be explained and relativism can be avoided without resorting to universals or absolutes. (shrink)

In my book In Defense of Pure Reason, I offer an extended defense of the idea of a priori justification and, more specifically, of a rationalist conception of such justification: one according to which rational insight or intuition provides genuine justification for claims that need not be merely definitional or tautological in character. In the relatively brief space available to me on the present occasion, I want to present and defend, necessarily in rather broad strokes, four of the most (...) central claims that are discussed at much greater length in that book. I will say the most about the first of these theses, somewhat less about the second and third, and only a very little about the fourth. (shrink)

Empiricist theories of knowledge are attractive for they offer the prospect of a unitary theory of knowledge based on relatively well understood physiological and cognitive processes. Mathematical knowledge, however, has been a traditional stumbling block for such theories. There are three primary features of mathematical knowledge which have led epistemologists to the conclusion that it cannot be accommodated within an empiricist framework: 1) mathematical propositions appear to be immune from empirical disconfirmation; 2) mathematical propositions appear to be known with certainty; (...) and 3) mathematical propositions are necessary. Epistemologists who believe that some nonmathematical propositions, such as logical or ethical propositions, cannot be known a posteriori also typically appeal to the three factors cited above in defending their position. The primary purpose of this paper is to examine whether any of these alleged features of mathematical propositions establishes that knowledge of such propositions cannot be a posteriori. (shrink)

A relationist will account for the use of ‘left’ and ‘right’ in terms of relative orientations, and other properties and relations invariant under mirroring. This analysis will apply whenever mirroring is a symmetry, so it certainly applies to classical mechanics; we argue it applies to any physical theory formulated on a manifold: it is in this sense an a priori symmetry. It should apply in particular to parity violating theories in quantum mechanics; mirror symmetry is only broken in (...) such theories as a special symmetry. (shrink)

Abstract: This article contends that the relation of early logical empiricism to Kant was more complex than is often assumed. It argues that Reichenbach's early work on Kant and Einstein, entitled The Theory of Relativity and A Priori Knowledge (1920) aimed to transform rather than to oppose Kant's Critique of Pure Reason. One the one hand, I argue that Reichenbach's conception of coordinating principles, derived from Kant's conception of synthetic a priori principles, offers a valuable way of accounting (...) for the historicity of scientific paradigms. On the other hand, I show that even Reichenbach, in line with Neo-Kantianism, associated Kant's view of synthetic a priori principles too closely with Newtonian physics and, consequently, overestimated the difference between Kant's philosophy and his own. This is even more so, I point out, in the retrospective account logical empiricism presented of its own history. Whereas contemporary reconstructions of this history, including Michael Friedman's, tend to endorse this account, I offer an interpretation of Kant's conception of a priori principles that contrasts with the one put forward by both Neo-Kantianism and logical empiricism. On this basis, I re-examine the early Reichenbach's effort to accommodate these principles to the paradigm forged by Einstein. (shrink)

Consider the proposition, “Neither the motion of a body nor the action of a force affects space and time themselves”. We rejected this proposition when, in accepting the general theory of relativity, we accepted that the movement of a body or the action of a force affects the curvature of space-time. Compare the following proposition: “p and if and only if or ”. We think this is logically true; at least, most of us do. Some don’t, on empirical grounds—claiming that (...) we should interpret quantum mechanics as showing that the left-hand side can be true when the right-hand side is false. The idea is that the motions of bodies and actions of forces not only affect space-time relations, they also, as it were, affect logical relations as well. I think evidence from quantum mechanics—like empirical evidence generally—cannot possibly show that the equivalence fails to hold. I am convinced that I know a priori that p and if and only if or. My aim here is to explain the basis of this conviction. (shrink)

In this dissertation, I present a novel account of the components that have a peculiar epistemic role in our scientific inquiries, since they contribute to establishing a form of coordination. The issue of coordination is a classic epistemic problem concerning how we justify our use of abstract conceptual tools to represent concrete phenomena. For instance, how could we get to represent universal gravitation as a mathematical formula or temperature by means of a numerical scale? This problem is particularly pressing when (...) justification for using these abstract tools comes, in part or entirely, from knowledge which is not independent from them, thus leading to threats of circularity. Achieving coordination between some abstract conceptual tools and the concrete phenomena that they are supposed to represent is usually a complex process, which involves several epistemic components. Some of these components eventually provide stable conditions for applying those abstract representations to concrete phenomena. It is in this sense of providing certain conditions of applicability that different philosophical traditions, as well as some contemporary reappraisals, view these components as constitutive or a priori. In this work, I present a new gradualist, contextualist, and relational approach to understand these constitutive components of scientific inquiry. It is gradualist inasmuch as the degree to which some component is constitutive depends on three quantifiable features: quasi-axiomaticity, generative potential, and empirical shielding. Since the quantification of these three features impinges on the history and practice of using these components in a scientific context, my approach is a contextualist one. Finally, my approach is relational in a double sense: first, it identifies ordinal relationships among epistemic components with respect to their constitutive character; second, these relationships are relative to a scientific framework of inquiry. After introducing my account and a classic example of constitutively a priori principles, i.e., Friedman’s (2001) analysis of Newtonian mechanics, I turn to my own case studies to demonstrate the advantages of my approach. Firstly, I discuss Okasha’s (2018) view of endogenization as a pervasive theoretical strategy in evolutionary biology and suggest that the constitutive character of the core Darwinian principles progressively increases with endogenization. Secondly, I apply a conceptual distinction between two varieties or scopes of coordination – general coordination and coordination in measurement – to Ohm’s work on electrical conductivity. This distinction allows me to pinpoint to what extent components along different dimensions (e.g., instrumentation, measurement, theorising, etc.) were constitutive of the forms of coordination which Ohm relied on. Thirdly, I discuss the epistemic function of the Hardy-Weinberg principle in the history and practice of population genetics. I assess this principle in terms of my account and identify approximation and stability as two components that are highly constitutive, in that they contribute to justifying its use in population genetics. Finally, applying my account to these case studies enables me to identify at least three qualitatively different types of constitutive components: domain-specific theoretical principles, material components, and domain-independent assumptions underlying reasoning abilities. In the light of my results, I draw some general conclusions on epistemic justification and scientific knowledge. (shrink)

Two-dimensional semantics, which can represent the distinction between a priority and necessity, has wielded considerable influence in the philosophy of language. In this paper, I axiomatize the dagger operator of Stalnaker’s “Assertion” in the formal context of two-dimensional modal logic. The language contains modalities of actuality, necessity, and a priority, but is also able to represent diagonalization, a conceptually important operation in a variety of contexts, including models of the relative a priori and a posteriori often appealed to (...) Bayesian and Gricean contexts. Finally, I sketch the prospects for extending this two-dimensional upgrade to other kinds of modal logics for natural language. (shrink)

In Frege’s Puzzle, Nathan Salmon argues that his theory of singular propositions enables him to refute Saul Kripke’s claim that some identity statements are necessary and yet a posteriori. In this paper, through a critical examination of Salmon’s rejoinders to my earlier objections to his argument, I show what implications the theory of singular propositions has for the notion of apriority. I argue that Salmon’s handling of the ‘trivialization problem,’ which presents serious difficulties for his ‘absolute’ account of apriority, leaves (...) a great deal to be desired. I suggest, in conclusion, that the theorist of singular propositions should hold a relative view of apriority. (shrink)

In this paper, I discuss Whiting’s (2021) account of rational belief and discuss some unresolved issues arising from its reliance on epistemic possibility and, by extension, perspective-relative aprioricity.

TGiulio Preti, born in Pavia (Italy) in 1911 and dead in Djerba (Tunisia) in 1972, represents one of the most subtle Italian thinkers of the latter half of the twentieth century. After graduating in 1933 discussing a thesis about The Husserl’s historical significance, he connected more and more to the Antonio Banfi’s lesson of critical rationalism and he elected him as his master. Starting from Banfi’s The principles of a reason theory (1927), Preti studied in depth the program of historization (...) of the Kantian transcendental both in books such as Idealism and positivism (1942), and in Praxis and empiricism (1957), in Rhetoric and logic (1968), and then in his numerous essay studies, later collected in fundamental posthumous volumes, Philosophical essays (1976, 2 vol.). Preti’s decisive problem is the following question: how is it possible to historicize human knowledge without a relativization? According to Preti, in order to answer this question, it is necessary to acknowledge the objectivity of scientific knowledge. The objective knowledge mustn’t be confused with an absolute knowledge or, least of all, with a subjective, or toutcourt relative, knowledge. Therefore it is necessary to avoid either opposite poles, but specular, in which the different epistemologicaltraditions of the last century are, on the contrary, stopped. In Preti’s opinion, the objectivity of knowledge arises from the eidetic, linguistic and operative structures, within the limits of which develops a determinate form of human scientific knowledge. In other words: every scientific knowledge, structured into a particularscientific theory and relating to a particular technological heritage, consists of a precise theoretical-practical horizon, that determines, with Husserl’s words, a specific “ontological region”, or, with Bachelard’s words, a specific “ontogenesis”. So Preti recovers the heuristic rule of the Kant’s transcendental reason. Nevertheless, unlike Kant, Preti believes the aprioristic structures of our ideas always have a conventional and historical foundation. In this way, the Kantian a priori changes into an historical and relativistic a priori. Certainly in Kant’s opinion an historical and relativistic a priori would have looked like a “round-square”, an authentic contradiction, a pure logical impossibility. According to Preti, on the contrary, this paradoxical aspect is the true distinctive feature of scientificknowledge objectivity, which has no more any eternal or absolute value, but is always built by men born to die and is always bound to determinate historical forms of civilization. Starting from these assumptions, Preti builds, in this way, a research programme on the possibility to individualize a form of “critic ontologism”, which hasn’t any more connection with the claims and the traditional metaphysical structures of the “Being qua Being”. On the contrary, Preti thinks the only “being” we can rationally talk about is the one constituted within the different cognitive ambits. Philosophy then must be able to develop a “meta-reflection” on different knowledge elaborated by single sciences. According to Preti, in fact, philosophy is the formality of human culture, it is, in other words, a form of self-reflection by the human culture about itself. Therefore philosophy has no more any privileged subject, but it must be always able to reflect, with great theoretical humility, on the different cognitive forms, in order to study languages, structures, methods, extension and limits of the human knowledge. In this way Preti’s “critic ontologism” is a kind of historical-objective transcendentalism, able to study the different configurations of the technical-scientific heritage produced by mankind during his history. (shrink)

In his celebrated historic-epistemological work Identité et réalité, Émile Meyerson claimed that the scientific conservation principles were first suggested and accepted for philosophical reasons, and only afterwards were submitted to experimental tests. One of the instances he discussed in his book is the principle of mass conservation in chemical reactions. Meyerson pointed out that several authors, from Antiquity to Kant, accepted the idea of quantitative conservation of matter; and Lavoisier himself was strongly influenced by a priori ideas, using this (...) principle instead of attempting to test it. This paper will review Meyerson’s claim and historic evidence, focusing especially the late nineteenth and early twentieth century, when the principle of mass conservation was tested in highly accurate experiments. Instead of confirming the principle, some of those experiments led to the detection of anomalies. Hans Landolt, for instance, noticed that there were some small violations of the principle. He observed mass variations of about 10−6 in chemical reactions produced in hermetically sealed glass tubes. Since Landolt was a famous chemist, his results produced a strong response. Several researchers repeated his experiments, with different results. Landolt himself improved his experiments, with a balance that could detect mass changes of 10−7. After changes of the experimental procedure, the chemical reactions did not show significant mass changes. There was not, however, any “crucial experiment” “proving” that mass was conserved. The observed anomalies were set aside mainly by theoretical reasons, after the discovery of radioactivity and the development of the theory of relativity. (shrink)

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)