Arguments to the effect that Church's thesis is intrinsically unprovable because proof cannot relate an informal, intuitive concept to a mathematically defined one are unconvincing, since other 'theses' of this kind have indeed been proved, and Church's thesis has been proved in one direction. However, though evidence for the truth of the thesis in the other direction is overwhelming, it does not yet amount to proof.

Schurz (2019, ch. 4) argues that probabilistic accounts of induction fail. In particular, he criticises probabilistic accounts of induction that appeal to direct inference principles, including subjective Bayesian approaches (e.g., Howson 2000) and objective Bayesian approaches (see, e.g., Williamson 2017). In this paper, I argue that Schurz’ preferred direct inference principle, namely Reichenbach’s Principle of the Narrowest Reference Class, faces formidable problems in a standard probabilistic setting. Furthermore, the main alternative direct inference principle, Lewis’ Principal Principle, is also hard to (...) reconcile with standard probabilism. So, I argue, standard probabilistic approaches cannot appeal to direct inference to explicate the logic of induction. However, I go on to defend a non-standard objective Bayesian account of induction: I argue that this approach can both accommodate direct inference and provide a viable account of the logic of induction. I then defend this account against Schurz’ criticisms. (shrink)

The core of the problem discussed in this paper is the following: the Church-Turing Thesis states that Turing Machines formally explicate the intuitive concept of computability. The description of Turing Machines requires description of the notation used for the input and for the output. Providing a general definition of notations acceptable in the process of computations causes problems. This is because a notation, or an encoding suitable for a computation, has to be computable. Yet, using the concept of computation, in (...) a definition of a notation, which will be further used in a definition of the concept of computation yields an obvious vicious circle. The circularity of this definition causes trouble in distinguishing on the theoretical level, what is an acceptable notation from what is not an acceptable notation, or as it is usually referred to in the literature, “deviant encodings”. Deviant encodings appear explicitly in discussions about what is an adequate or correct conceptual analysis of the concept of computation. In this paper, I focus on philosophical examples where the phenomenon appears implicitly, in a “disguised” version. In particular, I present its use in the analysis of the concept of natural number. I also point at additional phenomena related to deviant encodings: conceptual fixed points and apparent “computability” of uncomputable functions. In parallel, I develop the idea that Carnapian explications provide a much more adequate framework for understanding the concept of computation, than the classical philosophical analysis. (shrink)

Howson famously argues that the no-miracles argument, stating that the success of science indicates the approximate truth of scientific theories, is a base rate fallacy: it neglects the possibility of an overall low rate of true scientific theories. Recently a number of authors has suggested that the corresponding probabilistic reconstruction is unjust, as it concerns only the success of one isolated theory. Dawid and Hartmann, in particular, suggest to use the frequency of success in some field of research \ to (...) infer a probability of truth for a new theory from \. I here shed doubts on the justification of this and similar moves and suggest a way to directly bound the probability of truth. As I will demonstrate, my bound can become incompatible with the assumption specific testing and Dawid and Hartmann’s estimate for success. (shrink)

We give an account of stable reasoning, a recent and novel approach to problem solving from a formal, logical point of view. We describe the underlying logic of stable reasoning and illustrate how it is used to model different domains and solve practical reasoning problems. We discuss some of the main differences with respect to reasoning in classical logic and we examine an ongoing research programme for the rational reconstruction of human knowledge that may be considered a successor to the (...) logical empiricists’ programme of the mid-twentieth century. (shrink)

According to a widespread but implicit thesis in Bayesian confirmation theory, two confirmation measures are considered equivalent if they are ordinally equivalent—call this the “ordinal equivalence thesis”. I argue that adopting OET has significant costs. First, adopting OET renders one incapable of determining whether a piece of evidence substantially favors one hypothesis over another. Second, OET must be rejected if merely ordinal conclusions are to be drawn from the expected value of a confirmation measure. Furthermore, several arguments and applications of (...) confirmation measures given in the literature already rely on a rejection of OET. I also contrast OET with stronger equivalence theses and show that they do not have the same costs as OET. On the other hand, adopting a thesis stronger than OET has costs of its own, since a rejection of OET ostensibly implies that people’s epistemic states have a very fine-grained quantitative structure. However, I suggest that the normative upshot of the paper in fact has a conditional form, and that other Bayesian norms can also fruitfully be construed as having a similar conditional form. (shrink)

Con el objeto de dar cuenta de la dinámica del derecho, Alchourrón y Bulygin distinguen los conceptos de sistema jurídico y de orden jurídico. El primero hace referencia a un conjunto de enunciados que contiene todas sus consecuencias deductivas, entre las cuales hay normas cuyo contenido son actos coactivos. Se trata de una entidad estática. El orden jurídico, por su parte, es concebido como una secuencia de sistemas jurídicos enlazados por algún criterio de legalidad o validez, y conserva su identidad (...) a través de los cambios producidos por la sanción o derogación de normas. Es mi propósito presentar argumentos tendientes a sostener que la noción de orden jurídico no es adecuada para los fines que se propone y, además, su postulación, con el sentido que le atribuyen los autores, resulta innecesaria. Aiming to account for the dynamic nature of law, the Argentinian philosophers Carlos Alchourrón and Eugenio Bulygin discriminate the concepts of legal system and legal order. The first makes reference to a set of statements that includes all their deductive consequences, among which there are norms that prescribe coercive acts. It is a static entity. legal order, on the other hand, is conceived as a sequence of legal systems connected by some criterion of legal validity and keeps its identity through the changes produced by the passing or abrogation of laws. The aim of this paper is to present arguments leading to support that the notion of legal order is inadequate for its declared purpose and, furthermore, its conception, with the meaning the authors assign to it, is unnecessary. (shrink)

The concept of fitness has generated a lot of discussion in philosophy of biology. There is, however, relative agreement about the need to distinguish at least two uses of the term: ecological fitness on the one hand, and population genetics fitness on the other. The goal of this paper is to give an explication of the concept of ecological fitness by providing a reconstruction of the theory of natural selection in which this concept was framed, that is, based on the (...) way the theory was put to use in Darwin’s main texts. I will contend that this reconstruction enables us to account for the current use of the theory of natural selection. The framework presupposed in the analysis will be that of metatheoretical structuralism. This framework will provide both a better understanding of the nature of ecological fitness and a more complete reconstruction of the theory. In particular, it will provide what I think is a better way of understanding how the concept of fitness is applied through heterogeneous cases. One of the major advantages of my way of thinking about natural selection theory is that it would not have the peculiar metatheoretical status that it has in other available views. I will argue that in order to achieve these goals it is necessary to make several concepts explicit, concepts that are frequently omitted in usual reconstructions. (shrink)

A central problem in the interpretation of non-relativistic quantum mechanics is to relate the conceptual structure of the theory to the classical idea of the state of a physical system. This paper approaches the problem by presenting an analysis of the notion of an elementary physical proposition. The notion is shown to be realized in standard formulations of the theory and to illuminate the significance of proofs of the impossibility of hidden variable extensions. In the interpretation of quantum mechanics that (...) emerges from this analysis, the philosophically distinctive features of the theory derive from the fact that it seeks to represent a reality of which complete knowledge is essentially unattainable. (shrink)

This paper attempts to place Goodman's "New Riddle of Induction" within the context of a subjectivist understanding of inductive logic. It will be argued that predicates such as 'grue' cannot be denied projectible status in any a priori way, but must be considered in the context of a situation of inductive support. In particular, it will be argued that questions of projectibility are to be understood as a variety of questions about the ways a given sample is random. Various examples (...) are considered, including cases when 'grue' (as opposed to 'green') should be projected, and some remarks are offered on what is meant when it is claimed that a sample is random (in ways relevant to inductive support) and how such randomness is determined. The view presented helps to make clear the relation between such apparently non-projectible predicates as 'grue' and the concept of being examined. (shrink)

Common probability theories only allow the deduction of probabilities by using previously known or presupposed probabilities. They do not, however, allow the derivation of probabilities from observed data alone. The question thus arises as to how probabilities in the empirical sciences, especially in medicine, may be arrived at. Carnap hoped to be able to answer this question byhis theory of inductive probabilities. In the first four sections of the present paper the above mentioned problem is discussed in general. After a (...) short presentation of Carnap''s theory it is then shown that this theory cannot claim validity for arbitrary random processes. It is suggested that the theory be only applied to binomial and multinomial experiments. By application of de Finetti''s theorem Carnap''s inductive probabilities are interpreted as consecutive probabilities of the Bayesian kind. Through the introduction of a new axiom the decision parameter can be determined even if no a priori knowledge is given. Finally, it is demonstrated that the fundamental problem of Wald''s decision theory, i.e., the determination of a plausible criterion where no a priori knowledge is available, can be solved for the cases of binomial and multinomial experiments. (shrink)

An inexact generalization like ‘ravens are black’ will be symbolized as a prepositional function with free variables thus: ‘Rx ⇒ Bx.’ The antecedent ‘Rx’ and consequent ‘Bx’ will themselves be called absolute formulas, while the result of writing the non-boolean connective ‘⇒’ between them is conditional. Absolute formulas are arbitrary first-order formulas and include the exact generalization ‘(x)(Rx → Bx)’ and sentences with individual constants like ‘Rc & Bc.’ On the other hand the non-boolean conditional ‘⇒’ can only occur as (...) the main connective in a formula. We shall also need to consider formulas with more than one free variable such as ‘xHy ⇒ xTy,’ which might express ‘if x is the husband of y then x is taller than y.’ Though it is inessential, it will simplify things to work in ‘n-languages’ with a finite number of individual constants c1,…, cn, which are interpreted as denoting the elements of the domains of the ‘n-models’ to be described below. (shrink)

The concept of causal specificity is drawing considerable attention from philosophers of biology. It became the rationale for rejecting (and occasionally, accepting) a thesis of causal parity of developmental factors. This literature assumes that attributing specificity to causal relations is at least in principle a straightforward (if not systematic) task. However, the parity debate in philosophy of biology seems to be stuck at a point where it is not the biological details that will help move forward. In this paper, I (...) take a step back to reexamine the very idea of causal specificity and its intended role in the parity dispute in philosophy of biology. I contend that the idea of causal specificity across variations as currently discussed in the literature is irreducibly twofold in nature: it is about two independent components that are not mutually entailed. I show this to be the source of prior complications with the notion of specificity itself that ultimately affect the purposes for which it is often invoked, notably to settle the parity dispute. (shrink)

Decision-making procedures in medical practice are often analysed by both philosophers of science and ethicists, as well as statisticians, clinicians and methodologists. The paper focuses on decisions made by patients in situations of moral dilemma. The main purpose is to analyse the strategies used in resolving such dilemmas. First, the concept of a ‘situation of moral dilemma’ is clarified. Then, two types of strategies for resolving such situations are distinguished. The first strategy requires revising the patient’s belief system or moral (...) orientation. The second one includes a group of non-revision beliefs strategies (NRB). The authors argue in support of the thesis that NRB strategies are, in fact, the patient’s first choice when it comes to resolving moral dilemmas. The paper analyses situations where the NRB strategies may prove effective, as well as situations where they fail and where the solution of the moral dilemma must be addressed by revising the accepted belief system. The findings will help to better understand patients’ decision-making processes. (shrink)

Georg Kreisel suggested various ways out of the Gödel incompleteness theorems. His remarks on ways out were somewhat parenthetical, and suggestive. He did not develop them in subsequent papers. One aim of this paper is not to develop those remarks, but to show how the basic idea that they express can be used to reason about the Lucas-Penrose-Putnam arguments that human minds are not finitary computational machines. Another aim is to show how one of Putnam’s two anti-functionalist arguments avoids the (...) logical error in the Lucas-Penrose arguments, extends those arguments, but succumbs to an absurdity. A third aim is to provide a categorization of the Lucas-Penrose-Putnam anti-functionalist arguments. (shrink)

How should we understand the relationship between binary belief and degree of belief? To answer this question, we should look to desire. Whatever relationship we think holds between desire and degree of desire should be used as our model for the relationship we think holds between belief and degree of belief. This parity pushes us towards an account that treats the binary attitudes as primary. But if we take binary beliefs as primary, we seem to face a serious problem. Binary (...) beliefs are insufficiently discriminating. If we treat them as primary, we will lack the resources needed for fruitful theorizing. This problem can, I argue, be solved if we think of an agent’s degree of belief that p as reducible to her binary believing that p and the change in the apparent reasons that would be needed to get her to withhold. (shrink)

The analysis and theorizing about concepts like “knowledge” and “justification” has played a central role in much of epistemology in the past half century. This dissertation argues for the claim that we should understand this conceptual concern as one of design. Concepts are tools and the concepts of interest to epistemologists must be those that we can best use in service of our epistemic interests. On this understanding of the conceptual project, we determine the content of epistemic concepts, not by (...) consulting our naïve linguistic intuitions, but by determining what concepts will best help us express and enforce the epistemic norms that serve our interests. The determination of what concepts will do this job best will pull on information from many empirical sources like psychology and sociology. It will also require some means of determining what our epistemic interests are. In defending this view of the methodology of epistemology, we examine how one might go about designing and thinking about the purposes of an example epistemic concept: “epistemic ought”. We also consider how thinking about things from a design prospective can help in the determination of our epistemic interests by considering how design considerations feature in the debate between scientific realism and anti-realism. We also examine and respond to a few potential problems for this methodological view from Selim Berker’s arguments against epistemic teleology to problems with the design method’s potentially problematically self-undermining or self-reinforcing character. Advisor: David Henderson. (shrink)

The following well-known problem motivated my handling more general problems. As we surely know, our pupils and even students are confronted with much more trouble when learning mathematics (and even physics) than when they learn ‘empirical’ sciences like biology, mineralogy etc. There are many factors that can at least partially explain this phenomenon. I would however mention one factor that is not too frequently adduced: mathematics, logic, and much of physics use concepts that are abstract while the empirical sciences seem (...) to support understanding by using expressions concerning (denoting? expressing?) concrete objects. Therefore the first topic to be explained (or explicated) is: Abstract vs. concrete. The second point will consist of applying the first point to explanation of the trouble with learning mathematics. The third point will ask Logical Analysis of Natural Language how to tell abstract expressions from concrete ones. The fourth point will confront the concept described in the foregoing point with conceptions trying to abandon the distinction between analytic and empirical expressions. Here it will be shown that the empiricism representing this latter conception deprives semantics as applied to Natural language of important features of expressivity. (shrink)

You receive a pink packet from Miss Lead, a notoriously deceptive truth-teller. You know that if you open the packet and do not find blank pages, then you will justifiably change your mind about the evidence being misleading. Indeed, you will infer that your previous fears about misleading evidence were themselves founded on misleading evidence. Should you open the pink packet? No, answers an advocate of self-censorship. Yes, answers an advocate of the principle that you should base conclusions on all (...) the available evidence. Your final deliberations will be guided by Gilbert Harman’s Thought. Ultimately, the case against opening the packet prevails. (shrink)

Scientists and Bayesian statisticians often study hypotheses that they know to be false. This creates an interpretive problem because the Bayesian probability of a hypothesis is supposed to represent the probability that the hypothesis is true. I investigate whether Bayesianism can accommodate the idea that false hypotheses are sometimes approximately true or that some hypotheses or models can be closer to the truth than others. I argue that the idea that some hypotheses are approximately true in an absolute sense is (...) hard to square with Bayesianism, but that the notion that some hypotheses are comparatively closer to the truth than others can be made compatible with Bayesianism, and that this provides an adequate and potentially useful solution to the interpretive problem. Finally, I compare my ``verisimilitude'' solution to the interpretive problem with a ``counterfactual'' solution recently proposed by Jan Sprenger. (shrink)

Gentzen’s approach to deductive systems, and Carnap’s and Popper’s treatment of probability in logic were two fruitful ideas that appeared in logic of the mid-twentieth century. By combining these two concepts, the notion of sentence probability, and the deduction relation formalized in the sequent calculus, we introduce the notion of ’probabilized sequent’ \ with the intended meaning that “the probability of truthfulness of \ belongs to the interval [a, b]”. This method makes it possible to define a system of derivations (...) based on ’axioms’ of the form \, obtained as a result of empirical research, and then infer conclusions of the form \. We discuss the consistency, define the models, and prove the soundness and completeness for the defined probabilized sequent calculus. (shrink)

I reconsider the monism/pluralism debate about natural kinds. Monism claims that there is a privileged division of reality into natural kinds, while pluralism states that there are many ways of classifying objects according to different purposes. I compare three different monistic accounts of natural kinds with the pluralism advocated by promiscuous realism. The analysis of some examples of the classification of celestial objects suggest that there are indeed different legitimate ways of classifying things according to different purposes; contrary to monism, (...) the boundaries between kinds are not fixed. These results show that promiscuous realism is a better account of natural kind. (shrink)

We live in a world in which scientific expertise and its epistemic authority become more important. On the other hand, the financial interests in research, which could potentially corrupt science, are increasing. Due to these two tendencies, a concern for the integrity of scientific research becomes increasingly vital. This concern is, however, hollow if we do not have a clear account of research integrity. Therefore, it is important that we explicate this concept. Following Rudolf Carnap’s characterization of the task of (...) explication, this means that we should develop a concept that is (1) similar to our common sense notion of research integrity, (2) exact, (3) fruitful, and (4) as simple as possible. Since existing concepts do not meet these four requirements, we develop a new concept in this article. We describe a concept of epistemic integrity that is based on the property of deceptiveness, and argue that this concept does meet Carnap’s four requirements of explication. To illustrate and support our claims we use several examples from scientific practice, mainly from biomedical research. (shrink)

This paper is an extended review of the book Error and Inference, edited by Deborah Mayo and Aris Spanos, about their frequentist and philosophical perspective on testing of hypothesis and on the criticisms of alternatives like the Bayesian approach.

Predictions about the future and unrestricted universal generalizations are never logically implied by our observational evidence, which is limited to particular facts in the present and past. Nevertheless, propositions of these and other kinds are often said to be confirmed by observational evidence. A natural place to begin the study of confirmation theory is to consider what it means to say that some evidence E confirms a hypothesis H.

By “Propensities” I mean the kind of probabilities that figure in laws of nature. Propensities might be (i) relative frequencies, finite or long run, de facto or modalized, or (ii) reflections of our epistemic probabilities or (iii) sui generus theoretical notions. I believe that the whole family of relative frequency proposals (i) are inadequate. As an alternative I wish to suggest (ii) an epistemic account of propensities and of nomic force in general, in the spirit of Hume, Mill, DeFinetti, Ayer, (...) Suppes and Jeffrey. Whether accounts of the third kind differ in substance or in name only from the sort of account that I am proposing is a nice question, to which. I will devote some brief closing remarks. (shrink)