I argue here for a number of ways that modern computational science requires a change in the way we represent the relationship between theory and applications. It requires a switch away from logical reconstruction of theories in order to take surface mathematical syntax seriously. In addition, syntactically different versions of the same theory have important differences for applications, and this shows that the semantic account of theories is inappropriate for some purposes. I also argue against formalist approaches in the philosophy (...) of science and for a greater role for perceptual knowledge rather than propositional knowledge in scientific empiricism. (shrink)

In this essay we argue that the notion of machine necessarily includes its being designed for a purpose. Therefore, being a mechanical system is not enough for being a machine. Since the experimental scientific method excludes any consideration of finality on methodological grounds, it is then also insufficient to fully understand what machines are. Instead in order to understand a machine it is first required to understand its purpose, along with its structure, in clear parallel with Aristotle’s final and formal (...) causes. Obviously, purpose and structure are not machine components that can physically interact with other components; nonetheless they are essential to understanding their operation. This casts an interesting light on the relationship between mind and body: for just as an artifact’s finality and structure explain its operation, so also consciousness is the explanation—not the efficient cause—of specifically human behavior. What machines and human beings have in common is that, in order to understand them, it is necessary to appeal to the principle of finality. Yet while finality is given and extrinsic in the case of machines, we human beings are characterized by the ability to self-propose our own ends. Since the principle of finality is essential to understanding the production of machines, the traditional view in modern Western philosophy that finality lies beyond the scope of objective/scientific knowledge should be rectified to allow for a genuine science of the artificial. We think a correct understanding of final causality will overcome current resistance to this principle. (shrink)

For years, experimental philosophers have attempted to discern whether laypeople find free will compatible with a scientifically deterministic understanding of the universe, yet no consensus has emerged. The present work provides one potential explanation for these discrepant findings: People are strongly motivated to preserve free will and moral responsibility, and thus do not have stable, logically rigorous notions of free will. Seven studies support this hypothesis by demonstrating that a variety of logically irrelevant (but motivationally relevant) features influence compatibilist judgments. (...) In Study 1, participants who were asked to consider the possibility that our universe is deterministic were more compatibilist than those not asked to consider this possibility, suggesting that determinism poses a threat to moral responsibility, which increases compatibilist responding (thus reducing the threat). In Study 2, participants who considered concrete instances of moral behavior found compatibilist free will more sufficient for moral responsibility than participants who were asked about moral responsibility more generally. In Study 3a, the order in which participants read free will and determinism descriptions influenced their compatibilist judgments—and only when the descriptions had moral significance: Participants were more likely to report that determinism was compatible with free will than that free will was compatible with determinism. In Study 3b, participants who read the free will description first (the more compatibilist group) were particularly likely to confess that their beliefs in free will and moral responsibility and their disbelief in determinism influenced their conclusion. In Study 4, participants reduced their compatibilist beliefs after reading a passage that argued that moral responsibility could be preserved even in the absence of free will. Participants also reported that immaterial souls were compatible with scientific determinism, most strongly among immaterial soul believers (Study 5), and evaluated information about the capacities of primates in a biased manner favoring the existence of human free will (Study 6). These results suggest that people do not have one intuition about whether free will is compatible with determinism. Instead, people report that free will is compatible with determinism when desiring to uphold moral responsibility. Recommendations for future work are discussed. (shrink)

The relationship between consciousness and brain, subject and body, appears today far away from being elucidated. All attempts to reduce consciousness and subject to the brain end up abolishing the subject, i.e., what is evidently most relevant for each one of us. Luigi Giussani proposes a method to investigate human consciousness based on the analysis of oneself personal experience, verifiable by every human being. He is very attentive to avoiding during the experiential analysis interference of prejudices, ideological conceptions, and conjectures. (...) His method remains perfectly coherent and open to all contributions from neuroscience and scientific discoveries. He leaves completely open the major question about the relationship between brain physical-chemical functioning and subjective experience, individual consciousness. A comparison between Giussani’s method and the starting point and the fundamental assumption that lays the basis of various modern neuroscientific conceptions of consciousness is conducted. A discussion about the assumption that stays at the basis of the various neuroscientific currents appears necessary and the method proposed by Giussani may constitute a common and acceptable by everyone background for future development and advances in studying the greatest problem of our culture, the relation between brain and human consciousness. (shrink)

Inductive reasoning aims at constructing rules and models of general applicability from a restricted set of observations. Induction is a keystone in natural sciences, and it influences diverse application fields such as engineering, medicine and economics. More generally, induction plays a major role in the way humans learn and operate in their everyday life. The level of reliability that a model achieves depends on how informative the observations are relative to the flexibility of the process by which the model is (...) constructed. When the process is articulated so that the model can incorporate descriptive details and subtleties, a large set of informative observations are required to reliably tune the model, whereas models obtained from simple procedures can be tuned with fewer observations. This article introduces the concept of “dominance”, which refers to the situation in which a reduced subset of observations suffices to reconstruct the model. A mathematical framework is presented to quantify the reliability of learning procedures as a function of the size of the subset of dominant observations. Although limited in scope, we believe that our study can contribute to the understanding of some fundamental mechanisms by which knowledge is generated from observations in inductive reasoning. (shrink)

Pierre Duhem can be looked upon as one of the heirs of a tradition of historical and philosophical researches that flourished in the second half of the nineteenth century. This tradition opposed the naïve historiography and epistemology of the positivist school. Beside the positivists of different leanings such as Littré, Laffitte, Wyrouboff, and Berthelot, we find Cournot, Naville, and Tannery, who developed sophisticated histories and philosophies of science focusing on the real scientific practice and its history. They unfolded elements of (...) continuity and discontinuity in the history of science, and enlightened the complex relationship among experimental, mathematical, logical and philosophical components in scientific practice. In Pierre Duhem we find a systematic and vivid interpretation of these meta-theoretical issues, and a meaningful development of a cultural tradition that re-emerged in the second half of the twentieth century. (shrink)

Ernst Cassirer’s epistemological trilogy – Substanzbegriff und Funktionsbegriff (1910), Zur Einsteinschen Relativitätstheorie (1921) and Determinismus und Indeterminismus (1937) – is well known to Western scholars, some of whom recently devoted a number of in-depth and interesting studies to Cassirer’s epistemology. Nonetheless, they overlooked aspects of Cassirer’s concept of idealisation and his model of science as found in his last epistemological work: Determinismus und Indeterminismus. In this essay I will consider these two almost disregarded aspects of Cassirer’s epistemology in order to (...) provide a better understanding of his idea of science. (shrink)

Based on Kolchinsky and Wolpert’s work on the semantics of autonomous agents, I propose an application of Mathematical Logic and Probability to model cognitive processes. In this work, I will follow Bateson’s insights on the hierarchy of learning in complex organisms and formalize his idea of applying Russell’s Type Theory. Following Weaver’s three levels for the communication problem, I link the Kolchinsky–Wolpert model to Bateson’s insights, and I reach a semantic and conceptual hierarchy in living systems as an explicative model (...) of some adaptive constraints. Due to the generality of Kolchinsky and Wolpert’s hypotheses, I highlight some fundamental gaps between the results in current Artificial Intelligence and the semantic structures in human beings. In light of the consequences of my model, I conclude the paper by proposing a general definition of knowledge in probabilistic terms, overturning de Finetti’s Subjectivist Definition of Probability. (shrink)

The metamathematical tradition, tracing back to Hilbert, employs syntactic modeling to study the methods of contemporary mathematics. A central goal has been, in particular, to explore the extent to which infinitary methods can be understood in computational or otherwise explicit terms. Ergodic theory provides rich opportunities for such analysis. Although the field has its origins in seventeenth century dynamics and nineteenth century statistical mechanics, it employs infinitary, nonconstructive, and structural methods that are characteristically modern. At the same time, computational concerns (...) and recent applications to combinatorics and number theory force us to reconsider the constructive character of the theory and its methods. This paper surveys some recent contributions to the metamathematical study of ergodic theory, focusing on the mean and pointwise ergodic theorems and the Furstenberg structure theorem for measure preserving systems. In particular, I characterize the extent to which these theorems are nonconstructive, and explain how proof-theoretic methods can be used to locate their "constructive content.". (shrink)

This paper presents an overview on the concept of cardinal utility in its relations with the literature since the beginning of the XVIIIth century (Part I); an estimate of the cardinal utility function for its negative values, thus completing the estimate of this function for its positive values given in my 1984 Venice paper (Part II); and finally different applications to the theory of choices in the presence of risk and to the wealth transfer and tax questions (Part III).

In this review article we present different formal frameworks for the description of generalized probabilities in statistical theories. We discuss the particular cases of probabilities appearing in classical and quantum mechanics, possible generalizations of the approaches of A. N. Kolmogorov and R. T. Cox to non-commutative models, and the approach to generalized probabilities based on convex sets.

It is commonly thought that before the introduction of quantum mechanics, determinism was a straightforward consequence of the laws of mechanics. However, around the nineteenth century, many physicists, for various reasons, did not regard determinism as a provable feature of physics. This is not to say that physicists in this period were not committed to determinism; there were some physicists who argued for fundamental indeterminism, but most were committed to determinism in some sense. However, for them, determinism was often not (...) a provable feature of physical theory, but rather an a priori principle or a methodological presupposition. Determinism was strongly connected with principles of causality and continuity and the principle of sufficient reason; this thesis examines the relevance of these principles in the history of physics. Moreover, the history of determinism in this period shows that there were essential changes in the relation between mathematics and physics: whereas in the eighteenth century, there were metaphysical arguments which lent support to differential calculus, by the early twentieth century the development of rigorous foundations of differential calculus led to concerns about its applicability in physics. The thesis consists of six papers. In the first paper, "On the origins and foundations of Laplacian determinism", I argue that Laplace, who is usually pointed out as the first major proponent of scientific determinism, did not derive his statement of determinism directly from the laws of mechanics; rather, his determinism has a background in eighteenth century Leibnizian metaphysics, and is ultimately based on the law of continuity and the principle of sufficient reason. These principles also provided a basis for the idea that one can find laws of nature in the form of differential equations which uniquely determine natural processes. In "The Norton dome and the nineteenth century foundations of determinism", I argue that an example of indeterminism in classical physics which has attracted attention in philosophy of physics in recent years, namely the Norton come, was already discussed during the nineteenth century. However, the significance which this type of indeterminism had back then is very different from the significance which the Norton dome currently has in philosophy of physics. This is explained by the fact that determinism was conceived of in an essentially different way: in particular, the nineteenth century authors who wrote about this type of indeterminism regarded determinism as an a priori principle rather than as a property of the equations of physics. In "Vital instability: life and free will in physics and physiology, 1860-1880", I show how Maxwell, Cournot, Stewart and Boussinesq used the possibility of unstable or indeterministic mechanical systems to argue that the will or a vital principle can intervene in organic processes without violating the laws of physics, so that a strictly dualist account of life and the mind is possible. Moreover, I show that their ideas can be understood as a reaction to the law of conservation of energy and to the way it was used in physiology to exclude vital and mental causes. In "The nineteenth century conflict between mechanism and irreversibility", I show that in the late nineteenth century, there was a widespread conflict between the aim of reducing physical processes to mechanics and the recognition that certain processes are irreversible. Whereas the so-called reversibility objection is known as an objection that was made to the kinetic theory of gases, it in fact appeared in a wide range of arguments, and was susceptible to very different interpretations. It was only when the project of reducing all of physics to mechanics lost favor, in the late nineteenth century, that the reversibility objection came to be used as an argument against mechanism and against the kinetic theory of gases. In "Continuity in nature and in mathematics: Boltzmann and Poincaré", I show that the development of rigorous foundations of differential calculus in the nineteenth century led to concerns about its applicability in physics: through this development, differential calculus was made independent of empirical and intuitive notions of continuity and was instead based on mathematical continuity conditions, and for Boltzmann and Poincaré, the applicability of differential calculus in physics depended on whether these continuity conditions could be given a foundation in intuition or experience. In the final paper, "Determinism around 1900", I briefly discuss the implications of the developments described in the previous two papers for the history of determinism in physics, through a discussion of determinism in Mach, Poincaré and Boltzmann. I show that neither of them regards determinism as a property of the laws of mechanics; rather, for them, determinism is a precondition for science, which can be verified to the extent that science is successful. (shrink)

This paper addresses the question of how we should regard the probability distributions introduced into statistical mechanics. It will be argued that it is problematic to take them either as purely ontic, or purely epistemic. I will propose a third alternative: they are almost objective probabilities, or epistemic chances. The definition of such probabilities involves an interweaving of epistemic and physical considerations, and thus they cannot be classified as either purely epistemic or purely ontic. This conception, it will be argued, (...) resolves some of the puzzles associated with statistical mechanical probabilities: it explains how probabilistic posits introduced on the basis of incomplete knowledge can yield testable predictions, and it also bypasses the problem of disastrous retrodictions, that is, the fact the standard equilibrium measures yield high probability of the system being in equilibrium in the recent past, even when we know otherwise. As the problem does not arise on the conception of probabilities considered here, there is no need to invoke a Past Hypothesis as a special posit to avoid it. (shrink)

I show how classical and quantum physics approach the problem of randomness and probability. Contrary to popular opinions, neither we can prove that classical mechanics is a deterministic theory, nor that quantum mechanics is a nondeterministic one. In other words it is not possible to show that randomness in classical mechanics has a purely epistemic character and that of quantum mechanics an ontic one. Nevertheless, recent developments of quantum theory and increasing experimental possibilities to check its predictions call for returning (...) to the problem of comparing possibilities given by classical and quantum physics to accommodate and prove the existence of a `genuine randomness'. Recent results concerning `amplification of randomness' show that, in certain sense, quantum physics is in fact ‘more random’ that classical and outperforms it in producing a `truly random process'. (shrink)

There are many ontologies of the world or of specific phenomena such as time, matter, space, and quantum mechanics1. However, ontologies of information are rather rare. One of the reasons behind this is that information is most frequently associated with communication and computing, and not with ‘the furniture of the world’. But what would be the nature of an ontology of information? For it to be of significant import it should be amenable to formalization in a logico-grammatical formalism. A candidate (...) ontology satisfying such a requirement can be found in some of the ideas of K. Turek, presented in this paper. Turek outlines the ontology of information conceived of as a part of nature, and provides the ‘missing link’ to the Z axiomatic set theory, offering a proposal for developing a formal ontology of information both in its philosophical and logicogrammatical representations. (shrink)

In my dissertation I define historical disciplines as disciplines that aim to give a historical interpretation of the evidence. Phylogenetic systematics is a historical discipline and therefore in my definition phylogenies should be thought of as historical interpretations of relationships between taxa.