Hume: Induction

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)

Neste texto inrodutório, apresento brevemente o que normalmente se entende pelo velho problema da indução e, em seguida, apresento um pouco mais detidamente, acentuando as diferenças e semelhanças, o novo enigma da indução.

This is partly fictional. It is chiefly a reconstruction (not always faithful) of Hume’s fundamental uses of notions of similarity, mostly based on Enquiry. It is the first part (out of four) of a monograph on the evolution of similarity toolmaking. Histories of doctrines are common in our discipline, not so for histories of tools; this is what it’s about. What’s disturbing: I write as if I were talking about the customs and beliefs of ancient tribes instead of real philosophers. (...) Advantages: helps focus on what similarity tools are apt to, I don’t have to worry about my Hume being merely MY Hume; more fun. Here is the thematic layout: 1.1: (very fictional) methodological introduction; page 2. 1.2: on the origin of ideas + missing shade of blue; p. 4. 1.3: the Xenophobia model; p. 12. 1.4: case studies of cognitive trickery; p. 16 : 1.4.1: arguments from experience; p. 17. 1.4.2: the idea of necessary connection; p. 21. 1.4.3: abstract and very general ideas; p. 23. 1.5: conceptual distinctions between used similarity tools and a few comments; p. 29. (shrink)

It is usually accepted that deductions are non-informative and monotonic, inductions are informative and nonmonotonic, abductions create hypotheses but are epistemically irrelevant, and both deductions and inductions can’t provide new insights. In this article, I attempt to provide a more cohesive view of the subject with the following hypotheses: (1) the paradigmatic examples of deductions, such as modus ponens and hypothetical syllogism, are not inferential forms, but coherence requirements for inferences; (2) since any reasoner aims to be coherent, any inference (...) must be deductive; (3) a coherent inference is an intuitive process where the premises should be taken as sufficient evidence for the conclusion, which on its turn should be viewed as necessary evidence for the premises in some modal range; (4) inductions, properly understood, are abductions, but there are no abductions beyond the fact that in any inference the conclusion should be regarded as necessary evidence for the premises; (5) monotonicity is not only compatible with the retraction of past inferences given new information, but it is a requirement for it; (6) this explanation of inferences holds true for discovery processes, predictions and trivial inferences. (shrink)

Hume’s argument against believing the testimony of miracles is the most influential treatment of the topic, but there is not yet a consensus on how to interpret his argument. Two arguments are attributed to him. First, Hume seems to start with the infrequency of miracles and uses this to infer that the testimony of a miracle is exceedingly unlikely, and this then creates strong but defeasible evidence against the testimony of any miracle. Second, perhaps Hume takes the constancy of our (...) experience of the laws of nature as decisive or indefeasible evidence against the testimony of any miracle. I explain the basis for each of these interpretations of Hume’s argument, and then develop a novel criticism of his view: namely, any inductive inference depends on the relevant similarity between the observed and the unobserved, but we may have reason for thinking that purported miracles are not relevantly similar, and thus our past experience cannot be used as reliable evidence about the testimony of (some) miracles. (shrink)

The subject of this essay is the classical problem of induction, which is sometimes attributed to David Hume and called “the Humean Problem of Induction.” Here, I examine a certain sort of Neo-Aristotelian solution to the problem, which appeals to the concept of natural kinds in its response to the inductive skeptic. This position is most notably represented by Howard Sankey and Marc Lange. The purpose of this paper is partly destructive and partly constructive. I raise two questions. The first (...) is: Are the natural kind solutions to the problem successful? The first thesis of this paper is that they are not, and I will show how and why they fail. And the second question I raise here is: Is there nonetheless some alternative Neo-Aristotelian solution to the problem which is successful and can overcome the shortcomings endemic to the Sankey-Lange account? The second thesis is that there is, and I’ll attempt to sketch one. My stance here may be summarized by saying that, while I agree with Sankey and Lange that the problem of induction can be adequately resolved, and while I am on the whole sympathetic with the Aristotelian spirit of their account, I am, for all that, dissatisfied with the letter of them. Nothing short of a more thoroughgoing Aristotelianism about the epistemology of induction will do. (shrink)

En este artículo se sostiene la siguiente hipótesis: si una hipótesis tiene valor epistémico para Hume, este valor tiene que provenir de la intuición. Para ello se consideran las tres posibles fuentes de conocimiento en su pensamiento: la demostración, la experiencia y la intuición. Considerando que Hume presenta su doctrina de la creencia como una hipótesis, se argumenta que el valor epistémico de las hipótesis no puede provenir de la demostración ni de la experiencia y, por tanto, o las hipótesis (...) carecen de valor epistémico o su valor epistémico proviene de la intuición. Para sostener la hipótesis propuesta se ofrece un análisis de la evidencia textual sobre la hipótesis y la intuición a la luz de la literatura disponible sobre el tema. (shrink)

Gözlemlenenlerden gözlemlen(e)meyenlere diğer bir deyişle genel yasalara ulaşma imkânı veren çıkarım yöntemi olarak tümevarımsal ya da endüktif akıl yürütmenin rasyonel olarak temellendirilmesinin imkanına yönelik soruşturma tarih içerisinde tümevarım sorunu ya da endüksiyon problemi olarak tezahür etmiştir. Bu sorunun temel argümanı tarihsel okumalara baktığımızda İskoç ampirist filozof David Hume tarafından öne sürülmüştür. Hume, tümevarımsal çıkarımlar temelinde, gözlenmeyen meseleler hakkındaki inançlarımıza hangi gerekçelerle ulaştığımızı soruşturmaktadır. Hume soruşturmasının sonucunda gözlemlenenden gözlemlen(e)meyen durumlara ilişkin yapılan olgu meseleleri ile ilgili bütün tümevarımsal akıl yürütmelerin dolaylı ya (...) da dolaysız olarak nedensellik ilişkisine ve bu ilişkinin temelinde yer alan doğanın düzenliliği ilkesi ya da “gelecek her zaman geçmişe benzer” önermesine dayandığını ifade ederek bütün tümevarımsal akıl yürütmelerde ortak olan geleceğin her zaman geçmişe benzeyeceği ifadesinin rasyonel olarak temellendirilmesinin mümkün olmadığını belirtmektedir. Bu bağlamda, çalışmada tümevarımsal akıl yürütme sonucunda ulaşılan sonuca inanmanın hiçbir rasyonel temelinin olamayacağı yönündeki Hume’un görüşü argüman formunda yeniden yapılandırılarak ortaya konulacaktır. (shrink)

Interpreters of Hume on causation consider that an advantage of the ‘quasi-realist’ reading is that it does not commit him to scepticism or to an error theory about causal reasoning. It is unique to quasi-realism that it maintains this positive epistemic result together with a rejection of metaphysical realism about causation: the quasi-realist supplies an appropriate semantic theory in order to justify the practice of talking ‘as if’ there were causal powers in the world. In this paper, I problematise the (...) quasi-realist reading of Hume on causation by showing how quasi-realism does not speak to inductive scepticism. I also offer evidence that Hume takes inductive scepticism to result from his theory of causation, and that his scepticism is tied to his rejection of metaphysical causal realism. (shrink)

Nesse artigo, apresento a crítica de Hume de seu Tratado da natureza humana contra a garantia de inferência de causalidade a partir de argumentos de cunho psicológico e de um argumento lógico. Em seguida, são esclarecidos os detalhes da crítica que Popper dirige contra Hume em seu artigo Ciência: Conjecturas e refutações, no qual foca em uma solução do Problema de Hume – considerado como uma faceta do Problema da Demarcação. Explicarei que Popper defende que a ciência avança sempre da (...) teoria em direção à observação – e não o contrário – e que uma atitude crítica em relação às inferências de causalidade pode nos livrar de um dogmatismo irracional. Ainda assim, sustento que Popper está mais para um reformador do pensamento de Hume do que para um demolidor. (shrink)

There is a tradition perhaps as old as philosophy itself which sees the rationality of man – and in particular, the rationality of the philosopher - as both his essential and his redeeming characteristic; it can not unfairly be said that the discipline of philosophy at least is characterised by its dependence on reason. In this context, the philosophy of David Hume presents something of a stark challenge: Although interpretations vary as to the extent and nature of his scepticism, one (...) of the themes of his work is the limits and imperfections of human reason and the sceptical concerns this engenders. On Hume's system, reason is not the overlord of the imagination but at least in part subordinate to it, and can discover little or nothing without recourse to experience. -/- My aim here is to pinpoint the true nature of Hume's scepticism regarding reason, drawing chiefly on the Treatise but also to a lesser extent the Enquiry. After a brief overview of his project in the Treatise in section 1, I go on to give an account of Hume's conception of reason or the understanding, and the epistemological distinction between demonstrative and probable reasoning, in section 2. In section 3 I examine Hume's famous argument concerning induction, arguing that to read Hume as a sceptic regarding inference is a mistake and that to say induction is grounded in principles of the imagination is not to say that it is therefore irrational. In section 4 I examine the argument of Treatise 1.4.1, 'Of scepticism with regard to reason', and in section 5 the 'dangerous dilemma' to which it leads Hume in 1.4.7, arguing that whilst his treatment of the issues it raises is somewhat unsatisfactory in this section of the Treatise a better solution can be fashioned by appealing to a distinction between the general and the trivial properties of the imagination drawn elsewhere in both the Treatise and the Enquiry. Then in section 6 I conclude by offering my own attempt at characterising the extent of Hume's scepticism regarding reason, arguing that his “mitigated” scepticism is a scepticism about knowledge but not about belief, and that its chief aim is to ensure that we philosophise only on those subjects which are suitable for enquiry given the limits and frailties of our faculties; the “reflections of common life, methodized and corrected” (Enquiry 12.25, p.208) rather than “divinity” or “school metaphysics” (Enquiry 12.34, p.211). (shrink)

Disputants in the debate regarding whether Hume's argument on induction is descriptive or normative have by and large ignored Hume’s positive argument (that custom is what determines inferences to the unobserved), largely confining themselves to intricate debates within the negative argument (that inferences to the unobserved are not founded on reason). I believe that this is a mistake, for I think Hume’s positive argument to have significant implications for the interpretation of his negative argument. In this paper, I will argue (...) that Hume’s positive and negative arguments should be read as addressing the same issues, whether normative or causal. I will then focus on the Enquiry version of Hume’s positive argument, arguing that it carries a significant normative conclusion: there, Hume argues that custom plays a normative role in justifying our inductive inferences. Given that Hume’s positive argument should be read as addressing the same issues as his negative argument, we should correspondingly read Hume’s negative argument in the Enquiry as having a normative conclusion. (shrink)

In this paper I adduce a new argument in support of the claim that IBE is an autonomous form of inference, based on a familiar, yet surprisingly, under-discussed, problem for Hume’s theory of induction. I then use some insights thereby gleaned to argue for the claim that induction is really IBE, and draw some normative conclusions.

This paper offers and account of the "system" of probable reasoning presented in Hume's Treatise and first Enquiry. The system is sceptical because it takes our beliefs to be the product of naturally occurring psychological mechanisms rather than logically sound judgment, and because it declares those beliefs to be ultimately unjustifiable. This paper explains how Hume was nonetheless able to provide for a logic of probable reasoning, grounded on natural, but unjustifiable beliefs.

In this paper, I discuss Eino Kaila's (1890-1958) understanding of David Hume. Kaila was one of the leading Finnish philosophers of the 20th century and a correspondent of the Vienna Circle. He introduced logical empiricism into Finland and taught Georg Henrik von Wright. Final draft.

It was Hume's concept of knowledge that marked Masaryk's philosophy more than influential Kant. Masaryk devoted Hume his inaugural lecture The Probability Calculus and Hume's Scepticism at Prague University in 1882. He tried to face his scepticism concerning causation and induction by a formula P = n: or P = : where P means the increasing probability that an event that had happened n times in the past will happen again. Hume stresses that there is an essential difference between probability (...) and certainty, and we have no logical reason to presuppose that the past experience is legitimate for expectation that the future will resemble to the past. Only our belief, not knowledge, leads us to that. Although Masaryk did not accept Hume's scepticism, he had deep understanding for his way of thinking. Reflection of Hume's influence on Masaryk in Czech philosophy is unsatisfactory, which is stated in this article. (shrink)

Where does the necessity that seems to accompany causal inferences come from? “Why [do] we conclude that … particular causes must necessarily have such particular effects?” In 1.3.6 of the Treatise, Hume entertains the possibility that this necessity is a function of reason. However, he eventually dismisses this possibility, where this dismissal consists of Hume’s “negative” argument concerning induction. This argument has received, and continues to receive, a tremendous amount of attention. How could causal inferences be justified if they are (...) not justified by reason? If we believe that p causes q, isn’t it reason that allows us to conclude q when we see p with some assurance, i.e. with some necessity? (shrink)

In a recent Philosophy of Science article Gerhard Schurz proposes meta-inductivistic prediction strategies as a new approach to Hume's. This comment examines the limitations of Schurz's approach. It can be proven that the meta-inductivist approach does not work any more if the meta-inductivists have to face an infinite number of alternative predictors. With his limitation it remains doubtful whether the meta-inductivist can provide a full solution to the problem of induction.

Meu objetivo neste artigo é destacar algumas das ideias centrais defendidas por Hume e, a fim de caracterizar a natureza de sua filosofia, contrapor duas interpretações frequentes de sua obra: a interpretação cética e interpretação naturalista. A fim de apontar as principais razões que estão por trás dessas duas interpretações que tentam apreender a natureza da filosofia de Hume, procuro abordar inicialmente alguns dos princípios centrais da teoria humeana e, em seguida, especialmente sua análise das inferências causais. No final, argumento (...) que o ceticismo e o naturalismo de Hume não são incompatíveis. Ao contrário, devem ser entendidos como duas faces de uma mesma filosofia. (shrink)

I outline Hume’s views about conceivability evidence. Then I critically scrutinize two threats to conceivability-based modal epistemology. Both arise from Hume’s criticism of claims to knowing necessary causal relationships: Firstly, a sceptical stance towards causal necessity may carry over to necessity claims in general. Secondly, since – according to a sceptical realist reading – Hume grants the eventuality of causal powers grounded in essential features of objects, conceivability-based claims to comprehensive metaphysical possibilities seem endangered. I argue that although normal conceivability-based (...) claims are defeasible, they are prima facie vindicated. (shrink)

In “The Constraints of Hume’s Naturalism” Barry Stroud takes on the task of looking at Hume’s negative and positive accounts of induction in conjunction. Stroud goes about doing this so that we might walk away with “a more general lesson about naturalism, at least when it is indulged in for philosophical purposes”. Given the boldness of Stroud’s quote from above there should be some explicit talk of this general lesson about naturalism outside of Hume’s, but there is none that is (...) readily apparent. If a more general and philosophically motivated lesson about naturalism is to be gleaned from Stroud’s investigation of Hume, then we should take this to be a lesson implicit in Stroud and not Hume. Hence I shall argue that Stroud tacitly endorses the skeptical conclusions of David Hume about naturalism in general when indulged for philosophical purposes. (shrink)

Alice encounters at least three distinct problems in her struggles to understand and navigate Wonderland. The first arises when she attempts to predict what will happen in Wonderland based on what she has experienced outside of Wonderland. In many cases, this proves difficult -- she fails to predict that babies might turn into pigs, that a grin could survive without a cat or that playing cards could hold criminal trials. Alice's second problem involves her efforts to figure out the basic (...) nature of Wonderland. So, for example, there is nothing Alice could observe that would allow her to prove whether Wonderland is simply a dream. The final problem is manifested by Alice's attempts to understand what the various residents of Wonderland mean when they speak to her. In Wonderland, "mock turtles" are real creatures and people go places with a "porpoise" (and not a purpose). All three of these problems concern Alice's attempts to infer information about unobserved events or objects from those she has observed. In philosophical terms, they all involve *induction*. -/- In this essay, I will show how Alice's experiences can be used to clarify the relation between three more general problems related to induction. The first problem, which concerns our justification for beliefs about the future, is an instance of David Hume's classic *problem of induction*. Most of us believe that rabbits will not start talking tomorrow -- the problem of induction challenges us to justify this belief. Even if we manage to solve Hume's puzzle, however, we are left with what W.V.O. Quine calls the problems of *underdetermination *and *indeterminacy.* The former problem asks us to explain how we can determine *what the world is really like *based on *everything that could be observed about the world. *So, for example, it seems plausible that nothing that Alice could observe would allow her to determine whether eating mushrooms causes her to grow or the rest of the world to shrink. The latter problem, which might remain even if resolve the first two, casts doubt on our capacity to determine *what a certain person means *based on *which words that person uses.* This problem is epitomized in the Queen's interpretation of the Knave's letter. The obstacles that Alice faces in getting around Wonderland are thus, in an important sense, the same types of obstacles we face in our own attempts to understand the world. Her successes and failures should therefore be of real interest. (shrink)

This article considers two arguments that purport to show that inductive reasoning is unjustified: the argument adduced by Sextus Empiricus and the (better known and more formidable) argument given by Hume in the Treatise. While Sextus’ argument can quite easily be rebutted, a close examination of the premises of Hume’s argument shows that they are seemingly cogent. Because the sceptical claim is very unintuitive, the sceptical argument constitutes a paradox. And since attributions of justification are theoretical, and the claim that (...) they are never (or seldom) true isn’t preposterous, the correct response to the paradox may well be to admit that the sceptic has exposed our error in making them. (shrink)

In 1947 Donald Cary Williams claimed in The Ground of Induction to have solved the Humean problem of induction, by means of an adaptation of reasoning first advanced by Bernoulli in 1713. Later on David Stove defended and improved upon Williams’ argument in The Rational- ity of Induction (1986). We call this proposed solution of induction the ‘Williams-Stove sampling thesis’. There has been no lack of objections raised to the sampling thesis, and it has not been widely accepted. In our (...) opinion, though, none of these objections has the slightest force, and, moreover, the sampling thesis is undoubtedly true. What we will argue in this paper is that one particular objection that has been raised on numerous occasions is misguided. This concerns the randomness of the sample on which the inductive extrapolation is based. (shrink)

: In this paper I argue that Hume's famous discussion of probability and induction, as originally presented in the Treatise, is significantly motivated by irreligious objectives. A particular target of Hume's arguments is Joseph Butler's Analogy of Religion. In the Analogy Butler intends to persuade his readers of both the credibility and practical importance of the doctrine of a future state of rewards and punishments. The argument that he advances relies on probable reasoning and proceeds on the assumption that our (...) past experience in this life serves as a reliable and effective guide for our expectations concerning a future state. In the relevant sections of the Treatise Hume aims to discredit this religious argument and the practical objectives associated with it. (shrink)

An examination of the role played by general rules in Hume's positive (nonskeptical) epistemology. General rules for Hume are roughly just general beliefs. The difference between justified and unjustified belief is a matter of the influence of good versus bad general rules, the good general rules being the "extensive" and "constant" ones.

On the basis of the distinction between logical and factual probability, epistemic justification is distinguished from logical justification of induction. It is argued that, contrary to the accepted interpretation of Hume, Hume believes that inductive inferences are epistemically legitimate and justifiable. Hence the beliefs arrived at via (correct) inductive inferences are rational beliefs. According to this interpretation, Hume is not a radical skeptic about induction.

David Hume's famous riddle of induction implies a second problem related to the question of whether the laws and principles of nature might change in the course of time. Claims have been made that modern developments in physics and astrophysics corroborate the translational invariance of the laws of physics in time. However, the appearance of a new general principle of nature, which might not be derivable from the known laws of physics, or that might actually be a non-physical one (this (...) means completely independent of physical science) supports the notion that the course of nature can change in time. Here it is argued that natural selection satisfies the criteria that identify a general principle of nature which so far, appears to be non-derivable from the known laws of physics and therefore, it is likely that it arose in the course of time, thus leaving open again the quest for a true solution to Hume's second problem. (shrink)

In this paper I raise concerns that I have with what I perceive to be as a complete lack of warrant for Hume’s assertion that there are only two types of reasoning – demonstrative and probable. (Hume’s fork) What I leave for others to decide is whether this lack of warrant therefore successfully undercuts Hume’s argument for the Problem of Induction.

The word ‘induction’ is derived from Cicero’s ‘inductio’, itself a translation of Aristotle’s ‘epagôgê’. In its traditional sense this denotes the inference of general laws from particular instances, but within modern philosophy it has usually been understood in a related but broader sense, covering any non-demonstrative reasoning that is founded on experience. As such it encompasses reasoning from observed to unobserved, both inference of general laws and of further particular instances, but it excludes those cases of reasoning in which the (...) conclusion is logically implied by the premises, such as induction by complete enumeration. (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)