English translation of a paper intially publisdhed in French in Dialogue under the title 'Une solution pour le paradoxe de Goodman'. In the classical version of Goodman's paradox, the universe where the problem takes place is ambiguous. The conditions of induction being accurately described, I define then a framework of n-universes, allowing the distinction, among the criteria of a given n-universe, between constants and variables. Within this framework, I distinguish between two versions of the problem, respectively taking place: (...) (i) in an n-universe the variables of which are colour and time; (ii) in an n-universe the variables of which are colour, time and space. Finally, I show that each of these versions admits a specific resolution. (shrink)

On page 14 of "Reconceptions in Philosophy and Other Arts and Sciences" (section 4 of chapter 1) by Nelson Goodman and Catherine Z. Elgin is written: “Since ‘blue’ and ‘green’ are interdefinable with ‘grue’ and ‘bleen’, the question of which pair is basic and which pair derived is entirely a question of which pair we start with”. This paper points out that an example of interdefinability is also that one about the predicate “grueb”, which is a predicate that applies (...) to an object if the object either is green and examined before time b, or is non-green and not examined before time b. The three predicates “green”, “grueb”, “examined before time b” are interdefinable. According to Goodman, since the predicates “blue” and “green” are interdefinable with the predicates “grue” and “bleen”, “if we can tell which objects are blue and which objects are green, we can tell which ones are grue and which ones are bleen” [pages 12-13 of “Reconceptions in Philosophy and Other Arts and Sciences”]. But , even though the predicates “green” and “examined before time b” are interdefinable, being able to tell if an object is green does not imply being able to tell if an object is examined before time b. The interdefinability among three elements is a type of interdefinability present, for example, also among the logical connectives. Another example of interdefinability is that one about a decidable predicate PD, which is interdefinable with an undecidable predicate PU: therefore even though we can tell whether an object is PD and whether an object is non-PD, we cannot tell whether an object is PU (since PU is an undecidable predicate) and whether an object is non-PU. Although the predicates PD and PU are interdefinable, the possibility to determine whether an object is PD does not imply the possibility to determine whether an object is PU (since PU is an undecidable predicate). Similarly, although the predicates “green” and “grue” are interdefinable, the possibility to determine whether an object is “green” even in absence of temporal information does not imply the possibility to determine whether an object is “grue” even in absence of temporal information. These and other examples about “grue” and “bleen” point out that even in case two predicates are interdefinable, the possibility to apply a predicate P does not imply the possibility to apply a predicate interdefinable with P. And that the possibility to apply the predicate “green” without having temporal information does not imply the possibility to apply the predicate “grue” without having temporal information. According to Goodman, if it is possible to determine if an object is green without needing temporal information, then it is also possible to determine if an object is grue without needing temporal information. But, knowing that an object is both green and grue implies temporal information: in fact, we know by definition that a grue object can only be: 1) either green (in case the object is examined before time t); 2) or blue (in case the object is not examined before time t). Thus, knowing that an object is both grue and green, we know that we are faced with case 1, the case of a grue object that is green and examined before time t. Then the paper points out why the Goodman-Kripke paradox is a paradox about meaning that cannot have repercussions on induction. Finally the paper points out why Hume’s problem is a problem different from Goodman’s paradox and requires a specific treatment. (shrink)

This paper reports (in section 1 “Introduction”) some quotes from Nelson Goodman which clarify that, contrary to a common misunderstanding, Goodman always denied that “grue” requires temporal information and “green” does not require temporal information; and, more in general, that Goodman always denied that grue-like predicates require additional information compared to what green-like predicates require. One of the quotations is the following, taken from the first page of the Foreword to chapter 8 “Induction” of the Goodman’s book “Problems (...) and Projects”: “Nevertheless, we may by now confidently conclude that no general distinction between projectible and non- projectible predicates can be drawn on syntactic or even on semantic grounds. Attempts to distinguish projectible predicates as purely qualitative, or non-projectible ones as time-dependent, for example, have plainly failed”. Barker and Achinstein in their famous paper of 1960 tried to demonstrate that the grue-speaker (named Mr. Grue in their paper) needs temporal information to be able to determine whether an object is grue, but Goodman replied (in “Positionality and Pictures”, contained in his book “Problems and Projects”, chapter 8, section 6b) that they failed to prove that Mr. Grue needs temporal information to determine whether an object is grue. According to Goodman, since the predicates “blue” and “green” are interdefinable with the predicates “grue” and “bleen”, “if we can tell which objects are blue and which objects are green, we can tell which ones are grue and which ones are bleen” [pages 12-13 of “Reconceptions in Philosophy and Other Arts and Sciences”]. But this paper points out that an example of interdefinability is also that one about the predicate “gruet”, which is a predicate that applies to an object if the object either is green and examined before time t, or is non-green and not examined before time t. The three predicates “green”, “gruet”, “examined before time t” are interdefinable: and even though the predicates “green” and “examined before time t” are interdefinable, being able to tell if an object is green does not imply being able to tell if an object is examined before time t (the interdefinability among three elements is a type of interdefinability present, for example, also among the logical connectives). Thus, it is wrong the Goodman’s thesis according to which if it is possible to determine without having temporal information whether the predicate “green” has to be applied to an object, then it is also possible to determine without having temporal information whether a predicate interdefinable with “green” has to be applied to an object. Another example of interdefinability is that one about a decidable predicate PD, which is interdefinable with an undecidable predicate PU: therefore even though we can tell whether an object is PD and whether an object is non-PD, we cannot tell whether an object is PU (since PU is an undecidable predicate) and whether an object is non-PU. Although the predicates PD and PU are interdefinable, the possibility to determine whether an object is PD does not imply the possibility to determine whether an object is PU (since PU is an undecidable predicate). Similarly, although the predicates “green” and “grue” are interdefinable, the possibility to determine whether an object is “green” even in absence of temporal information does not imply the possibility to determine whether an object is “grue” even in absence of temporal information. These and other examples about “grue” and “bleen” point out that even in case two predicates are interdefinable, the possibility to apply a predicate P does not imply the possibility to apply a predicate interdefinable with P. And that the possibility to apply the predicate “green” without having temporal information does not imply the possibility to apply the predicate “grue” without having temporal information. Furthermore, knowing that an object is both green and grue implies temporal information: in fact, we know by definition that a grue object can only be: 1) either green (in case the object is examined before time t); 2) or blue (in case the object is not examined before time t). Thus, knowing that an object is both grue and green, we know that we are faced with case 1, the case of a grue object that is green and examined before time t. Then the paper points out why the Goodman-Kripke paradox is a paradox about meaning that cannot have repercussions on induction. Finally the paper points out why Hume’s problem is a problem different from Goodman’s paradox and requires a specific treatment. -/- . (shrink)

Historically, Nelson Goodman’s paradox involving the predicates ‘grue’ and ‘bleen’ has been taken to furnish a serious blow to Carl Hempel’s theory of confirmation in particular and to purely formal theories of confirmation in general. In this paper, I argue that Goodman’s paradox is no more serious of a threat to Hempel’s theory of confirmation than is Hempel’s own paradox of the ravens. I proceed by developing a suggestion from R. D. Rosenkrantz into an argument for (...) the conclusion that these paradoxes are, in fact, equivalent. My argument, if successful, is of both historical and philosophical interest. Goodman himself maintained that Hempel’s theory of confirmation was capable of handling the paradox of the ravens. And Hempel eventually conceded that Goodman’s paradox showed that there could be no adequate, purely syntactical theory of confirmation. The conclusion of my argument entails, by contrast, that Hempel’s theory of confirmation is incapable of handling Goodman’s paradox if and only if it is incapable of handling the paradox of the ravens. It also entails that for any adequate solution to one of these paradoxes, there is a corresponding and equally adequate solution to the other. (shrink)

The extensions of Goodman’s ‘grue’ predicate and Kripke’s ‘quus’ are constructed from the extensions of more familiar terms via a reinterpretation that permutes assignments of reference. Since this manoeuvre is at the heart of Putnam’s model-theoretic and permutation arguments against metaphysical realism (‘Putnam’s Paradox’), both Goodman’s New Riddle of Induction and the paradox about meaning that Kripke attributes to Wittgenstein are instances of Putnam’s. Evidence cannot selectively confirm the green-hypothesis and disconfirm the grue-hypothesis, because the theory (...) of which the green-hypothesis is a part has an unintended model in which the grue-hypothesis is equally confirmed; and there are no meaning-facts that determine reference, because the objects referred to by the referring terms of any language or set of intentional mental states are permutable in a way that is consistent with the truth-values of all other sentences in that language or beliefs in that set. The upshot is that the three paradoxes need to be solved in a unified way. (shrink)

Hempel‘s paradox of the ravens, and his take on it, are meant to be understood as being restricted to situations where we have no additional background information. According to him, in the absence of any such information, observations of FGs confirm the hypothesis that all Fs are G. In this paper I argue against this principle by way of considering two other paradoxes of confirmation, Goodman‘s 'grue‘ paradox and the 'tacking‘ (or 'irrelevant conjunct‘) paradox. What these (...) paradoxes reveal, I argue, is that a presumption of causal realism is required to ground any confirmation; but once we grant causal realism, we have no reason to accept the central principles giving rise to the paradoxes. (shrink)

Article presenting basic methodological tenets in Goodman's philosophical development with their mutual connections, like the new riddle of indutcion, counterfactual conditionals and his use of reflective equilibrium as a methodological basis.

Essential for the concept of the law of nature is not only spatio-temporal universality, but also functionality in the sense of the dependency on physical conditions of natural entities. In the following it is explained in detail that just the neglect of this functional property is to be understood as the real reason for the occurrence of the Goodman paradox – with the consequence, that the behavior of things seems to be completely at the mercy of change of unique (...) unrepeatable temporal points. It is exactly this (mis-)understanding that also generated the induction problem. From the intrinsic connection between universality and functionality, however, – that is my claim – the ontological consequence of a nature results, for which lawfulness is coupled to essentially functionally defined time sequences, thereby implying a potentiality dimension of nature, too. (shrink)

The Kripke/Wittgenstein paradox and Goodman’s riddle of induction can be construed as problems of multiple redescription, where the relevant sceptical challenge is to provide factual grounds justifying the description we favour. A choice of description or predicate, in turn, is tantamount to the choice of a curve over a set of data, a choice apparently governed by implicitly operating constraints on the relevant space of possibilities. Armed with this analysis of the two paradoxes, several realist solutions of Kripke’s (...) class='Hi'>paradox are examined that appeal to dispositions or other non-occurrent properties. It is found that all neglect crucial epistemological issues: the entities typically appealed to are not observational and must be inferred on the basis of observed entities or events; yet, the relevant sceptical challenge concerns precisely the factual basis on which this inference is made and the constraints operating on it. All disposition ascriptions, the thesis goes on to argue, contain elements of idealization. To ward off the danger of vacuity resulting from the fact that any disposition ascription is true under just the right ideal conditions, dispositional theories need to specify limits on legitimate forms of idealization. This is best done by construing disposition ascriptions as forms of (implicit) curve-fitting, I argue, where the “data” is not necessarily numeric, and the “curve” fitted not necessarily graphic. This brings us full circle: Goodman’s and Kripke’s problems are problems concerning curve-fitting, and the solutions for it appeal to entities the postulation of which is the result of curve-fitting. The way to break the circle must come from a methodology governing the idealizations, or inferences to the best idealization, that are a part of curve-fitting. The thesis closes with an argument for why natural science cannot be expected to be of much help in this domain, given the ubiquity of idealization. (shrink)

I explain the New Riddle of Induction (Goodman 1946, 1955) in very brief words.

Essential for the concept of the law of nature is not only spatio-temporal universality, but also functionality in the sense of the dependency on physical conditions of natural entities. In the following it is explained in detail that just the neglect of this functional property is to be understood as the real reason for the occurrence of the Goodman paradox. As a consequence, the behavior of things seems to be completely at the mercy of the temporal change of unique (...) absolute temporal points. It is exactly this (mis-)understanding that also generated the induction problem. From the intrinsic connection between universality and functionality, however, - that is my claim - the ontological consequence of a nature results, for which the potentiality of lawfulness is coupled to essentially functionally defined time sequences. (shrink)

Extant literature on Goodman’s ‘New Riddle of Induction’ deals mainly with two versions. I consider both of them, starting from the (‘epistemic’) version of Goodman’s classic of 1954. It turns out that it belongs to the realm of applications of inductive logic, and that it can be resolved by admitting only significant evidence (as I call it) for confirmations of hypotheses. Sect. 1 prepares some ground for the argument. As much of it depends on the notion of evidential significance, this (...) concept is defined and its introduction motivated. Further, I introduce and explain the distinction between support and confirmation: put in a slogan, ‘confirmation is support by significant evidence’. The second section deals with the Riddle itself. I demonstrate that, given the provisions of the first section, not ‘anything confirms anything’: significant green-evidence confirms only green-hypotheses (and no grue-hypotheses), and significant grue-evidence confirms only grue-hypotheses (and no green-hypotheses), whichever terms we use for expressing these evidences or hypotheses. The third section rounds off my treatment. First I show that Frank Jackson’s use of his counterfactual condition is unsuccessful. Further, I argue that no unwanted consequences result, if one starts from the other, ‘objective’, definition of ‘grue’, as it constitutes no more than a mere fact of logic that cannot do any harm. Finally, I present a grue-case involving both kinds of definition, where the exclusive confirmation of either the green- or the grue-hypothesis is shown. (shrink)

Paradoxes and their Resolutions is a ‘thematic compilation’ by Avi Sion. It collects in one volume the essays that he has written in the past (over a period of some 27 years) on this subject. It comprises expositions and resolutions of many (though not all) ancient and modern paradoxes, including: the Protagoras-Euathlus paradox (Athens, 5th Cent. BCE), the Liar paradox and the Sorites paradox (both attributed to Eubulides of Miletus, 4th Cent. BCE), Russell’s paradox (UK, 1901) (...) and its derivatives the Barber paradox and the Master Catalogue paradox (also by Russell), Grelling’s paradox (Germany, 1908), Hempel's paradox of confirmation (USA, 1940s), and Goodman’s paradox of prediction (USA, 1955). This volume also presents and comments on some of the antinomic discourse found in some Buddhist texts (namely, in Nagarjuna, India, 2nd Cent. CE; and in the Diamond Sutra, date unknown, but probably in an early century CE). (shrink)

This paper advocates a new reading of Nelson Goodman’s new riddle of induction. According to Ian Hacking, this famous problem conveys a “pure nominalism”, as it grounds Goodman’s denial regarding the existence of natural kinds. While this interpretation is somewhat convincing, it suffers the major flaw of not corresponding to what Goodman himself understood by “nominalism”. Nominalism, in a goodmanian sense, is indeed primarily a technical demand, which stems from the so-called “calculus of individuals”. I argue that this mereological definition (...) of nominalism allows to understand the new riddle of induction afresh. As a result, Goodman’s riddle is “hyper-nominalist”, i.e., nominalist in a distinct and stronger sense than what Hacking suggested. (shrink)

It is a common intuition in scientific practice that positive instances confirm. This confirmation, at least based purely on syntactic considerations, is what Nelson Goodman’s ‘Grue Problem’, and more generally the ‘New Riddle’ of Induction, attempt to defeat. One treatment of the Grue Problem has been made along Bayesian lines, wherein the riddle reduces to a question of probability assignments. In this paper, I consider this so-called Bayesian Grue Problem and evaluate how one might proffer a solution (...) to this problem utilizing what I call a phenomenological approach. I argue that this approach to the problem can be successful on the Bayesian framework. (shrink)

Israel 2004 claims that numerous philosophers have misinterpreted Goodman’s original ‘New Riddle of Induction’, and weakened it in the process, because they do not define ‘grue’ as referring to past observations. Both claims are false: Goodman clearly took the riddle to concern the maximally general problem of “projecting” any type of characteristic from a given realm of objects into another, and since this problem subsumes Israel’s, Goodman formulated a stronger philosophical challenge than the latter surmises.

The limited aim here is to explain what John Dewey might say about the formulation of the grue example. Nelson Goodman’s problem of distinguishing good and bad inductive inferences is an important one, but the grue example misconstrues this complex problem for certain technical reasons, due to ambiguities that contemporary logical theory has not yet come to terms with. Goodman’s problem is a problem for the theory of induction and thus for logical theory in general. Behind the whole (...) discussion of these issues over the last several decades is a certain view of logic hammered out by Russell, Carnap, Tarski, Quine, and many others. Goodman’s nominalism hinges in essential ways on a certain view of formal logic with an extensional quantification theory at its core. This raises many issues, but the one issue most germane here is the conception of predicates ensconced in this view of logic. (shrink)

In an unpublished speech from 1991, David Lewis told his audience that he counted ‘the metaphysician Carnap ’ amongst his historical ancestors. Here I provide a novel interpretation of the Aufbau that allows us to make sense of Lewis’s claim. Drawing upon Lewis’s correspondence, I argue it was the Carnap of the Aufbau whom Lewis read as a metaphysician, because Carnap’s appeal to the notion of founded relations in the Aufbau echoes Lewis’s own appeal to the metaphysics of natural properties. (...) I further maintain that Lewis was right to read Carnap this way and that the notion of a founded relation has a legitimate claim to be both logical and metaphysical. I also argue that Carnap’s initial response to Goodman’s puzzle about ‘grue’ relies upon a metaphysics of simple properties which also prefigures Lewis’s own response to Goodman invoking natural properties. (shrink)

I describe in this paper the basic elements of the n-universes, a methodological tool originally introduced in Franceschi (2001) in the context of the study of Goodman's paradox. As the n-universes can be used in wide-ranging applications, such as thought experiments, I describe them from an essentially pragmatic standpoint, i.e. by describing accurately the step-by-step process which leads to a given modelisation.

The aim of this paper is to show that (elementary) topology may be useful for dealing with problems of epistemology and metaphysics. More precisely, I want to show that the introduction of topological structures may elucidate the role of the spatial structures (in a broad sense) that underly logic and cognition. In some detail I’ll deal with “Cassirer’s problem” that may be characterized as an early forrunner of Goodman’s “grue-bleen” problem. On a larger scale, topology turns out to be (...) useful in elaborating the approach of conceptual spaces that in the last twenty years or so has found quite a few applications in cognitive science, psychology, and linguistics. In particular, topology may help distinguish “natural” from “not-so-natural” concepts. This classical problem that up to now has withstood all efforts to solve (or dissolve) it by purely logical methods. Finally, in order to show that a topological perspective may also offer a fresh look on classical metaphysical problems, it is shown that Leibniz’s famous principle of the identity of indiscernibles is closely related to some well-known topological separation axioms. More precisely, the topological perspective gives rise in a natural way to some novel variations of Leibniz’s principle. (shrink)

There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and (...) logic-based approaches are compared by means of an experiment to show that SP is not basically causal. (shrink)

I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act as (...) if one has substantive information about the world when one does not. I sketch the outlines of a solution in part I, showing how it differs from others, with full details to follow in subsequent parts. The solution is pragmatic in sentiment (though differs in specifics to arguments from, for example, William James); the conceptions we use to guide our actions are and should be at least partly determined by preferences. This is cashed out in a reformulation of decision theory motivated by a non-reductive formulation of hypotheses and logic. A distinction emerges between initial assumptions--that can be non-dogmatic--and effective assumptions that can simultaneously be substantive. An explanation is provided for the plausibility arguments used to explain assigned probabilities in BCT. -/- In subsequent parts, logic is constructed from principles independent of language and mind. In particular, propositions are defined to not have form. Probabilities are logical and uniquely determined by assumptions. The problems considered fatal to logical probabilities--Goodman's `grue' problem and the uniqueness of priors problem are dissolved due to the particular formulation of logic used. Other problems such as the zero-prior problem are also solved. -/- A universal theory of (non-linguistic) meaning is developed. Problems with counterfactual conditionals are solved by developing concepts of abstractions and corresponding pictures that make up hypotheses. Spaces of hypotheses and the version of Bayes' theorem that utilises them emerge from first principles. -/- Theoretical virtues for hypotheses emerge from the theory. Explanatory force is explicated. The significance of effective assumptions is partly determined by combinatoric factors relating to the structure of hypotheses. I conjecture that this is the origin of simplicity. (shrink)

This paper consists of an investigation of three debates concerning propositional identity: the tension between structured propositions and higher-order logic, the principle Only Logical Circles, and Kaplan’s Paradox. The literature at large has mistaken the consequences of each of these debates. Structuralists are not committed to the claim that identical properties have different extensions; rather, they are committed to existence monism. Only Logical Circles does not preclude the identification of green in terms of grue; some further (and, as (...) of yet, undisclosed) principle is required for that result. And Kaplan’s Paradox does not count against the possible-worlds conception of propositions; it applies to every account of propositions whatsoever. (shrink)

There are three questions associated with Simpson’s paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP? and (iii) How to proceed when confronted with SP? An adequate analysis of the paradox starts by distinguishing these three questions. Then, by developing a formal account of SP, and substantiating it with a counterexample to causal accounts, we argue that there are no causal factors at play in answering questions (i) and (ii). Causality enters only in connection with (...) action. (shrink)

Fitch’s Paradox shows that if every truth is knowable, then every truth is known. Standard diagnoses identify the factivity/negative infallibility of the knowledge operator and Moorean contradictions as the root source of the result. This paper generalises Fitch’s result to show that such diagnoses are mistaken. In place of factivity/negative infallibility, the weaker assumption of any ‘level-bridging principle’ suffices. A consequence is that the result holds for some logics in which the “Moorean contradiction” commonly thought to underlie the result (...) is in fact consistent. This generalised result improves on the current understanding of Fitch’s result and widens the range of modalities of philosophical interest to which the result might be fruitfully applied. Along the way, we also consider a semantic explanation for Fitch’s result which answers a challenge raised by Kvanvig. (shrink)

Nelson Goodman (1906–1998) is one of the leading American philosophers of the twentieth century. His well-known book Languages of Art is considered a major contribution to analytical aesthetics. While his views on particular issues have often been criticized, on the whole, he is considered to be a leading figure in twentieth-century aesthetics. Contrary to such a stance, I intend to argue that Goodman’s overall contribution to aesthetics is not as outstanding and valuable as is often maintained. Rather, I will try (...) to show that his aesthetic views are grounded on a distorted representation of the earlier aesthetic tradition, without which they lose the novelty and originality ascribed to them. Once that representation is corrected, some of Goodman’s proposals turn out to be derivative and redundant. Additionally, where they do actually diverge from the earlier tradition and might stake a claim to originality, they turn out to be simply erroneous and misconceived, and sometimes even logically flawed. To conclude, Goodman’s lofty reputation as an aesthetician certainly requires major revision. (shrink)

In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, (...) but not jointly, lack the problematic feature. (shrink)

We address the need for a model by considering two competing theories regarding the origin of life: (i) the Metabolism First theory, and (ii) the RNA World theory. We discuss two interrelated points, namely: (i) Models are valuable tools for understanding both the processes and intricacies of origin-of-life issues, and (ii) Insights from models also help us to evaluate the core objection to origin-of-life theories, called “the inefficiency objection”, which is commonly raised by proponents of both the Metabolism First theory (...) and the RNA World theory against each other. We use Simpson’s Paradox (SP) as a tool for challenging this objection. We will use models in various senses, ranging from taking them as representations of reality to treating them as theories/accounts that provide heuristics for probing reality. In this paper, we will frequently use models and theories interchangeably. Additionally, we investigate Conway’s Game of Life and contrast it with our SP-based approach to emergence-of-life issues. Finally, we discuss some of the consequences of our view. A scientific model is testable in three senses: (i) a logical sense, (ii) a nomological sense, and (iii) a current technological sense. The SP-based model is testable in the first two senses but it is not feasible to test it using current technology. (shrink)

The grue paradox, also called the new riddle of induction, posed a great challenge to the common understanding about induction. This paper shows that there is a close relation between the grue paradox and the problem of conditionals. This paper presents a general form of the grue predicate. Based on the general form, this paper argues that this kind of predicates can not be used for induction and prediction.

In this paper, I examine Nelson Goodman’s pluriworldism, understood as the claim that there exists a plurality of actual worlds. This proposal has generally been quickly dismissed in the philosophical literature. I argue that we ought to take it more seriously. As I show, many of the prima facie objections to pluriworldism may receive straightforward answers. I also examine in detail Goodman’s argument for the conclusion that there are many worlds and attempt to show how it might be supported. Eventually, (...) I discuss some underexplored challenges to pluriworldism. (shrink)

If I were to say, “Agnes does not know that it is raining, but it is,” this seems like a perfectly coherent way of describing Agnes’s epistemic position. If I were to add, “And I don’t know if it is, either,” this seems quite strange. In this chapter, we shall look at some statements that seem, in some sense, contradictory, even though it seems that these statements can express propositions that are contingently true or false. Moore thought it was paradoxical (...) that statements that can express true propositions or contingently false propositions should nevertheless seem absurd like this. If we can account for the absurdity, we shall solve Moore’s Paradox. In this chapter, we shall look at Moore’s proposals and more recent discussions of Moorean absurd thought and speech. (shrink)

I argue that Meno’s Paradox targets the type of knowledge that Socrates has been looking for earlier in the dialogue: knowledge grounded in explanatory definitions. Socrates places strict requirements on definitions and thinks we need these definitions to acquire knowledge. Meno’s challenge uses Socrates’ constraints to argue that we can neither propose definitions nor recognize them. To understand Socrates’ response to the challenge, we need to view Meno’s challenge and Socrates’ response as part of a larger disagreement about the (...) value of inquiry. (shrink)

Logical and Spiritual Reflections is a collection of six shorter philosophical works, including: Hume’s Problems with Induction; A Short Critique of Kant’s Unreason; In Defense of Aristotle’s Laws of Thought; More Meditations; Zen Judaism; No to Sodom. Of these works, the first set of three constitutes the Logical Reflections, and the second set constitutes the Spiritual Reflections. Hume’s Problems with Induction, which is intended to describe and refute some of the main doubts and objections David Hume raised with regard to (...) inductive reasoning. It replaces the so-called problem of induction with a principle of induction. David Hume’s notorious skepticism was based on errors of observation and reasoning, with regard to induction, causation, necessity, the self and freewill. These are here pointed out and critically analyzed in detail – and more accurate and logical theories are proposed. The present work also includes refutations of Hempel’s and Goodman’s alleged paradoxes of induction. A Short Critique of Kant’s Unreason, which is a brief critical analysis of some of the salient epistemological and ontological ideas and theses in Immanuel Kant’s famous Critique of Pure Reason. It shows that Kant was in no position to criticize reason, because he neither sufficiently understood its workings nor had the logical tools needed for the task. Kant’s transcendental reality, his analytic-synthetic dichotomy, his views on experience and concept formation, and on the forms of sensibility (space and time) and understanding (his twelve categories), are here all subjected to rigorous logical evaluation and found deeply flawed – and more coherent theories are proposed in their stead. In Defense of Aristotle’s Laws of Thought, which addresses, from a phenomenological standpoint, numerous modern and Buddhist objections and misconceptions regarding the basic principles of Aristotelian logic. Many people seem to be attacking Aristotle’s Laws of Thought nowadays, some coming from the West and some from the East. It is important to review and refute such ideas as they arise. More Meditations, which is a sequel to the author’s earlier work, Meditations. It proposes additional practical methods and theoretical insights relating to meditation and Buddhism. It also discusses certain often glossed over issues relating to Buddhism – notably, historicity, idolatry, messianism, importation to the West. Zen Judaism, which is a frank reflection on the tensions between reason and faith in today’s context of knowledge, and on the need to inject Zen-like meditation into Judaism. This work also treats some issues in ethics and theodicy. No to Sodom, which is an essay against homosexuality, using biological, psychological, spiritual, ethical and political arguments. (shrink)

Since it was presented in 1963, Chisholm’s paradox has attracted constant attention in the deontic logic literature, but without the emergence of any definitive solution. We claim this is due to its having no single solution. The paradox actually presents many challenges to the formalization of deontic statements, including (1) context sensitivity of unconditional oughts, (2) formalizing conditional oughts, and (3) distinguishing generic from nongeneric oughts. Using the practical interpretation of ‘ought’ as a guideline, we propose a linguistically (...) motivated logical solution to each of these problems, and explain the relation of the solution to the problem of contrary-to-duty obligations. (shrink)

We shall evaluate two strategies for motivating the view that knowledge is the norm of belief. The first draws on observations concerning belief's aim and the parallels between belief and assertion. The second appeals to observations concerning Moore's Paradox. Neither of these strategies gives us good reason to accept the knowledge account. The considerations offered in support of this account motivate only the weaker account on which truth is the fundamental norm of belief.

This paper argues that justification is accessible in the sense that one has justification to believe a proposition if and only if one has higher-order justification to believe that one has justification to believe that proposition. I argue that the accessibility of justification is required for explaining what is wrong with believing Moorean conjunctions of the form, ‘p and I do not have justification to believe that p.’.

This paper is about the relevance of attitude-ascriptions to debates about singular thought. It examines a methodology (common to early acquaintance theorists [Kaplan 1968] and recent critics of acquaintance [Hawthorne and Manley 2012], which assumes that the behaviour of ascriptions can be used to draw conclusions about singular thought. Although many theorists (e.g. [Recanati 2012]) reject this methodology, the literature lacks a detailed examination of its implications and the challenges faced by proponents and critics. I isolate an assumption of the (...) methodology, which I call the tracking assumption: that an attitude-ascription which states that s Φ's that P is true iff s has an attitude, of Φ-ing, which is an entertaining of the content P (with entertain used in a stipulated sense). I argue that the tracking assumption must be rejected, not because it has deflationary consequences, but because it leads to unstable commitments. I also show that there are independent reasons to reject it, because ordinary attitude ascriptions underdetermine even the truth-conditions of the mental-states they ascribe. However, I argue, this does not involve rejecting the claim that attitude-ascriptions express relations between agents and contents. Instead, they state different relations depending on contextual factors other than the nature of the mental-states ascribed. (shrink)

This paper updates (2017) a previously-presented* model of models, which can be used to clarify discussion and analysis in a variety of disputes and debates, since many such discussions hinge on displaying or implying models about how things are related. Knowing about models does not itself supply any new information about our world, but it might help us to recognize when and how information is being conveyed on these matters, or where possibly it is being obscured. If a claim P (...) is expressed in the context of a certain model, a disagreement about P may actually not be about whether the underlying model is accurate; it could reflect misunderstandings about the model’s assumptions or conventions. Also, in practice, constructed models are rarely fully elaborated for every detail, so misunderstandings can arise from apparent “gaps” in the model. In that case, developing and considering complementary versions of models can sometimes clarify ambiguities. Following the main analysis are several extended Case examples to illustrate the wide applicability of the models approach, for clarifying, if not necessarily “resolving”, numerous debates and issues. For example, a famous “counter example” by Nelson Goodman to a logical model proposed by Carnap is shown to be not as deal-breaking as presumed historically, if only plausible complementary models had been explored. And models sometimes presented as competing in Artificial Intelligence research— “Declarative” versus “Procedural”—can instead be viewed as good examples of “complementary” models. Also reconsidered in this light are some well-known, competing positions, by Russell, Strawson, and Kripke, in the literature regarding names, pointing, definite descriptions and “using” sentences, and so on. All these concepts are locatable within the presently proposed models analysis. Questions such as where “truth” resides (whether in sentences or in uses of sentences) are not settled in this paper; yet, practical questions about how testable claims about the world can be expressed by models are clarified. _* Original version presented at a University of Waterloo Philosophy Colloquium 1984. (shrink)

I give an interpretation according to which Meno’s paradox is an epistemic regress problem. The paradox is an argument for skepticism assuming that (1) acquired knowledge about an object X requires prior knowledge about what X is and (2) any knowledge must be acquired. (1) is a principle about having reasons for knowledge and about the epistemic priority of knowledge about what X is. (1) and (2) jointly imply a regress-generating principle which implies that knowledge always requires an (...) infinite sequence of known reasons. Plato’s response to the problem is to accept (1) but reject (2): some knowledge is innate. He argues from this to the conclusion that the soul is immortal. This argument can be understood as a response to an Eleatic problem about the possibility of coming into being that turns on a regress-generating causal principle analogous to the regress-generating principle presupposed by Meno’s paradox. (shrink)

The Torah lays out a rich idea of God’s governance in the Scroll of Esther: Circumstance lays the warp, but human choices weave the woof of destiny. God remains unseen. Delegation of agency, including human freedom, is implicit in the act of creation: God does not clutch efficacy jealously to his breast. Biblically, God acts through nature, making the elements his servitors. Miracles do not violate God’s covenant with nature. Maimonides, following rabbinic homilies, finds them embedded in that covenant. Divine (...) agency is clearest today in evolution and its special case, the emergence of autonomy and the rise of consciousness and personhood. (shrink)

Moore’s Paradox is a test case for any formal theory of belief. In Knowledge and Belief, Hintikka developed a multimodal logic for statements that express sentences containing the epistemic notions of knowledge and belief. His account purports to offer an explanation of the paradox. In this paper I argue that Hintikka’s interpretation of one of the doxastic operators is philosophically problematic and leads to an unnecessarily strong logical system. I offer a weaker alternative that captures in a more (...) accurate way our logical intuitions about the notion of belief without sacrificing the possibility of providing an explanation for problematic cases such as Moore’s Paradox. (shrink)

An important suggestion of objective Bayesians is that the maximum entropy principle can replace a principle which is known to get into paradoxical difficulties: the principle of indifference. No one has previously determined whether the maximum entropy principle is better able to solve Bertrand’s chord paradox than the principle of indifference. In this paper I show that it is not. Additionally, the course of the analysis brings to light a new paradox, a revenge paradox of the chords, (...) that is unique to the maximum entropy principle. (shrink)

Expressivists explain the expression relation which obtains between sincere moral assertion and the conative or affective attitude thereby expressed by appeal to the relation which obtains between sincere assertion and belief. In fact, they often explicitly take the relation between moral assertion and their favored conative or affective attitude to be exactly the same as the relation between assertion and the belief thereby expressed. If this is correct, then we can use the identity of the expression relation in the two (...) cases to test the expressivist account as a descriptive or hermeneutic account of moral discourse. I formulate one such test, drawing on a standard explanation of Moore's paradox. I show that if expressivism is correct as a descriptive account of moral discourse, then we should expect versions of Moore's paradox where we explicitly deny that we possess certain affective or conative attitudes. I then argue that the constructions that mirror Moore's paradox are not incoherent. It follows that expressivism is either incorrect as a hermeneutic account of moral discourse or that the expression relation which holds between sincere moral assertion and affective or conative attitudes is not identical to the relation which holds between sincere non-moral assertion and belief. A number of objections are canvassed and rejected. (shrink)

The principle of indifference is supposed to suffice for the rational assignation of probabilities to possibilities. Bertrand advances a probability problem, now known as his paradox, to which the principle is supposed to apply; yet, just because the problem is ill‐posed in a technical sense, applying it leads to a contradiction. Examining an ambiguity in the notion of an ill‐posed problem shows that there are precisely two strategies for resolving the paradox: the distinction strategy and the well‐posing strategy. (...) The main contenders for resolving the paradox, Marinoff and Jaynes, offer solutions which exemplify these two strategies. I show that Marinoff’s attempt at the distinction strategy fails, and I offer a general refutation of this strategy. The situation for the well‐posing strategy is more complex. Careful formulation of the paradox within measure theory shows that one of Bertrand’s original three options can be ruled out but also shows that piecemeal attempts at the well‐posing strategy will not succeed. What is required is an appeal to general principle. I show that Jaynes’s use of such a principle, the symmetry requirement, fails to resolve the paradox; that a notion of metaindifference also fails; and that, while the well‐posing strategy may not be conclusively refutable, there is no reason to think that it can succeed. So the current situation is this. The failure of Marinoff’s and Jaynes’s solutions means that the paradox remains unresolved, and of the only two strategies for resolution, one is refuted and we have no reason to think the other will succeed. Consequently, Bertrand’s paradox continues to stand in refutation of the principle of indifference. (shrink)

Although at first glance, “facts” are the paradigms of straightforwardness, something about facts seems to invite perpetual controversy and dichotomizing. Innumerable bifurcations on the topic have included "Facts vs. Theories”, “Facts vs. Appearance”, "Facts vs. Values", ... and, popular nowadays, "(Real)Facts vs. Fake Facts". This paper most aligns with the facts vs. theories model, so far as whatever facts are, theories seem to be constructed stories that are necessary for connecting and interpreting the facts. Yet the boundary between the two (...) is fluid and fuzzy: Fact in one context is theory in another, depending on what is being accepted or contested at the time. This paper’s views are compatible with—but neutral on the plausibility of having—an optimism like Peirce’s that scientific inquiry may nonetheless converge towards a consensus. To illustrate the challenges of finding “straightforward” facts, the paper includes a case example, related to research on possible health effects of exposure to electromagnetic-field radiation (EMF). _ The source paper for this 2018 update was originally presented at the University of Waterloo 30th Anniversary Philosophy Conference, 1993. (shrink)

It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what (...) was perceived by classical philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the co-incidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato’s Theory of Forms and Aristotle’s metaphysics and logic. Plato’s and Aristotle’s systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a ‘principle of contradiction’ is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing “space” as the seat of stability, and “time” as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion ‘separable system’, related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of ‘non-locality’ as related to it, indicating the need to re-think the notions system, entity, as well as the implications of the operation ‘measurement’, which is seen here as an application of classical logic (including its ontological consequences) on the material world. (shrink)

According to the “paradox of knowability”, the moderate thesis that all truths are knowable – ... – implies the seemingly preposterous claim that all truths are actually known – ... –, i.e. that we are omniscient. If Fitch’s argument were successful, it would amount to a knockdown rebuttal of anti-realism by reductio. In the paper I defend the nowadays rather neglected strategy of intuitionistic revisionism. Employing only intuitionistically acceptable rules of inference, the conclusion of the argument is, firstly, not (...) ..., but .... Secondly, even if there were an intuitionistically acceptable proof of ..., i.e. an argument based on a different set of premises, the conclusion would have to be interpreted in accordance with Heyting semantics, and read in this way, the apparently preposterous conclusion would be true on conceptual grounds and acceptable even from a realist point of view. Fitch’s argument, understood as an immanent critique of verificationism, fails because in a debate dealing with the justification of deduction there can be no interpreted formal language on which realists and anti-realists could agree. Thus, the underlying problem is that a satisfactory solution to the “problem of shared content” is not available. I conclude with some remarks on the proposals by J. Salerno and N. Tennant to reconstruct certain arguments in the debate on anti-realism by establishing aporias. (shrink)

Zeno’s paradoxes of motion, allegedly denying motion, have been conceived to reinforce the Parmenidean vision of an immutable world. The aim of this article is to demonstrate that these famous logical paradoxes should be seen instead as paradoxes of immobility. From this new point of view, motion is therefore no longer logically problematic, while immobility is. This is convenient since it is easy to conceive that immobility can actually conceal motion, and thus the proposition “immobility is mere illusion of the (...) senses” is much more credible than the reverse thesis supported by Parmenides. Moreover, this proposition is also supported by modern depiction of material bodies: the existence of a ceaseless random motion of atoms—the ‘thermal agitation’—in the scope of contemporary atomic theory, can offer a rational explanation of this ‘illusion of immobility’. Our new approach to Zeno’s paradoxes therefore leads to presenting the novel concept of ‘impermobility’, which we think is a more adequate description of physical reality. (shrink)

Philosophy of science is seen by most as a meta-discipline – one that takes science as its subject matter, and seeks to acquire knowledge and understanding about science without in any way affecting, or contributing to, science itself. Karl Popper’s approach is very different. His first love is natural philosophy or, as he would put it, cosmology. This intermingles cosmology and the rest of natural science with epistemology, methodology and metaphysics. Paradoxically, however, one of his best known contributions, his proposed (...) solution to the problem of demarcation, helps to maintain the gulf that separates science from metaphysics, thus fragmenting cosmology into falsifiable science on the one hand, untestable philosophy on the other. This has damaging repercussions for a number of issues Popper tackles, from the problem of induction to simplicity of theory and quantum theory. But his proposed solution to the demarcation problem is untenable. Metaphysical assumptions are an integral part of scientific knowledge, inherent in the persistent acceptance of unified theories against the evidence. Once this is appreciated, it becomes obvious that natural philosophy, a synthesis of science and philosophy, is both more rigorous and of greater intellectual value than the two dissociated components we have today. What Popper sought for could come to full fruition. Problems that Popper tackled, from the problem of induction, to the problem of unity of theory, problems of quantum theory, and problems concerning the scope and limits of physics, all receive more adequate resolution within the new, fully-fledged natural philosophy. (shrink)

This paper takes up the challenge which Carnap poses in his Aufbau: to make of it a basis for continued epistemological research. I try to close some gaps in Carnap’s original presentation and to make at least the first few steps of his constructional outline more accessible to the modern reader. Particularly emphasized is Carnap’s implicit recognition that, to be effective, “structural” models of epistemology (using logical symbols) must be complemented with “procedural” models (his “fictitious operations”). The paper shows how (...) a procedural model, a computer program,can “bypass” Nelson Goodman’s counter example to Carnap’s logical construction of “similarity circles”. (shrink)