I present two generalizations of Putnam's model-theoretic argument against realism. The first replaces Putnam's model theory with some new, and substantially simpler, model theory, while the second replaces Putnam's model theory with some more accessible results from astronomy. By design, both of these new arguments fail. But the similarities between these new arguments and Putnam's original arguments illuminate the latter's overall structure, and the flaws in these new arguments highlight the corresponding flaws in Putnam's arguments.

Skolem's Paradox involves a seeming conflict between two theorems from classical logic. The Löwenheim Skolem theorem says that if a first order theory has infinite models, then it has models whose domains are only countable. Cantor's theorem says that some sets are uncountable. Skolem's Paradox arises when we notice that the basic principles of Cantorian set theory—i.e., the very principles used to prove Cantor's theorem on the existence of uncountable sets—can themselves be formulated as a collection of first order sentences. (...) How can the very principles which prove the existence of uncountable sets be satisfied by a model which is itself only countable? How can a countable model satisfy the first order sentence which says that there are uncountably many mathematical objects—e.g., uncountably many real numbers? (shrink)

In his new paper, “Eligibility and Inscrutability,” J. R. G. Williams presents a surprising new challenge to David Lewis’ theory of interpretation. Although Williams frames this challenge primarily as a response to Lewis’ criticisms of Putnam’s model-theoretic argument, the challenge itself goes to the heart of Lewis’ own account of interpretation. Further, and leaving Lewis’ project aside for a moment, Williams’ argument highlights some important—and some fairly general—points concerning the relationship between model theory and semantic determinacy.

In this dissertation we study two-cardinal phenomena—both of the admitting cardinals variety and of the Chang’s Conjecture variety—under the assumption that all our models have stable theories. All our results involve two, relatively widely accepted generalizations of the traditional definitions in this area. First, we allow the relevant subsets of our models to be picked out by (perhaps infinitary) partial types; second we consider δ-cardinal problems as well as two-cardinal problems.

The Lowenheim-Skolem theorems say that if a first-order theory has infinite models, then it has models which are only countably infinite. Cantor's theorem says that some sets are uncountable. Together, these theorems induce a puzzle known as Skolem's Paradox: the very axioms of set theory which prove the existence of uncountable sets can be satisfied by a merely countable model. ;This dissertation examines Skolem's Paradox from three perspectives. After a brief introduction, chapters two and three examine several formulations of Skolem's (...) Paradox in order to disentangle the roles which set theory, model theory, and philosophy play in these formulations. In these chapters, I accomplish three things. First, I clear up some of the mathematical ambiguities which have all too often infected discussions of Skolem's Paradox. Second, I isolate a key assumption upon which Skolem's Paradox rests, and I show why this assumption has to be false. Finally, I argue that there is no single explanation as to how a countable model can satisfy the axioms of set theory ;In chapter four, I turn to a second puzzle. Why, even though philosophers have known since the early 1920's that Skolem's Paradox has a relatively simple technical solution, have they continued to find this paradox so troubling? I argue that philosophers' attitudes towards Skolem's Paradox have been shaped by the acceptance of certain, fairly specific, claims in the philosophy of language. I then tackle these philosophical claims head on. In some cases, I argue that the claims depend on an incoherent account of mathematical language. In other cases, I argue that the claims are so powerful that they render Skolem's Paradox trivial. In either case, though, examination of the philosophical underpinnings of Skolem's Paradox renders that paradox decidedly unparadoxical. ;Finally, in chapter five, I turn away from "generic" formulations of Skolem's Paradox to examine Hilary Putnam's "model-theoretic argument against realism." I show that Putnam's argument involves mistakes of both the mathematical and the philosophical variety, and that these two types of mistake are closely related. Along the way, I clear up some of the mutual charges of question begging which have characterized discussions between Putnam and his critics. (shrink)

We examine two-cardinal problems for the class of O-minimal theories. We prove that an O-minimal theory which admits some must admit every. We also prove that every "reasonable" variant of Chang's Conjecture is true for O-minimal structures. Finally, we generalize these results from the two-cardinal case to the $\delta$-cardinal case for arbitrary ordinals $\delta$.

In 1999, Jeffrey Ketland published a paper which posed a series of technical problems for deflationary theories of truth. Ketland argued that deflationism is incompatible with standard mathematical formalizations of truth, and he claimed that alternate deflationary formalizations are unable to explain some central uses of the truth predicate in mathematics. He also used Beth’s definability theorem to argue that, contrary to deflationists’ claims, the T-schema cannot provide an ‘implicit definition’ of truth. In this article, I want to challenge (...) this final argument. Whatever other faults deflationism may have, the T-schema does provide an implicit definition of the truth predicate. Or so, at any rate, I shall argue. (shrink)

We examine two-cardinal problems for the class of O-minimal theories. We prove that an O-minimal theory which admits some (κ, λ) must admit every (κ , λ ). We also prove that every “reasonable” variant of Chang’s Conjecture is true for O-minimal structures. Finally, we generalize these results from the two-cardinal case to the δ-cardinal case for arbitrary ordinals δ.

This paper discusses two combinatorial problems in stability theory. First we prove a partition result for subsets of stable models: for any A and B, we can partition A into |B|$^{ |B|, then we try to find A' $\subset$ A and B' $\subset$ B such that |A'| is as large as possible, |B'| is as small as possible, and A' $\&2ADD;$ $\underset{B'}$ B. We prove some positive results in this direction, and we discuss the optimality of these results under ZFC (...) + GCH. (shrink)

Among three possible avenues toward a good society ? revolutionary Marxism, liberal?democratic reform, and radical citizenship education ? this paper examines and advocates the third. Societies are held to be ?good? so long as the Most Basic Rights are in fact enjoyed by all (i.e. the right (1) to stay alive, (2) to remain unmolested, and (3) to be free to develop one's potentialities). Some key propositions in ?contract theory? as represented by such diverse theorists as Socrates, Hobbes, Locke, Rousseau, (...) and Tussman and Meiklejohn are discussed, and an alternative tradition, ?freedom theory?, is sketched, with contributions from Socrates, Godwin, Thoreau, and Camus. An argument is then developed to the effect that the contract theorists have all contributed to the basis on which the contemporary ?liberal make?believe? rests. This term refers to the myth that our society is democratic, i.e. that working (only) within the system of our constitutional procedures will or can lead toward a just society. Finally, it is argued that the highest priority in citizenship education is to destroy this liberal make?believe, and that freedom theory provides a better foundation than contract theory in the struggle for human rights, and for mankind's survival. (shrink)

This paper discusses two combinatorial problems in stability theory. First we prove a partition result for subsets of stable models: for any A and B, we can partition A into |B |<κ(T ) pieces, Ai | i < |B |<κ(T ) , such that for each Ai there is a Bi ⊆ B where |Bi| < κ(T ) and Ai..

Background: Ethical care in maternity is fundamental to providing care that both prevents harm and does good, and yet, there is growing acknowledgement that disrespect and abuse routinely occur in this context, which indicates that current ethical frameworks are not adequate. Care ethics offers an alternative to the traditional biomedical ethical principles. Research aim: The aim of the study was to determine whether a correlation exists between midwifery-led care and care ethics as an important first step in an action research (...) project. Research design: Template analysis was chosen for this part of the action research. Template analysis is a design that tests theory against empirical data, which requires pre-set codes. Participants and context: A priori codes that represent midwifery-led care were generated by a stakeholder consultative group of nine childbearing women using nominal group technique, collected in Perth, Western Australia. The a priori codes were applied to a predesigned template with four domains of care ethics. Ethical considerations: Ethics approval was granted by the Edith Cowan University research ethics committee REMS no. 2019-00296-Buchanan. Findings: The participants generated eight a priori codes representing ethical midwifery care, such as: 1.1 Relationship with Midwife; 1.2 Woman-centred care; 2.1 Trust women’s bodies and abilities; 2.2. Protect normal physiological birth; 3.1. Information provision; 3.2. Respect autonomy; 4.1. Birth culture of fear and 4.2. Recognition of rite of passage. The a priori codes were mapped to the care ethics template. The template analysis found that midwifery-led care does indeed demonstrate care ethics. Discussion: Care ethics takes into consideration what principle-based bioethics have previously overlooked: relationship, context and power. Conclusion: Midwifery-led care has been determined in this study to demonstrate care ethics, which suggest that further research is defensible with the view that it could be incorporated into the ethical codes and conduct for the midwifery profession. (shrink)

Background The often poor prognosis associated with cancer necessitates empowering patients to express their care preferences. Yet, the prevalence of Advance Directives (AD) among oncology patients remains low. This study investigated oncologists' perspectives on the interests and challenges associated with implementing AD. Methods A French national online survey targeting hospital-based oncologists explored five areas: AD information, writing support, AD usage, personal perceptions of AD's importance, and respondent's profile. The primary outcome was to assess how frequently oncologists provide patients with information (...) about AD in daily clinical practice. Additionally, we examined factors related to delivering information on AD. Results Of the 410 oncologists (50%) who responded to the survey, 75% (n = 308) deemed AD relevant. While 36% (n = 149) regularly inform patients about AD, 25% (n = 102) remain skeptical about AD. Among the respondents who do not consistently discuss AD, the most common reason given is the belief that AD may induce anxiety (n = 211/353; 60%). Of all respondents, 90% (n = 367) believe patients require specific information to draft relevant AD. Physicians with experience in palliative care were more likely to discuss AD (43% vs 32.3%, p = 0.027). Previous experience in critical care was associated with higher levels of distrust towards AD (31.5% vs 18.8%, p = 0.003), and 68.5% (n = 281) of the respondents expressed that designating a “person of trust” would be more appropriate than utilizing AD. Conclusion Despite the perceived relevance of AD, only a third of oncologists regularly apprise their patients about them. Significant uncertainty persists about the safety and relevance of AD. (shrink)

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes's original paper to contemporary formal (...) learning theory. In a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes’s original paper to contemporary formal (...) learning theory.In a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)

We propose that children employ specialized cognitive systems that allow them to recover an accurate “causal map” of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or “Bayes nets”. Children’s causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2- to (...) 4-year-old children construct new causal maps and that their learning is consistent with the Bayes net formalism. (shrink)

Causal Bayes nets have been developed in philosophy, statistics, and computer sciences to provide a formalism to represent causal structures, to induce causal structure from data and to derive predictions. Causal Bayes nets have been used as psychological theories in at least two ways. They were used as rational, computational models of causal reasoning and they were used as formal models of mental causal models. A crucial assumption made by them is the Markov condition, which informally states (...) that variables are independent of other variables that are not their direct or indirect effects conditional on their immediate causes. Whether people’s inferences conform to the causal Markov and the faithfulness condition has recently been investigated empirically. A review of respective research indicates that inferences frequently violate these conditions. This finding challenges some uses of causal Bayes nets in psychology. They entail that causal Bayes nets may not be appropriate to derive predictions for causal model theories of causal reasoning. They also question whether causal Bayes nets as a rational model are empirically descriptive. They do not challenge, however, causal Bayes nets as normative models and their usage as formal models of causal reasoning. (shrink)

The problem addressed in this paper is “the main epistemic problem concerning science”, viz. “the explication of how we compare and evaluate theories [...] in the light of the available evidence” (van Fraassen, BC, 1983, Theory comparison and relevant Evidence. In J. Earman (Ed.), Testing scientific theories (pp. 27–42). Minneapolis: University of Minnesota Press). Sections 1– 3 contain the general plausibility-informativeness theory of theory assessment. In a nutshell, the message is (1) that there are two values a theory (...) should exhibit: truth and informativeness—measured respectively by a truth indicator and a strength indicator; (2) that these two values are conflicting in the sense that the former is a decreasing and the latter an increasing function of the logical strength of the theory to be assessed; and (3) that in assessing a given theory by the available data one should weigh between these two conflicting aspects in such a way that any surplus in informativeness succeeds, if the shortfall in plausibility is small enough. Particular accounts of this general theory arise by inserting particular strength indicators and truth indicators. In Section 4 the theory is spelt out for the Bayesian paradigm of subjective probabilities. It is then compared to incremental Bayesian confirmation theory. Section 4 closes by asking whether it is likely to be lovely. Section 5 discusses a few problems of confirmation theory in the light of the present approach. In particular, it is briefly indicated how the present account gives rise to a new analysis of Hempel’s conditions of adequacy for any relation of confirmation (Hempel, CG, 1945, Studies in the logic of comfirmation. Mind, 54, 1–26, 97–121.), differing from the one Carnap gave in § 87 of his Logical foundations of probability (1962, Chicago: University of Chicago Press). Section 6 adresses the question of justification any theory of theory assessment has to face: why should one stick to theories given high assessment values rather than to any other theories? The answer given by the Bayesian version of the account presented in section 4 is that one should accept theories given high assessment values, because, in the medium run, theory assessment almost surely takes one to the most informative among all true theories when presented separating data. The concluding section 7 continues the comparison between the present account and incremental Bayesian confirmation theory. (shrink)

Some naturalistic philosophers of mind subscribing to the predictive processing theory of mind have adopted a realist attitude towards the results of Bayesian cognitive science. In this paper, we argue that this realist attitude is unwarranted. The Bayesian research program in cognitive science does not possess special epistemic virtues over alternative approaches for explaining mental phenomena involving uncertainty. In particular, the Bayesian approach is not simpler, more unifying, or more rational than alternatives. It is also contentious that the Bayesian approach (...) is overall better supported by the empirical evidence. So, to develop philosophical theories of mind on the basis of a realist interpretation of results from Bayesian cognitive science is unwarranted. Naturalistic philosophers of mind should instead adopt an anti-realist attitude towards these results and remain agnostic as to whether Bayesian models are true. For continuing on with an exclusive focus and praise of Bayes within debates about the predictive processing theory will impede progress in philosophical understanding of scientific practice in computational cognitive science as well as of the architecture of the mind. (shrink)

This paper claims that adoption of Bayes's theorem as the schema for the appraisal of scientific theories can greatly reduce the distance between Kuhnians and logical empiricists. It is argued that plausibility considerations, which Kuhn considered outside of the logic of science, can be construed as prior probabilities, which play an indispensable role in the logic of science. Problems concerning likelihoods, especially the likelihood on the "catchall," are also considered. Severe difficulties concerning the significance of this probability arise (...) in the evaluation of individual theories, but they can be avoided by restricting our judgments to comparative assessments of competing theories. (shrink)

Can statistical inference shed any worthwhile light on theory change? For many years I have believed that the answer is “Yes.” Let me try to explain why I think so. On my first reading of Thomas S. Kuhn’s The Structure of Scientific Revolutions (1962) I was so deeply shocked at his repudiation of the distinction between the context of discovery and the context of justification that I put the book down without finishing it. By 1969, when a conference was held (...) at the Minnesota Center for Philosophy of Science on the relations between the history of science and the philosophy of science, I had returned to Structure and formed the view that Kuhn’s rejection of this fundamental distinction resulted from his adoption of an inadequate conception of scientific justification. It appeared that he saw scientific confirmation in terms of the traditional hypothetico-deductive (H-D) schema, according to which a scientific hypothesis (or theory) is confirmed by observing the truth of its logical consequences. (shrink)

Philosophers have long sought to explain perceptual constancy—the fact that objects appear to remain the same color, size and shape despite changes in the illumination condition, perspective and the relative distance—in terms of a mechanism that actively categorizes variable stimuli under the same pre-formed conceptual categories. Contemporary representationalists, on the other hand, explain perceptual constancy in terms of a modular mechanism that automatically discounts variation in the visual field to represent the stable properties of objects. In this paper I argue (...) that while the former view is unmotivated by empirical evidence, the later fails to account for inter- and intra-personal variability, the influence of expectations on constancy, and the systematic and normal failures of color constancy. A Bayesian approach that builds on the representational tradition in psychology solves both problems. (shrink)

Bayes’ rule shows how one might rationally change one’s beliefs in the light of evidence. It is the foundation of a statistical method called Bayesianism. In health care research, Bayesianism has its advocates but the dominant statistical method is frequentism. There are at least two important philosophical differences between these methods. First, Bayesianism takes a subjectivist view of probability (i.e. that probability scores are statements of subjective belief, not objective fact) whilst frequentism takes an objectivist view. Second, Bayesianism is (...) explicitly inductive (i.e. it shows how we may induce views about the world based on partial data from it) whereas frequentism is at least compatible with non-inductive views of scientific method, particularly the critical realism of Popper. Popper and others detail significant problems with induction. Frequentism’s apparent ability to avoid these, plus its ability to give a seemingly more scientific and objective take on probability, lies behind its philosophical appeal to health care researchers. However, there are also significant problems with frequentism, particularly its inability to assign probability scores to single events. Popper thus proposed an alternative objectivist view of probability, called propensity theory, which he allies to a theory of corroboration; but this too has significant problems, in particular, it may not successfully avoid induction. If this is so then Bayesianism might be philosophically the strongest of the statistical approaches. The article sets out a number of its philosophical and methodological attractions. Finally, it outlines a way in which critical realism and Bayesianism might work together. (shrink)

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of (...) subjectivist position. Indeed, the Theorem's central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology. (shrink)

The justification of Bayes' rule by cognitive rationality principles is undertaken by extending the propositional axiom systems usually proposed in two contexts of belief change: revising and updating. Probabilistic belief change axioms are introduced, either by direct transcription of the set-theoretic ones, or in a stronger way but nevertheless in the spirit of the underlying propositional principles. Weak revising axioms are shown to be satisfied by a General Conditioning rule, extending Bayes' rule but also compatible with others, and (...) weak updating axioms by a General Imaging rule, extending Lewis' rule. Strong axioms (equivalent to the Miller–Popper axiom system) are necessary to justify Bayes' rule in a revising context, and justify in fact an extended Bayes' rule which applies, even if the message has zero probability. (shrink)

The justification of Bayes' rule by cognitive rationality principles is undertaken by extending the propositional axiom systems usually proposed in two contexts of belief change: revising and updating. Probabilistic belief change axioms are introduced, either by direct transcription of the set-theoretic ones, or in a stronger way but nevertheless in the spirit of the underlying propositional principles. Weak revising axioms are shown to be satisfied by a General Conditioning rule, extending Bayes' rule but also compatible with others, and (...) weak updating axioms by a General Imaging rule, extending Lewis' rule. Strong axioms (equivalent to the Miller–Popper axiom system) are necessary to justify Bayes' rule in a revising context, and justify in fact an extended Bayes' rule which applies, even if the message has zero probability. (shrink)

Causal Bayes nets (CBNs) provide one of the most powerful tools for modelling coarse-grained type-level causal structure. As in other fields (e.g., thermodynamics) the question arises how such coarse-grained characterisations are related to the characterisation of their underlying structure (in this case: token-level causal relations). Answering this question meets what is called a “coherence-requirement” in the reduction debate: How are different accounts of one and the same system (or kind of system) related to each other. We argue that CBNs (...) as tools for type-level causal inference are abstract enough to roughly fit any current token-level theory of causation as long as certain modelling assumptions are satisfied, but accounts of actual causation, i.e. accounts that attempt to infer token-causation based on CBNs, for the very same reason, face certain limitations. (shrink)

Several leading topics outstanding after John Earman's Bayes or Bust? are investigated further, with emphasis on the relevance of Bayesian explication in epistemology of science, despite certain limitations. (1) Dutch Book arguments are reformulated so that their independence from utility and preference in epistemic contexts is evident. (2) The Bayesian analysis of the Quine-Duhem problem is pursued; the phenomenon of a "protective belt" of auxiliary statements around reasonably successful theories is explicated. (3) The Bayesian approach to understanding the (...) superiority of variety of evidence is pursued; a recent challenge (by Wayne) is converted into a positive result on behalf of the Bayesian analysis, potentially with far-reaching consequences. (4) The condition for applying the merger-of-opinion results and the thesis of underdetermination of theories are compared, revealing significant limitations in applicability of the former. (5) Implications concerning "diachronic Dutch Book" arguments and "non-Bayesian shifts" are drawn, highlighting the incompleteness, but not incorrectness, of Bayesian analysis. (shrink)

The advent of formal definitions of the simplicity of a theory has important implications for model selection. But what is the best way to define simplicity? Forster and Sober ([1994]) advocate the use of Akaike's Information Criterion (AIC), a non-Bayesian formalisation of the notion of simplicity. This forms an important part of their wider attack on Bayesianism in the philosophy of science. We defend a Bayesian alternative: the simplicity of a theory is to be characterised in terms of Wallace's Minimum (...) Message Length (MML). We show that AIC is inadequate for many statistical problems where MML performs well. Whereas MML is always defined, AIC can be undefined. Whereas MML is not known ever to be statistically inconsistent, AIC can be. Even when defined and consistent, AIC performs worse than MML on small sample sizes. MML is statistically invariant under 1-to-1 re-parametrisation, thus avoiding a common criticism of Bayesian approaches. We also show that MML provides answers to many of Forster's objections to Bayesianism. Hence an important part of the attack on Bayesianism fails. (shrink)

In this paper I reconstruct and evaluate the validity of two versions of causal exclusion arguments within the theory of causal Bayes nets. I argue that supervenience relations formally behave like causal relations. If this is correct, then it turns out that both versions of the exclusion argument are valid when assuming the causal Markov condition and the causal minimality condition. I also investigate some consequences for the recent discussion of causal exclusion arguments in the light of an interventionist (...) theory of causation such as Woodward's (2003) and discuss a possible objection to my causal Bayes net reconstruction. (shrink)

A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of each model or hypothesis. Thomas Bayes’ Theorem relates the data and prior information to posterior probabilities associated with differing models or hypotheses and thus is useful in identifying the roles played by the known data and the assumed prior information when making (...) inferences. Scientists, philosophers, and theologians accumulate knowledge when analyzing different aspects of reality and search for particular hypotheses or models to fit their respective subject matters. Of course, a main goal is then to integrate all kinds of knowledge into an all-encompassing worldview that would describe the whole of reality. A generous description of the whole of reality would span, in the order of complexity, from the purely physical to the supernatural. These two extreme aspects of reality are bridged by a nonphysical realm, which would include elements of life, man, consciousness, rationality, mental and mathematical abstractions, etc. An urgent problem in the theory of knowledge is what science is and what it is not. Albert Einstein’s notion of science in terms of sense perception is refined by defining operationally the data that makes up the subject matter of science. It is shown, for instance, that theological considerations included in the prior information assumed by Isaac Newton is irrelevant in relating the data logically to the model or hypothesis. In addition, the concepts of naturalism, intelligent design, and evolutionary theory are critically analyzed. Finally, Eugene P. Wigner’s suggestions concerning the nature of human consciousness, life, and the success of mathematics in the natural sciences is considered in the context of the creative power endowed in humans by God. (shrink)