Scientists often diverge widely when choosing between research programs. This can seem to be rooted in disagreements about which of several theories, competing to address shared questions or phenomena, is currently the most epistemically or explanatorily valuable—i.e. most successful. But many such cases are actually more directly rooted in differing judgments of pursuit-worthiness, concerning which theory will be best down the line, or which addresses the most significant data or questions. Using case studies from 16th-century astronomy and 20th-century geology and (...) biology, I argue that divergent theory choice is thus often driven by considerations of scientific process, even where direct epistemic or explanatory evaluation of its final products appears more relevant. Broadly following Kuhn’s analysis of theoretical virtues, I suggest that widely shared criteria for pursuit-worthiness function as imprecise, mutually-conflicting values. However, even Kuhn and others sensitive to pragmatic dimensions of theory ‘acceptance’, including the virtue of fruitfulness, still commonly understate the role of pursuit-worthiness—especially by exaggerating the impact of more present-oriented virtues, or failing to stress how ‘competing’ theories excel at addressing different questions or data. This framework clarifies the nature of the choice and competition involved in theory choice, and the role of alternative theoretical virtues. (shrink)

This paper deals with a relatively recent trend in the history of analytic philosophy, philosophical logic, and theory of science: the philosophical study of the role of inconsistency in empirical science. This paper is divided in three sections that correspond to the three types of inconsistencies identified: (i) factual, occurring between theory and observations, (ii) external, occurring between two mutually contradictory theories, and (iii) internal, characterising theories that entail mutually contradictory statements.

I argue that scientific and poetic modes of objectivity are perspectival duals: 'views' from and onto basic natural forces, respectively. I ground this analysis in a general account of objectivity, not in terms of either 'universal' or 'inter-subjective' validity, but as receptivity to basic features of reality. Contra traditionalists, bare truth, factual knowledge, and universally valid representation are not inherently valuable. But modern critics who focus primarily on the self-expressive aspect of science are also wrong to claim that our knowledge (...) is or should be ultimately mediated by ourselves. In objective science, we represent nature as a field of phenomena determined by and within explanatorily-basic physical structures that encode the causal impact of elemental physical forces. These causally-basic forces hence ground the possibility of objective scientific theory, even though (I argue) they are systematically excluded from its representational contents. I show how my notions of force and field emerge partly through my effort to naturalize concepts of 'God' and 'Laws' in 17th-century natural philosophy. In science, we use the structure of basic forces' impact to see corresponding objects. We do not see these forces themselves—and this relates to the 'transcendence' of 'God'. I supplement this historical analysis by critiquing standard accounts of objectivity, and by synthesizing elements from neo-Kantian epistemology and current 'structural' realism into a view that I call 'dynamic structuralism'. Finally, I argue that physics systematically relies on passive characterizations of phenomena like inertia and impressed force. Dynamic alternatives that are just as empirically adequate are possible, but they are non-scientific. Poetic objectivity involves a direct presentation of nature as an order of interacting forces. I elaborate first by developing a novel theory of the relation between beauty and sublimity, mediated by a basic category of 'sensory force' (e.g. a 'singing' tone in a beautiful melody). I then describe the interaction between sensory and affective dimensions of aesthetic experience, in relation to an original historical analysis of passion and 'disinterestedness' in Kant, Schiller and Nietzsche. I synthesize these lines of analysis into a critique of the role of 'expression' in art. I also resist 'spectator'-centric aesthetics, in this connection, by developing an account of artistic objectivity in dialogue with Ruskin's critique of the 'pathetic fallacy'. I contrast artistic objectivity with Romantic ideals of self-expression, while elaborating its positive relation to certain currents within Victorian and Modernist aesthetics, including Imagists' stress on 'exteriority'. My project creatively extends Nietzsche's view that philosophical and scientific theories are 'perspectival' expressions of theorists' drives. It is a virtue of Nietzsche's account that he takes the outlet of strong human drives in creative acts of theorizing to be just one among many higher modes of 'will to power' in nature—many of which are totally impersonal. But Nietzsche is still too focused on self-expression or willing one's own power. Objective science involves external forces' 'expression' in and through us, not just 'expressing' our own powers. And Nietzsche's vitalistic 'will to power' must be replaced by a basic ontology that better accommodates inorganic phenomena, like the 'lawful' order of celestial motions. Thus I aim to de-anthropomorphize and 'de-organicize' post-Kantian notions of willful striving and organic development, while preserving for force the primary ontological and evaluative status that theorists from Schiller and Goethe to Schelling and Schlegel to Emerson and Nietzsche attributed to will or to life. (shrink)

According to falsificationism, a theory is scientific if it can be incompatible with some empirically testable statements. This epistemological approach has been criticized because, in practice, it is impossible to decide when a particular fact should be considered incompatible with a theory. These criticisms, however, neglect the fact that the Popperian sense of falsification is a “logical sense.” Thus, the Popperian criterion of falsifiability only requires that, assuming certain auxiliary hypotheses, the theory in question be logically incompatible with some empirically (...) testable statements. This paper presents a reassessment of these criticisms, justifying that the criterion of falsifiability is unrenounceable insofar as our best theories should aspire to satisfy it. (shrink)

This chapter tries to answer the following question: How should we conceive of the method of mathematics, if we take a naturalist stance? The problem arises since mathematical knowledge is regarded as the paradigm of certain knowledge, because mathematics is based on the axiomatic method. Moreover, natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some authors tried to naturalize (...) mathematics by relying on evolutionism. But several difficulties arise when we try to do this. This chapter suggests that, in order to naturalize mathematics, it is better to take the method of mathematics to be the analytic method, rather than the axiomatic method, and thus conceive of mathematical knowledge as plausible knowledge. (shrink)

In the past century the received view of definition in mathematics has been the stipulative conception, according to which a definition merely stipulates the meaning of a term in other terms which are supposed to be already well known. The stipulative conception has been so absolutely dominant and accepted as unproblematic that the nature of definition has not been much discussed, yet it is inadequate. This paper examines its shortcomings and proposes an alternative, the heuristic conception.

In the first experiment, I exhibit unreliable judgment about the primeness or divisibility of four-digit numbers, in contrast to a seeming Excel program. In the second experiment, I exhibit an imperfect memory for arbitrary-seeming three-digit number and letter combinations, in contrast to my seeming collaborator with seemingly hidden notes. In the third experiment, I seem to suffer repeated defeats at chess. In all three experiments, the most straightforward interpretation of the experiential evidence is that something exists in the universe that (...) is superior in the relevant respects – theoretical reasoning (about primes), memorial retention (for digits and letters), or practical reasoning (at chess) – to my own solipsistically-conceived self. (shrink)

The ArgumentRecent studies in the philosophy of mathematics have increasingly stressed the social and historical dimensions of mathematical practice. Although this new emphasis has fathered interesting new perspectives, it has also blurred the distinction between mathematics and other scientific fields. This distinction can be clarified by examining the special interaction of thebodyandimagesof mathematics.Mathematics has an objective, ever-expanding hard core, the growth of which is conditioned by socially and historically determined images of mathematics. Mathematics also has reflexive capacities unlike those of (...) any other exact science. In no other exact science can the standard methodological framework usedwithinthe discipline also be used to study the nature of the discipline itself.Although it has always been present in mathematical research, reflexive thinking has become increasingly central to mathematics over the past century. Many of the images of the discipline have been dictated by the increase in reflexive thinking which has also determined a great portion of the contemporary philosophy and historiography of mathematics. (shrink)

This paper extends three decades of work arguing that researchers who discuss consciousness should not restrict themselves only to (adult) human minds, but should study (and attempt to model) many kinds of minds, natural and artificial, thereby contributing to our understanding of the space containing all of them. We need to study what they do or can do, how they can do it, and how the natural ones can be emulated in synthetic minds. That requires: (a) understanding sets of requirements (...) that are met by different sorts of minds, i.e. the niches that they occupy, (b) understanding the space of possible designs, and (c) understanding complex and varied relationships between requirements and designs. Attempts to model or explain any particular phenomenon, such as vision, emotion, learning, language use, or consciousness lead to muddle and confusion unless they are placed in that broader context. A methodology for making progress is summarised and a novel requirement proposed for a theory of how human minds work: the theory should support a single generic design for a learning, developing system that, in addition to meeting familiar requirements, should be capable of developing different and opposed philosophical viewpoints about consciousness, and the so-called hard problem. In other words, we need a common explanation for the mental machinations of mysterians, materialists, functionalists, identity theorists, and those who regard all such theories as attempting to answer incoherent questions. No designs proposed so far come close. (shrink)

According to quasi-empiricism, mathematics is very like a branch of natural science. But if mathematics is like a branch of science, and science studies real objects, then mathematics should study real objects. Thus a quasi-empirical account of mathematics must answer the old epistemological question: How is knowledge of abstract objects possible? This paper attempts to show how it is possible.The second section examines the problem as it was posed by Benacerraf in Mathematical Truth and the next section presents a way (...) of looking at abstract objects that purports to demythologize them. In particular, it shows how we can have empirical knowledge of various abstract objects and even how we might causally interact with them. (shrink)

The demarcation between science and non-science seems to play an important role in the process of scientific change, as theories regularly transition from being considered scientific to being considered unscientific and vice versa. However, theoretical scientonomy is yet to shed light on this process. The goal of this paper is to tackle the problem of demarcation from the scientonomic perspective. Specifically, we introduce scientificity as a distinct epistemic stance that an agent can take towards a theory. We contend that changes (...) in this stance are to be traced and explained by scientonomy. Thus, we formulate a new law of theory demarcation to account for changes in scientificity within the scientonomic framework. (shrink)

In this paper I formalise the falsificationist proposal omitting Popper’s requirement of consistency. This omission results in (i) trivial theories being falsifiable in an inappropriate sense of the term, but also in (ii) some inconsistent non-trivial theories being so in an appropriate one. This justifies a slight alteration of the definition of falsifiability that excludes (i) but allows (ii). Instead of requiring that a falsifiable theory be consistent, my proposal only requires that the intersection of its classes of potential corroborators (...) and falsifiers be empty. (shrink)

This paper considers whether philosophy of mathematics could benefit by the introduction of some sociology. It begins by considering Lakatos's arguments that philosophy of science should be kept free of any sociology. An attempt is made to criticize these arguments, and then a positive argument is given for introducing a sociological dimension into the philosophy of mathematics. This argument is illustrated by considering Brouwer's account of numbers as mental constructions. The paper concludes with a critical discussion of Azzouni's view that (...) mathematics differs fundamentally from other social practices. (shrink)

Despite having put the concept of HPS on the institutional map, N.R. Hanson’s distinctive account of the interdependence between history of science and philosophy of science has been mostly forgotten, and misinterpreted where it is remembered. It is argued that Hanson’s account is worthy of renewed attention and extension since, through its special emphasis on a variety of different normative criteria, it provides the framework for a fruitful and transformative interaction between the two disciplines. This essay also examines two separate (...) threads of Hanson’s account of philosophy of science: his analysis of the conceptual dynamics of science and of the interrelation of the history and philosophy of science. While the two strands appear incongruent, and were perhaps inconsistent, a new interpretation of them is offered which is both consistent with Hanson’s fundamental intuitions and defensible in its own right. It is demonstrated that Hanson’s account compares favorably with those of Kuhn and Lakatos, and that it may provide a constructive means of scaling the barriers erected by fears of the genetic fallacy and ‘whiggish’ history. (shrink)

This dissertation offers a proof of the logical possibility of testing empirical/factual theories that are inconsistent, but non-trivial. In particular, I discuss whether or not such theories can satisfy Popper's principle of falsifiablility. An inconsistent theory Ƭ closed under a classical consequence relation implies every statement of its language because in classical logic the inconsistency and triviality are coextensive. A theory Ƭ is consistent iff there is not a α such that Ƭ ⊢ α ∧ ¬α, otherwise it is inconsistent. (...) We say, instead, that Ƭ is non-trivial iff there is at least one α such that Ƭ ⊢ α, otherwise we say that it trivial. This happens because classical logic satisfies the principle of explosion, according ex contradictione sequitur quodlibet (from a contradiction anything follows). Under these conditions inconsistent classical theories would be compatible with any well-formed formula, which makes them useless for science. There are, however, so-called paraconsistent logics in which the principle of explosion does not generally hold and in which a theory can be (simply) inconsistent, but also absolutely consistent. It is in this logical framework that we can prove that some inconsistent theories can be falsifiable. (shrink)

Imre Lakatos gained fame in the English-speaking world as a follower and critic of philosopher of science Karl Popper. However, Lakatos’ background involved other philosophical and scientific sources from his native Hungary. Lakatos surreptitiously used Hegelian Marxism in his works on philosophy of science and mathematics, disguising it with the rhetoric of the Popper school. He also less surreptitiously incorporated, particularly in his treatment of mathematics, work of the strong tradition of heuristics in twentieth century Hungary. Both his Marxism and (...) his emphasis on heuristics contained a view of science and mathematics that contrasted with the mainstream of Anglo-American philosophy of science. Both involved a dynamic view of science, whether historical or psychological, and an emphasis on practice as opposed to static, formal representations of scientific theories. (shrink)

The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T1, ..., Tn in which Ti+1, for 1 ≤ i < n, supersedes Ti. This thesis has a great philosophical significance because it implies that there is a sense in which mathematical theories, (...) like the theories belonging to the empirical sciences, are fallible and that, consequently, mathematical knowledge has a quasi-empirical nature. The way I have chosen to provide evidence in favour of the correctness of the main thesis of this article consists in arguing that Cantor–Zermelo set theory is a Lakatosian Mathematical Research Programme (MRP). (shrink)

According to a view going back to Plato, the aim of philosophy is to acquire knowledge and there is a method to acquire knowledge, namely a method of discovery. In the last century, however, this view has been completely abandoned, the attempt to give a rational account of discovery has been given up, and logic has been disconnected from discovery. This paper outlines a way of reconnecting logic with discovery.

A famous essay by Wigner is reexamined in view of more recent developments around its topic, together with some remarks on the metaphysical character of its main question about mathematics and natural sciences.

It has been often claimed that the scientific process is quite opposite to the design process, mainly based on the former’s analysis of existing phenomena in order to develop a theory, while the design process is an act of synthesis that creates something new in the world. In the light of the developments that led to this conception, and with reference to the current views of the scientific process, we maintain that the scientific process has more similarities with the design (...) process than differences from it. As parallels can be drawn between the two processes, some implications for further research into the fundamentals of the design activity are discussed. (shrink)

Since the birth of computing as an academic discipline, the disciplinary identity of computing has been debated fiercely. The most heated question has concerned the scientific status of computing. Some consider computing to be a natural science and some consider it to be an experimental science. Others argue that computing is bad science, whereas some say that computing is not a science at all. This survey article presents viewpoints for and against computing as a science. Those viewpoints are analyzed against (...) basic positions in the philosophy of science. The article aims at giving the reader an overview, background, and a historical and theoretical frame of reference for understanding and interpreting some central questions in the debates about the disciplinary identity of computer science. The article argues that much of the discussion about the scientific nature of computing is misguided due to a deep conceptual uncertainty about science in general as well as computing in particular. (shrink)

Logical psychologism is the position that logic is a special branch of psychology, that logical laws are descriptíons of experience to be arrived at through observation, and are a posteriori.The accepted arguments against logical psychologism are effective only when directed against this extreme version. However, the clauses in the above characterization are independent and ambiguous, and may be considered separately. This separation permits a reconsideration of less extreme attempts to tie logic to psychology, such as those defended by Mill and (...) Boole. It also provides the basis for a reexamination of the relationship between logic and psychology, and raises the possibility of a deeper investigation into the nature of logic itself. (shrink)

The basic (negative and positive) methodological maxims of three currents of philosophy of science (logical empiricism, falsificationism, and postpositivism) are formulated. Many of these maxims (stratagems) are controversial, e.g., the stance about the nonsense of metaphysics, and that of its indispensability. The restricted validity of these maxims allows for their unification. Within the framework of most of them there may be a relationship of (synchronic, or diachronic) subordination of the contradicting desiderata. In this vein ten stratagems are formulated.

: In the last two decades, scientists, government officials, and science policy experts have expressed concerns about the increasing role of financial interests in research. Many believe that these interests are undermining research by causing bias and error, suppression of results, and even outright fraud. This paper seeks to shed some light on this view by (1) explicating the concept research bias, (2) describing some ways that financial interests can cause research biases, and (3) discussing some strategies for mitigating or (...) managing the influence of financial interests. These strategies include (a) using government funds to counter-balance privately funded research, (b) increasing public input into government funding decisions, (c) disclosing and managing conflicts of interest in research, (d) auditing data, (e) expanding access to data. Since it is neither possible nor desirable to eliminate financial interests from research, the wisest policy is to manage and counter-balance these interests for the good of science and society. (shrink)

The philosophy of mathematics of the last few decades is commonly distinguished into mainstream and maverick, to which a ‘third way’ has been recently added, the philosophy of mathematical practice. In this paper the limitations of these trends in the philosophy of mathematics are pointed out, and it is argued that they are due to the fact that all of them are based on a top-down approach, that is, an approach which explains the nature of mathematics in terms of some (...) general unproven assumption. As an alternative, a bottom-up approach is proposed, which explains the nature of mathematics in terms of the activity of real individuals and interactions between them. This involves distinguishing between mathematics as a discipline and the mathematics embodied in organisms as a result of biological evolution, which however, while being distinguished, are not opposed. Moreover, it requires a view of mathematical proof, mathematical definition and mathematical objects which is alternative to the top-down approach. (shrink)

A standard problem in empirical inquiry is how to adjudicate between contending theories when they work from different fundamental assumptions. In the field of political sociology, several strategies are adopted, from metatheoretical and comparative historical approaches to the recent formal models of scientific growth proposed by Imre Lakatos and Larry Laudan. After considering the limitations of these approaches, I develop an alternative strategy—"second—order empiricism"—based on the idea that successor theories have an onus to explain the apparent success of their rivals, (...) not only their own and their rivals' anomalies. Such a strategy, I argue, underscores some of the most effective analysis and argument in political sociology, yet is obscured by the appeal to other methodologies. (shrink)

Teilhard de Chardin's ideas about the mechanisms of biological evolution are revised and their connections with contemporary theories are reported. Teilhard de Chardin's main contribution is the proposal of a new scientific discipline, geobiology—the science of the biosphere evolving as a whole. The main fields of interest of geobiology are reported, and its relationships with contemporary hypotheses, such as Lovelock's Gaia, are discussed. The consequences of this kind of approach are the parallel evolution described as orthogenesis and the presence of (...) canalization phenomena. These Teilhardian hypotheses are discussed in relation to those of the process structuralists and to the novelties of the molecular evolution of the genome. Conclusions are that the mechanisms discussed by Teilhard are presently taken into consideration by contemporary evolutionists in order to construct a new theory of biological evolution. (shrink)

The modern mathematical theory of dynamical systems proposes a new model of mechanical motion. In this model the deterministic unstable systems can behave in a statistical manner. Both kinds of motion are inseparably connected, they depend on the point of view and researcher's approach to the system. This mathematical fact solves in a new way the old problem of statistical laws in the world which is essentially deterministic. The classical opposition: deterministic‐statistical, disappears in random dynamics. The main thesis of the (...) paper is that the new theory of motion is a revolution in the research programme of classical mechanics. It is the revolution brought about by the development of mathematics. (shrink)

The limits of ‘criterial rationality’ (that is, rationality as rule‐following) have been extensively explored in the philosophy of science by Kuhn and others. In this paper I attempt to extend this line of enquiry into mathematics by means of a pair of case studies in early algebra. The first case is the Ars Magna (Nuremburg 1545) by Jerome Cardan (1501–1576), in which a then recently‐discovered formula for finding the roots of some cubic equations is extended to cover all cubics and (...) proved. The second is the formulation by Albert Girard (1595–1632) of an early version of the fundamental theorem of algebra in his L'invention nouvelle en l'algèbre (Amsterdam, 1629). I conclude that in these cases at least, the questions raised in the philosophy of science debate can also be asked of the history of mathematics, and that a modest methodological anarchism is the appropriate stance. (shrink)

Klink rejects the use of ecological models in environmental decision making because their predictions cannot be tested by rigorous scientific methods. I argue that models that cannot be tested according to the rigorous standards of the physical sciences can still be considered “scientific”; they are useful (and, in practice, used) for assessing the impacts of human actions on the environment and choosing between alternative courses of action. It is, however, important to be aware of the uncertainties and to make corrections (...) as new data and insights become available. The interplay between (1) model‐based decisions and action and (2) their consequences and subsequent corrections can be regarded as a dialogue between humans and nature (or God) in the sense proposed by Klink. Klink also claims that future actions should be informed by the larger vision of theology and should not be based on science. I suggest that science has an indispensible role. The larger vision is needed to respond to the fundamental religious question: How should I live—and why? But this question cannot be answered without first addressing the fundamental scientific question: How does the world work? I suggest that responses to the first question can be formulated as visions of a future state of existence that we feel compelled to strive to realize, and that science is necessary to provide “maps of reality” needed to realize visions. I also suggest that Christian traditions can probably provide adequate visions; the crucial need is for improving our “maps of reality.”. (shrink)

Abstract The paper is an attempt to interpret Imre Lakatos's methodology of scientific research programmes (MSRP) on the basis of his mathematical methodology, the method of proofs and refutations (MPR). After sketching MSRP and MPR and analysing their relationship to Popper's and Poly a's work, I argue that MSRP was originally conceived as a methodology in the same sense as MPR. The most conspicuous difference between the two, namely that MSRP is fundamentally backward?looking, whereas MPR is primarily forward?looking, is due (...) to the fact that Lakatos could not carry out his project in the full sense. I also explain why he could not. (shrink)

According to a view going back to Plato, the aim of philosophy is to acquire knowledge and there is a method to acquire knowledge, namely a method of discovery. In the last century, however, this view has been completely abandoned, the attempt to give a rational account of discovery has been given up, and logic has been disconnected from discovery. This paper outlines a way of reconnecting logic with discovery.