The parallel between biological evolution and conceptual or ‘epistemic’ evolution can be seen as either literal or analogical. The literal version of evolutionary epistemology deeds biological evolution as the main cause of the growth of knowledge. On this view, called the ‘evolution of cognitive mechanic programs’, by Bradie (1986) and the ‘Darwinian approach to epistemology’ by Ruse (1986), that growth of knowledge occurs through blind variation and selective retention because biological natural selection itself is the cause of epistemic variation and selection. The most plausible version of the literal view does not hold that all human beliefs are innate but rather than the mental mechanisms that guide the acquisitions of non-innate beliefs are themselves innately and the result of biological natural selection. Ruse, (1986) demands of a version of literal evolutionary epistemology that he links to sociolology (Rescher, 1990).
On the analogical version of evolutionary epistemology, called the ‘evolution of theory’s program’, by Bradie (1986). The ‘Spenserians approach’ (after the nineteenth century philosopher Herbert Spencer) by Ruse (1986), the development of human knowledge is governed by a process analogous to biological natural selection, rather than by an instance of the mechanism itself. This version of evolutionary epistemology, introduced and elaborated by Donald Campbell (1974) as well as Karl Popper, sees the [partial] fit between theories and the world as explained by a mental process of trial and error known as epistemic natural selection.
Both versions of evolutionary epistemology are usually taken to be types of naturalized epistemology, because both take some empirical facts as a starting point for their epistemological project. The literal version of evolutionary epistemology begins by accepting evolutionary theory and a materialist approach to the mind and, from these, constructs an account of knowledge and its developments. In contrast, the metaphorical version does not require the truth of biological evolution: It simply draws on biological evolution as a source for the model of natural selection. For this version of evolutionary epistemology to be true, the model of natural selection need only apply to the growth of knowledge, not to the origin and development of species. Crudely put, evolutionary epistemology of the analogical sort could still be true even if Creationism is the correct theory of the origin of species.
Although they do not begin by assuming evolutionary theory, most analogical evolutionary epistemologists are naturalized epistemologists as well, their empirical assumptions, least of mention, implicitly come from psychology and cognitive science, not evolutionary theory. Sometimes, however, evolutionary epistemology is characterized in a seemingly non-naturalistic fashion. Campbell (1974) says that ‘if one is expanding knowledge beyond what one knows, one has no choice but to explore without the benefit of wisdom’, i.e., blindly. This, Campbell admits, makes evolutionary epistemology close to being a tautology (and so not naturalistic). Evolutionary epistemology does assert the analytic claim that when expanding one’s knowledge beyond what one knows, one must precessed to something that is already known, but, more interestingly, it also makes the synthetic claim that when expanding one’s knowledge beyond what one knows, one must proceed by blind variation and selective retention. This claim is synthetic because it can be empirically falsified. The central claim of evolutionary epistemology is synthetic, not analytic. If the central contradictory, which they are not. Campbell is right that evolutionary epistemology does have the analytic feature he mentions, but he is wrong to think that this is a distinguishing feature, since any plausible epistemology has the same analytic feature (Skagestad, 1978).
Two extraordinary issues lie to awaken the literature that involves questions about ‘realism’, i.e., What metaphysical commitment does an evolutionary epistemologist have to make? Progress, i.e., according to evolutionary epistemology, does knowledge develop toward a goal? With respect to realism, many evolutionary epistemologists endorse that is called ‘hypothetical realism’, a view that combines a version of epistemological ‘scepticism’ and tentative acceptance of metaphysical realism. With respect to progress, the problem is that biological evolution is not goal-directed, but the growth of human knowledge seems to be. Campbell (1974) worries about the potential dis-analogy here but is willing to bite the stone of conscience and admit that epistemic evolution progress toward a goal (truth) while biologic evolution does not. Many another has argued that evolutionary epistemologists must give up the ‘truth-topic’ sense of progress because a natural selection model is in essence, is non-teleological, as an alternative, following Kuhn (1970), and embraced in the accompaniment with evolutionary epistemology.
Among the most frequent and serious criticisms levelled against evolutionary epistemology is that the analogical version of the view is false because epistemic variation is not blind (Skagestad, 1978, 613-16, and Ruse, 1986, ch.2 (. Stein and Lipton (1990) have argued, however, that this objection fails because, while epistemic variation is not random, its constraints come from heuristics that, for the most part, are selective retention. Further, Stein and Lipton come to the conclusion that heuristics are analogous to biological pre-adaptions, evolutionary pre-biological pre-adaptions, evolutionary cursors, such as a half-wing, a precursor to a wing, which have some function other than the function of their descendable structures: The function of descendable structures, the function of their descendable character embodied to its structural foundations, is that of the guidelines of epistemic variation is, on this view, not the source of disanalogy, but the source of a more articulated account of the analology.
Many evolutionary epistemologists try to combine the literal and the analogical versions (Bradie, 1986, and Stein and Lipton, 1990), saying that those beliefs and cognitive mechanisms, which are innate results from natural selection of the biological sort and those that are innate results from natural selection of the epistemic sort. This is reasonable as long as the two parts of this hybrid view are kept distinct. An analogical version of evolutionary epistemology with biological variation as its only source of blondeness would be a null theory: This would be the case if all our beliefs are innate or if our non-innate beliefs are not the result of blind variation. An appeal to the legitimate way to produce a hybrid version of evolutionary epistemology since doing so trivializes the theory. For similar reasons, such an appeal will not save an analogical version of evolutionary epistemology from arguments to the effect that epistemic variation is blind (Stein and Lipton, 1990).
Although it is a new approach to theory of knowledge, evolutionary epistemology has attracted much attention, primarily because it represents a serious attempt to flesh out a naturalized epistemology by drawing on several disciplines. In science is relevant to understanding the nature and development of knowledge, then evolutionary theory is among the disciplines worth a look. Insofar as evolutionary epistemology looks there, it is an interesting and potentially fruitful epistemological programme.
What makes a belief justified and what makes a true belief knowledge? Thinking that whether a belief deserves one of these appraisals is natural depends on what caused the depicted branch of knowledge to have the belief. In recent decades a number of epistemologists have pursued this plausible idea with a variety of specific proposals. Some causal theories of knowledge have it that a true belief that ‘p’ is knowledge just in case it has the right causal connection to the fact that ‘p’. Such a criterion can be applied only to cases where the fact that ‘p’ is a sort that can enter into causal relations, as this seems to exclude mathematically and the necessary facts and perhaps any fact expressed by a universal generalization, and proponents of this sort of criterion have usually supposed that it is limited to perceptual representations where knowledge of particular facts about subjects’ environments.
For example, Armstrong (1973), predetermined that a position held by a belief in the form ‘This perceived object is ‘F’ is [non-inferential] knowledge if and only if the belief is a completely reliable sign that the perceived object is ‘F’, that is, the fact that the object is ‘F’ contributed to causing the belief and its doing so depended on properties of the believer such that the laws of nature dictated that, for any subject ‘÷’ and perceived object ‘y’, if ‘÷’ has those properties and believed that ‘y’ is ‘F’, then ‘y’ is ‘F’. (Dretske (1981) offers a rather similar account, in terms of the belief’s being caused by a signal received by the perceiver that carries the information that the object is ‘F’).
Goldman (1986) has proposed an importantly different causal criterion, namely, that a true belief is knowledge if it is produced by a type of process that is ‘globally’ and ‘locally’ reliable. Causing true beliefs is sufficiently high is globally reliable if its propensity. Local reliability has to do with whether the process would have produced a similar but false belief in certain counterfactual situations alternative to the actual situation. This way of marking off true beliefs that are knowledge does not require the fact believed to be causally related to the belief, and so it could in principle apply to knowledge of any kind of truth.
Goldman requires the global reliability of the belief-producing process for the justification of a belief, he requires it also for knowledge because justification is required for knowledge. What he requires for knowledge, but does not require for justification is local reliability. His idea is that a justified true belief is knowledge if the type of process that produced it would not have produced it in any relevant counterfactual situation in which it is false. Its purported theory of relevant alternatives can be viewed as an attempt to provide a more satisfactory response to this tension in our thinking about knowledge. It attempts to characterize knowledge in a way that preserves both our belief that knowledge is an absolute concept and our belief that we have knowledge.
According to the theory, we need to qualify rather than deny the absolute character of knowledge. We should view knowledge as absolute, reactive to certain standards (Dretske, 1981 and Cohen, 1988). That is to say, in order to know a proposition, our evidence need not eliminate all the alternatives to that preposition, rather for ‘us’, that we can know our evidence eliminates al the relevant alternatives, where the set of relevant alternatives (a proper subset of the set of all alternatives) is determined by some standard. Moreover, according to the relevant alternatives view, and the standards determining that of the alternatives is raised by the sceptic are not relevant. If this is correct, then the fact that our evidence cannot eliminate the sceptic’s alternative does not lead to a sceptical result. For knowledge requires only the elimination of the relevant alternatives, so the relevant alternative view preserves in both strands in our thinking about knowledge. Knowledge is an absolute concept, but because the absoluteness is relative to a standard, we can know many things.
The interesting thesis that counts as a causal theory of justification (in the meaning of ‘causal theory’ intended here) is that: A belief is justified in case it was produced by a type of process that is ‘globally’ reliable, that is, its propensity to produce true beliefs-that can be defined (to a good approximation) As the proportion of the beliefs it produces (or would produce) that is true is sufficiently great.
This proposal will be adequately specified only when we are told (i) how much of the causal history of a belief counts as part of the process that produced it, (ii) which of the many types to which the process belongs is the type for purposes of assessing its reliability, and (iii) relative to why the world or worlds are the reliability of the process type to be assessed the actual world, the closet worlds containing the case being considered, or something else? Let ‘us’ look at the answers suggested by Goldman, the leading proponent of a reliabilist account of justification.
(1) Goldman (1979, 1986) takes the relevant belief producing process to include only the proximate causes internal to the believer. So, for instance, when recently I believed that the telephone was ringing the process that produced the belief, for purposes of assessing reliability, includes just the causal chain of neural events from the stimulus in my ear’s inward ands other concurrent brain states on which the production of the belief depended: It does not include any events’ as the telephone, or the sound waves travelling between it and my ears, or any earlier decisions I made that were responsible for my being within hearing distance of the telephone at that time. It does seem intuitively plausible of a belief depends should be restricted to internal omnes proximate to the belief. Why? Goldman does not tell ‘us’. One answer that some philosophers might give is that it is because a belief’s being justified at a given time can depend only on facts directly accessible to the believer’s awareness at that time (for, if a believer ought to holds only beliefs that are justified, she can tell at any given time what beliefs would then be justified for her). However, this cannot be Goldman’s answer because he wishes to include in the relevantly process neural events that are not directly accessible to consciousness.
(2) Once the reliabilist has told ‘us’ how to delimit the process producing a belief, he needs to tell ‘us’ which of the many types to which it belongs is the relevant type. Coincide, for example, the process that produces your current belief that you see a book before you. One very broad type to which that process belongs would be specified by ‘coming to a belief as to something one perceives as a result of activation of the nerve endings in some of one’s sense-organs’. A constricted type, in which that unvarying processes belong would be specified by ‘coming to a belief as to what one sees as a result of activation of the nerve endings in one’s retinas’. A still narrower type would be given by inserting in the last specification a description of a particular pattern of activation of the retina’s particular cells. Which of these or other types to which the token process belongs is the relevant type for determining whether the type of process that produced your belief is reliable?
If we select a type that is too broad, as having the same degree of justification various beliefs that intuitively seem to have different degrees of justification. Thus the broadest type we specified for your belief that you see a book before you apply also to perceptual beliefs where the object seen is far away and seen only briefly is less justified. On the other hand, is we are allowed to select a type that is as narrow as we please, then we make it out that an obviously unjustified but true belief is produced by a reliable type of process. For example, suppose I see a blurred shape through the fog far in a field and unjustifiedly, but correctly, believe that it is a sheep: If we include enough details about my retinal image is specifying te type of the visual process that produced that belief, we can specify a type is likely to have only that one instanced and is therefore 100 percent reliable. Goldman conjectures (1986) that the relevant process type is ‘the narrowest type that is casually operative’. Presumably, a feature of the process producing beliefs were causally operatives in producing it just in case some alternative feature instead, but it would not have led to that belief. (We need to say ‘some’ here rather than ‘any’, because, for example, when I see an oak or pine tree, the particular ‘like-minded’ material bodies of my retinal image are casually clearly toward the operatives in producing my belief that what is seen as a tree, even though there are alternative shapes, for example, ‘pineish’ or ‘birchness’ ones, that would have produced the same belief.)
(3) Should the justification of a belief in a hypothetical, non-actual example turn on the reliability of the belief-producing process in the possible world of the example? That leads to the implausible result in that in a world run by a Cartesian demon-a powerful being who causes the other inhabitants of the world to have rich and coherent sets of perceptual and memory impressions that are all illusory the perceptual and memory beliefs of the other inhabitants are all unjustified, for they are produced by processes that are, in that world, quite unreliable. If we say instead that it is the reliability of the processes in the actual world that matters, we get the equally undesired result that if the actual world is a demon world then our perceptual and memory beliefs are all unjustified.
Goldman’s solution (1986) is that the reliability of the process types is to be gauged by their performance in ‘normal’ worlds, that is, worlds consistent with ‘our general beliefs about the world . . . ‘about the sorts of objects, events and changes that occur in it’. This gives the intuitively right results for the problem cases just considered, but indicate by inference an implausible proportion of making compensations for alternative tending toward justification. If there are people whose general beliefs about the world are very different from mine, then there may, on this account, be beliefs that I can correctly regard as justified (ones produced by processes that are reliable in what I take to be a normal world) but that they can correctly regard as not justified.
However, these questions about the specifics are dealt with, and there are reasons for questioning the basic idea that the criterion for a belief’s being justified is its being produced by a reliable process. Thus and so, doubt about the sufficiency of the reliabilist criterion is prompted by a sort of example that Goldman himself uses for another purpose. Suppose that being in brain-state ‘B’ always causes one to believe that one is in brained-state ‘B’. Here the reliability of the belief-producing process is perfect, but ‘we can readily imagine circumstances in which a person goes into grain-state ‘B’ and therefore has the belief in question, though this belief is by no means justified’ (Goldman, 1979). Doubt about the necessity of the condition arises from the possibility that one might know that one has strong justification for a certain belief and yet that knowledge is not what actually prompts one to believe. For example, I might be well aware that, having read the weather bureau’s forecast that it will be much hotter tomorrow. I have ample reason to be confident that it will be hotter tomorrow, but I irrationally refuse to believe it until Wally tells me that he feels in his joints that it will be hotter tomorrow. Here what prompts me to believe dors not justify my belief, but my belief is nevertheless justified by my knowledge of the weather bureau’s prediction and of its evidential force: I can advert to any disavowable inference that I ought not to be holding the belief. Indeed, given my justification and that there is nothing untoward about the weather bureau’s prediction, my belief, if true, can be counted knowledge. This sorts of example raises doubt whether any causal conditions, are it a reliable process or something else, is necessary for either justification or knowledge.
Philosophers and scientists alike, have often held that the simplicity or parsimony of a theory is one reason, all else being equal, to view it as true. This goes beyond the unproblematic idea that simpler theories are easier to work with and gave greater aesthetic appeal.
One theory is more parsimonious than another when it postulates fewer entities, processes, changes or explanatory principles: The simplicity of a theory depends on essentially the same consecrations, though parsimony and simplicity obviously become the same. Demanding clarification of what makes one theory simpler or more parsimonious is plausible than another before the justification of these methodological maxims can be addressed.
If we set this description problem to one side, the major normative problem is as follows: What reason is there to think that simplicity is a sign of truth? Why should we accept a simpler theory instead of its more complex rivals? Newton and Leibniz thought that the answer was to be found in a substantive fact about nature. In ‘Principia,’ Newton laid down as his first Rule of Reasoning in Philosophy that ‘nature does nothing in vain . . . ‘for Nature is pleased with simplicity and affects not the pomp of superfluous causes’. Leibniz hypothesized that the actual world obeys simple laws because God’s taste for simplicity influenced his decision about which world to actualize.
The tragedy of the Western mind, described by Koyré, is a direct consequence of the stark Cartesian division between mind and world. We discovered the ‘certain principles of physical reality’, said Descartes, ‘not by the prejudices of the senses, but by the light of reason, and which thus possess so great evidence that we cannot doubt of their truth’. Since the real, or that which actually exists external to ourselves, was in his view only that which could be represented in the quantitative terms of mathematics, Descartes concludes that all quantitative aspects of reality could be traced to the deceitfulness of the senses.
The most fundamental aspect of the Western intellectual tradition is the assumption that there is a fundamental division between the material and the immaterial world or between the realm of matter and the realm of pure mind or spirit. The metaphysical frame-work based on this assumption is known as ontological dualism. As the word dual implies, the framework is predicated on an ontology, or a conception of the nature of God or Being, that assumes reality has two distinct and separable dimensions. The concept of Being as continuous, immutable, and having a prior or separate existence from the world of change dates from the ancient Greek philosopher Parmenides. The same qualities were associated with the God of the Judeo-Christian tradition, and they were considerably amplified by the role played in theology by Platonic and Neoplatonic philosophy.
Nicolas Copernicus, Galileo, Johannes Kepler, and Isaac Newton were all inheritors of a cultural tradition in which ontological dualism was a primary article of faith. Hence the idealization of the mathematical ideal as a source of communion with God, which dates from Pythagoras, provided a metaphysical foundation for the emerging natural sciences. This explains why, the creators of classical physics believed that doing physics was a form of communion with the geometrical and mathematical form’s resident in the perfect mind of God. This view would survive in a modified form in what is now known as Einsteinian epistemology and accounts in no small part for the reluctance of many physicists to accept the epistemology associated with the Copenhagen Interpretation.
At the beginning of the nineteenth century, Pierre-Sinon LaPlace, along with a number of other French mathematicians, advanced the view that the science of mechanics constituted a complete view of nature. Since this science, by observing its epistemology, had revealed itself to be the fundamental science, the hypothesis of God was, they concluded, entirely unnecessary.
LaPlace is recognized for eliminating not only the theological component of classical physics but the ‘entire metaphysical component’ as well’. The epistemology of science requires, he said, that we proceed by inductive generalizations from observed facts to hypotheses that are ‘tested by observed conformity of the phenomena’. What was unique about LaPlace’s view of hypotheses was his insistence that we cannot attribute reality to them. Although concepts like force, mass, motion, cause, and laws are obviously present in classical physics, they exist in LaPlace’s view only as quantities. Physics is concerned, he argued, with quantities that we associate as a matter of convenience with concepts, and the truths about nature are only the quantities.
As this view of hypotheses and the truths of nature as quantities were extended in the nineteenth century to a mathematical description of phenomena like heat, light, electricity, and magnetism. LaPlace’s assumptions about the actual character of scientific truths seemed correct. This progress suggested that if we could remove all thoughts about the ‘nature of’ or the ‘source of’ phenomena, the pursuit of strictly quantitative concepts would bring us to a complete description of all aspects of physical reality. Subsequently, figures like Comte, Kirchhoff, Hertz, and Poincaré developed a program for the study of nature hat was quite different from that of the original creators of classical physics.
The seventeenth-century view of physics as a philosophy of nature or as natural philosophy was displaced by the view of physics as an autonomous science that was ‘the science of nature’. This view, which was premised on the doctrine of positivism, promised to subsume all of the nature with a mathematical analysis of entities in motion and claimed that the true understanding of nature was revealed only in the mathematical description. Since the doctrine of positivism assumes that the knowledge we call physics resides only in the mathematical formalism of physical theory, it disallows the prospect that the vision of physical reality revealed in physical theory can have any other meaning. In the history of science, the irony is that positivism, which was intended to banish metaphysical concerns from the domain of science, served to perpetuate a seventeenth-century metaphysical assumption about the relationship between physical reality and physical theory.
Epistemology since Hume and Kant has drawn back from this theological underpinning. Indeed, the very idea that nature is simple (or uniform) has come in for a critique. The view has taken hold that a preference for simple and parsimonious hypotheses is purely methodological: It is constitutive of the attitude we call ‘scientific’ and makes no substantive assumption about the way the world is.
A variety of otherwise diverse twentieth-century philosophers of science have attempted, in different ways, to flesh out this position. Two examples must suffice here: Hesse (1969) as, for summaries of other proposals. Popper (1959) holds that scientists should prefer highly falsifiable (improbable) theories: He tries to show that simpler theories are more falsifiable, also Quine (1966), in contrast, sees a virtue in theories that are highly probable, he argues for a general connection between simplicity and high probability.
Both these proposals are global. They attempt to explain why simplicity should be part of the scientific method in a way that spans all scientific subject matters. No assumption about the details of any particular scientific problem serves as a premiss in Popper’s or Quine’s arguments.
Newton and Leibniz thought that the justification of parsimony and simplicity flows from the hand of God: Popper and Quine try to justify these methodologically median of importance is without assuming anything substantive about the way the world is. In spite of these differences in approach, they have something in common. They assume that all users of parsimony and simplicity in the separate sciences can be encompassed in a single justifying argument. That recent developments in confirmation theory suggest that this assumption should be scrutinized. Good (1983) and Rosenkrantz (1977) has emphasized the role of auxiliary assumptions in mediating the connection between hypotheses and observations. Whether a hypothesis is well supported by some observations, or whether one hypothesis is better supported than another by those observations, crucially depends on empirical background assumptions about the inference problem here. The same view applies to the idea of prior probability (or, prior plausibility). In of a single hypo-physical science if chosen as an alternative to another even though they are equally supported by current observations, this must be due to an empirical background assumption.
Principles of parsimony and simplicity mediate the epistemic connection between hypotheses and observations. Perhaps these principles are able to do this because they are surrogates for an empirical background theory. It is not that there is one background theory presupposed by every appeal to parsimony; This has the quantifier order backwards. Rather, the suggestion is that each parsimony argument is justified only to each degree that it reflects an empirical background theory about the subjective matter. On this theory is brought out into the open, but the principle of parsimony is entirely dispensable (Sober, 1988).
This ‘local’ approach to the principles of parsimony and simplicity resurrects the idea that they make sense only if the world is one way rather than another. It rejects the idea that these maxims are purely methodological. How defensible this point of view is, will depend on detailed case studies of scientific hypothesis evaluation and on further developments in the theory of scientific inference.
It is usually not found of one and the same that, an inference is a (perhaps very complex) act of thought by virtue of which act (1) I pass from a set of one or more propositions or statements to a proposition or statement and (2) it appears that the latter are true if the former is or are. This psychological characterization has occurred over a wider summation of literature under more lesser than inessential variations. Desiring a better characterization of inference is natural. Yet attempts to do so by constructing a fuller psychological explanation fail to comprehend the grounds on which inference will be objectively valid-A point elaborately made by Gottlob Frége. Attempts to understand the nature of inference through the device of the representation of inference by formal-logical calculations or derivations better (1) leave ‘us’ puzzled about the relation of formal-logical derivations to the informal inferences they are supposedly to represent or reconstruct, and (2) leaves ‘us’ worried about the sense of such formal derivations. Are these derivations inference? Are not informal inferences needed in order to apply the rules governing the constructions of formal derivations (inferring that this operation is an application of that formal rule)? These are concerns cultivated by, for example, Wittgenstein.
Coming up with an adequate characterization of inference-and even working out what would count as a very adequate characterization here is demandingly by no means nearly some resolved philosophical problem.
The rule of inference, as for raised by Lewis Carroll, the Zeno-like problem of how a ‘proof’ ever gets started. Suppose I have as premises (i) ‘p’ and (ii) p q. Can I infer ‘q’? Only, it seems, if I am sure of (iii) (p & p q) q. Can I then infer ‘q’? Only, it seems, if I am sure that (iv) (p & p q & (p & p q) q) q. For each new axiom (N) I need a further axiom (N + 1) telling me that the set so far implies ‘q’, and the regress never stops. The usual solution is to treat a system as containing not only axioms, but also rules of inference, allowing movement from the axioms. The rule ‘modus ponens’ allow ‘us’ to pass from the first premise to ‘q’. Carroll’s puzzle shows that distinguishing two theoretical categories is essential, although there may be choice about which theses to put in which category.
Traditionally, a proposition that is not a ‘conditional’, as with the ‘affirmative’ and ‘negative’, modern opinion is wary of the distinction, since what appears categorical may vary with the choice of a primitive vocabulary and notation. Apparently categorical propositions may also turn out to be disguised conditionals: ‘X’ is intelligent (categorical?) Equivalent, if ‘X’ is given a range of tasks, she does them better than many people (conditional?). The problem is not merely one of classification, since deep metaphysical questions arise when facts that seem to be categorical and therefore solid, come to seem by contrast conditional, or purely hypothetical or potential.
Its condition of some classified necessity is so proven sufficient that if ‘p’ is a necessary condition of ‘q’, then ‘q’ cannot be true unless ‘p’; is true? If ‘p’ is a sufficient condition, thus steering well is a necessary condition of driving in a satisfactory manner, but it is not sufficient, for one can steer well but drive badly for other reasons. Confusion may result if the distinction is not heeded. For example, the statement that ‘A’ causes ‘B’ may be interpreted to mean that ‘A’ is itself a sufficient condition for ‘B’, or that it is only a necessary condition fort ‘B’, or perhaps a necessary parts of a total sufficient condition. Lists of conditions to be met for satisfying some administrative or legal requirement frequently attempt to give individually necessary and jointly sufficient sets of conditions.
What is more, that if any proposition of the form ‘if p then q’. The condition hypothesized, ‘p’. Is called the antecedent of the conditionals, and ‘q’, the consequent? Various kinds of conditional have been distinguished. Its weakest is that of ‘material implication’, merely telling that either ‘not-p’, or ‘q’. Stronger conditionals include elements of ‘modality’, corresponding to the thought that ‘if p is truer then q must be true’. Ordinary language is very flexible in its use of the conditional form, and there is controversy whether conditionals are better treated semantically, yielding differently finds of conditionals with different meanings, or pragmatically, in which case there should be one basic meaning with surface differences arising from other implicatures.
It follows from the definition of ‘strict implication’ that a necessary proposition is strictly implied by any proposition, and that an impossible proposition strictly implies any proposition. If strict implication corresponds to ‘q follows from p’, then this means that a necessary proposition follows from anything at all, and anything at all follows from an impossible proposition. This is a problem if we wish to distinguish between valid and invalid arguments with necessary conclusions or impossible premises.
The Humean problem of induction is that if we would suppose that there is some property ‘A’ concerning and observational or an experimental situation, and that out of a large number of observed instances of ‘A’, some fraction m/n (possibly equal to 1) has also been instances of some logically independent property ‘B’. Suppose further that the background proportionate circumstances not specified in these descriptions has been varied to a substantial degree and that there is no collateral information available concerning the frequency of ‘B’s’ among ‘A’s or concerning causal or nomologically connections between instances of ‘A’ and instances of ‘B’.
In this situation, an ‘enumerative’ or ‘instantial’ induction inference would move rights from the premise, that m/n of observed ‘A’s’ are ‘B’s’ to the conclusion that approximately m/n of all ‘A’s’ are ‘B’s. (The usual probability qualification will be assumed to apply to the inference, rather than being part of the conclusion.) Here the class of ‘A’s’ should be taken to include not only unobserved ‘A’s’ and future ‘A’s’, but also possible or hypothetical ‘A’s’ (an alternative conclusion would concern the probability or likelihood of the adjacently observed ‘A’ being a ‘B’).
The traditional or Humean problem of induction, often referred to simply as ‘the problem of induction’, is the problem of whether and why inferences that fit this schema should be considered rationally acceptable or justified from an epistemic or cognitive standpoint, i.e., whether and why reasoning in this way is likely to lead to true claims about the world. Is there any sort of argument or rationale that can be offered for thinking that conclusions reached in this way are likely to be true in the corresponding premisses is true or even that their chances of truth are significantly enhanced?
Hume’s discussion of this issue deals explicitly only with cases where all observed ‘A’s’ are ‘B’s’ and his argument applies just as well to the more general case. His conclusion is entirely negative and sceptical: Inductive inferences are not rationally justified, but are instead the result of an essentially a-rational process, custom or habit. Hume (1711-76) challenges the proponent of induction to supply a cogent line of reasoning that leads from an inductive premise to the corresponding conclusion and offers an extremely influential argument in the form of a dilemma (a few times referred to as ‘Hume’s fork’), that either our actions are determined, in which case we are not responsible for them, or they are the result of random events, under which case we are also not responsible for them.
Such reasoning would, he argues, have to be either deductively demonstrative reasoning in the concerning relations of ideas or ‘experimental’, i.e., empirical, that reasoning concerning matters of fact or existence. It cannot be the former, because all demonstrative reasoning relies on the avoidance of contradiction, and it is not a contradiction to suppose that ‘the course of nature may change’, that an order that was observed in the past and not of its continuing against the future: But it cannot be, as the latter, since any empirical argument would appeal to the success of such reasoning about an experience, and the justifiability of generalizing from experience are precisely what is at issue-so that any such appeal would be question-begging. Hence, Hume concludes that there can be no such reasoning (1748).
An alternative version of the problem may be obtained by formulating it with reference to the so-called Principle of Induction, which says roughly that the future will resemble the past or, somewhat better, that unobserved cases will resemble observed cases. An inductive argument may be viewed as enthymematic, with this principle serving as a supposed premiss, in which case the issue is obviously how such a premiss can be justified. Hume’s argument is then that no such justification is possible: The principle cannot be justified a prior because having possession of been true in experiences without obviously begging the question is not contradictory to have possession of been true in experiences without obviously begging the question.
The predominant recent responses to the problem of induction, at least in the analytic tradition, in effect accept the main conclusion of Hume’s argument, namely, that inductive inferences cannot be justified in the sense of showing that the conclusion of such an inference is likely to be true if the premise is true, and thus attempt to find another sort of justification for induction. Such responses fall into two main categories: (i) Pragmatic justifications or ‘vindications’ of induction, mainly developed by Hans Reichenbach (1891-1953), and (ii) ordinary language justifications of induction, whose most important proponent is Frederick, Peter Strawson (1919-). In contrast, some philosophers still attempt to reject Hume’s dilemma by arguing either (iii) That, contrary to appearances, induction can be inductively justified without vicious circularity, or (iv) that an anticipatory justification of induction is possible after all. In that:
(1) Reichenbach’s view is that induction is best regarded, not as a form of inference, but rather as a ‘method’ for arriving at posits regarding, i.e., the proportion of ‘A’s’ remain additionally of ‘B’s’. Such a posit is not a claim asserted to be true, but is instead an intellectual wager analogous to a bet made by a gambler. Understood in this way, the inductive method says that one should posit that the observed proportion is, within some measure of an approximation, the true proportion and then continually correct that initial posit as new information comes in.
The gambler’s bet is normally an ‘appraised posit’, i.e., he knows the chances or odds that the outcome on which he bets will actually occur. In contrast, the inductive bet is a ‘blind posit’: We do not know the chances that it will succeed or even that success is that it will succeed or even that success is possible. What we are gambling on when we make such a bet is the value of a certain proportion in the independent world, which Reichenbach construes as the limit of the observed proportion as the number of cases increases to infinity. Nevertheless, we have no way of knowing that there are even such a limit, and no way of knowing that the proportion of ‘A’s’ are in addition of ‘B’s’ converges in the end on some stable value than varying at random. If we cannot know that this limit exists, then we obviously cannot know that we have any definite chance of finding it.
What we can know, according to Reichenbach, is that ‘if’ there is a truth of this sort to be found, the inductive method will eventually find it’. That this is so is an analytic consequence of Reichenbach’s account of what it is for such a limit to exist. The only way that the inductive method of making an initial posit and then refining it in light of new observations can fail eventually to arrive at the true proportion is if the series of observed proportions never converges on any stable value, which means that there is no truth to be found pertaining the proportion of ‘A’s additionally constitute ‘B’s’. Thus, induction is justified, not by showing that it will succeed or indeed, that it has any definite likelihood of success, but only by showing that it will succeed if success is possible. Reichenbach’s claim is that no more than this can be established for any method, and hence that induction gives ‘us’ our best chance for success, our best gamble in a situation where there is no alternative to gambling.
This pragmatic response to the problem of induction faces several serious problems. First, there are indefinitely many other ‘methods’ for arriving at posits for which the same sort of defence can be given-methods that yield the same results as the inductive method over time but differ arbitrarily before long. Despite the efforts of others, it is unclear that there is any satisfactory way to exclude such alternatives, in order to avoid the result that any arbitrarily chosen short-term posit is just as reasonable as the inductive posit. Second, even if there is a truth of the requisite sort to be found, the inductive method is only guaranteed to find it or even to come within any specifiable distance of it in the indefinite long run. All the same, any actual application of inductive results always takes place in the presence to the future eventful states in making the relevance of the pragmatic justification to actual practice uncertainly. Third, and most important, it needs to be emphasized that Reichenbach’s response to the problem simply accepts the claim of the Humean sceptic that an inductive premise never provides the slightest reason for thinking that the corresponding inductive conclusion is true. Reichenbach himself is quite candid on this point, but this does not alleviate the intuitive implausibility of saying that we have no more reason for thinking that our scientific and commonsense conclusions that result in the induction of it ‘ . . . is true’ than, to use Reichenbach’s own analogy (1949), a blind man wandering in the mountains who feels an apparent trail with his stick has for thinking that following it will lead him to safety.
An approach to induction resembling Reichenbach’s claiming in that those particular inductive conclusions are posits or conjectures, than the conclusions of cogent inferences, is offered by Popper. However, Popper’s view is even more overtly sceptical: It amounts to saying that all that can ever be said in favour of the truth of an inductive claim is that the claim has been tested and not yet been shown to be false.
(2) The ordinary language response to the problem of induction has been advocated by many philosophers, none the less, Strawson claims that the question whether induction is justified or reasonable makes sense only if it tacitly involves the demand that inductive reasoning meet the standards appropriate to deductive reasoning, i.e., that the inductive conclusions are shown to follow deductively from the inductive assumption. Such a demand cannot, of course, be met, but only because it is illegitimate: Inductive and deductive reasons are simply fundamentally different kinds of reasoning, each possessing its own autonomous standards, and there is no reason to demand or expect that one of these kinds meet the standards of the other. Whereas, if induction is assessed by inductive standards, the only ones that are appropriate, then it is obviously justified.
The problem here is to understand to what this allegedly obvious justification of an induction amount. In his main discussion of the point (1952), Strawson claims that it is an analytic true statement that believing it a conclusion for which there is strong evidence is reasonable and an analytic truth that inductive evidence of the sort captured by the schema presented earlier constitutes strong evidence for the corresponding inductive conclusion, thus, apparently yielding the analytic conclusion that believing it a conclusion for which there is inductive evidence is reasonable. Nevertheless, he also admits, indeed insists, that the claim that inductive conclusions will be true in the future is contingent, empirical, and may turn out to be false (1952). Thus, the notion of reasonable belief and the correlative notion of strong evidence must apparently be understood in ways that have nothing to do with likelihood of truth, presumably by appeal to the standard of reasonableness and strength of evidence that are accepted by the community and are embodied in ordinary usage.
Understood in this way, Strawson’s response to the problem of inductive reasoning does not speak to the central issue raised by Humean scepticism: The issue of whether the conclusions of inductive arguments are likely to be true. It amounts to saying merely that if we reason in this way, we can correctly call ourselves ‘reasonable’ and our evidence ‘strong’, according to our accepted community standards. Nevertheless, to the undersealing of issue of wether following these standards is a good way to find the truth, the ordinary language response appears to have nothing to say.
(3) The main attempts to show that induction can be justified inductively have concentrated on showing that such as a defence can avoid circularity. Skyrms (1975) formulate, perhaps the clearest version of this general strategy. The basic idea is to distinguish different levels of inductive argument: A first level in which induction is applied to things other than arguments: A second level in which it is applied to arguments at the first level, arguing that they have been observed to succeed so far and hence are likely to succeed in general: A third level in which it is applied in the same way to arguments at the second level, and so on. Circularity is allegedly avoided by treating each of these levels as autonomous and justifying the argument at each level by appeal to an argument at the next level.
One problem with this sort of move is that even if circularity is avoided, the movement to higher and higher levels will clearly eventually fail simply for lack of evidence: A level will reach at which there have been enough successful inductive arguments to provide a basis for inductive justification at the next higher level, and if this is so, then the whole series of justifications collapses. A more fundamental difficulty is that the epistemological significance of the distinction between levels is obscure. If the issue is whether reasoning in accord with the original schema offered above ever provides a good reason for thinking that the conclusion is likely to be true, then it still seems question-begging, even if not flatly circular, to answer this question by appeal to anther argument of the same form.
(4) The idea that induction can be justified on a pure priori basis is in one way the most natural response of all: It alone treats an inductive argument as an independently cogent piece of reasoning whose conclusion can be seen rationally to follow, although perhaps only with probability from its premise. Such an approach has, however, only rarely been advocated (Russell, 19132 and BonJour, 1986), and is widely thought to be clearly and demonstrably hopeless.
Many on the reasons for this pessimistic view depend on general epistemological theses about the possible or nature of anticipatory cognition. Thus if, as Quine alleges, there is no a prior justification of any kind, then obviously a prior justification for induction is ruled out. Or if, as more moderate empiricists have in claiming some preexistent knowledge should be analytic, then again a prevenient justification for induction seems to be precluded, since the claim that if an inductive premise ids truer, then the conclusion is likely to be true does not fit the standard conceptions of ‘analyticity’. A consideration of these matters is beyond the scope of the present spoken exchange.
There are, however, two more specific and quite influential reasons for thinking that an early approach is impossible that can be briefly considered, first, there is the assumption, originating in Hume, but since adopted by very many of others, that a move forward in the defence of induction would have to involve ‘turning induction into deduction’, i.e., showing, per impossible, that the inductive conclusion follows deductively from the premise, so that it is a formal contradiction to accept the latter and deny the former. However, it is unclear why a prior approach need be committed to anything this strong. It would be enough if it could be argued that it is deductively unlikely that such a premise is true and corresponding conclusion false.
Second, Reichenbach defends his view that pragmatic justification is the best that is possible by pointing out that a completely chaotic world in which there is simply not true conclusion to be found as to the proportion of ‘A’s’ in addition that occurs of, but B’s’ is neither impossible nor unlikely from a purely a prior standpoint, the suggestion being that therefore there can be no a prior reason for thinking that such a conclusion is true. Nevertheless, there is still a substring wayin laying that a chaotic world is a prior neither impossible nor unlikely without any further evidence does not show that such a world os not a prior unlikely and a world containing such-and-such regularity might anticipatorially be somewhat likely in relation to an occurrence of a long-run patten of evidence in which a certain stable proportion of observed ‘A’s’ are ‘B’s’ ~. An occurrence, it might be claimed, that would be highly unlikely in a chaotic world (BonJour, 1986).
Goodman’s ‘new riddle of induction’ purports that we suppose that before some specific time ’t’ (perhaps the year 2000) we observe a larger number of emeralds (property A) and find them all to be green (property B). We proceed to reason inductively and conclude that all emeralds are green Goodman points out, however, that we could have drawn a quite different conclusion from the same evidence. If we define the term ‘grue’ to mean ‘green if examined before ’t’ and blue examined after t , then all of our observed emeralds will also be gruing. A parallel inductive argument will yield the conclusion that all emeralds are gruing, and hence that all those examined after the year 2000 will be blue. Presumably the first of these concisions is genuinely supported by our observations and the second is not. Nevertheless, the problem is to say why this is so and to impose some further restriction upon inductive reasoning that will permit the first argument and exclude the second.
The obvious alternative suggestion is that ‘grue. Similar predicates do not correspond to genuine, purely qualitative properties in the way that ‘green’ and ‘blueness’ does, and that this is why inductive arguments involving them are unacceptable. Goodman, however, claims to be unable to make clear sense of this suggestion, pointing out that the relations of formal desirability are perfectly symmetrical: Grue’ may be defined in terms if, ‘green’ and ‘blue’, but ‘green’ an equally well be defined in terms of ‘grue’ and ‘green’ (blue if examined before ‘t’ and green if examined after ‘t’).
The ‘grued, paradoxes’ demonstrate the importance of categorization, in that sometimes it is itemized as ‘gruing’, if examined of a presence to the future, before future time ‘t’ and ‘green’, or not so examined and ‘blue’. Even though all emeralds in our evidence class grue, we ought must infer that all emeralds are gruing. For ‘grue’ is unprojectible, and cannot transmit credibility form known to unknown cases. Only projectable predicates are right for induction. Goodman considers entrenchment the key to projectibility having a long history of successful protection, ‘grue’ is entrenched, lacking such a history, ‘grue’ is not. A hypothesis is projectable, Goodman suggests, only if its predicates (or suitable related ones) are much better entrenched than its rivalrous past successes that do not assume future ones. Induction remains a risky business. The rationale for favouring entrenched predicates is pragmatic. Of the possible projections from our evidence class, the one that fits with past practices enables ‘us’ to utilize our cognitive resources best. Its prospects of being true are worse than its competitors’ and its cognitive utility is greater.
So, to a better understanding of induction we should then term is most widely used for any process of reasoning that takes ‘us’ from empirical premises to empirical conclusions supported by the premises, but not deductively entailed by them. Inductive arguments are therefore kinds of applicative arguments, in which something beyond the content of the premise is inferred as probable or supported by them. Induction is, however, commonly distinguished from arguments to theoretical explanations, which share this applicative character, by being confined to inferences in which he conclusion involves the same properties or relations as the premises. The central example is induction by simple enumeration, where from premises telling that Fa, Fb, Fc . . . ‘where a, b, c’s, are all of some kind ‘G’, it is inferred that G’s from outside the sample, such as future G’s, will be ‘F’, or perhaps that all G’s are ‘F’. In this, which and the other persons deceive them, children may infer that everyone is a deceiver: Different, but similar inferences of a property by some object to the same object’s future possession of the same property, or from the constancy of some law-like pattern in events and states of affairs ti its future constancy. All objects we know of attract each other with a force inversely proportional to the square of the distance between them, so perhaps they all do so, and will always do so.
The rational basis of any inference was challenged by Hume, who believed that induction presupposed belie in the uniformity of nature, but that this belief has no defence in reason, and merely reflected a habit or custom of the mind. Hume was not therefore sceptical about the role of reason in either explaining it or justifying it. Trying to answer Hume and to show that there is something rationally compelling about the inference referred to as the problem of induction. It is widely recognized that any rational defence of induction will have to partition well-behaved properties for which the inference is plausible (often called projectable properties) from badly behaved ones, for which it is not. It is also recognized that actual inductive habits are more complex than those of similar enumeration, and that both common sense and science pay attention to such giving factors as variations within the sample giving ‘us’ the evidence, the application of ancillary beliefs about the order of nature, and so on.
Nevertheless, the fundamental problem remains that ant experience condition by application show ‘us’ only events occurring within a very restricted part of a vast spatial and temporal order about which we then come to believe things.
Uncompounded by its belonging of a confirmation theory finding of the measure to which evidence supports a theory fully formalized confirmation theory would dictate the degree of confidence that a rational investigator might have in a theory, given some-body of evidence. The grandfather of confirmation theory is Gottfried Leibniz (1646-1718), who believed that a logically transparent language of science would be able to resolve all disputes. In the 20th century a fully formal confirmation theory was a main goal of the logical positivist, since without it the central concept of verification by empirical evidence itself remains distressingly unscientific. The principal developments were due to Rudolf Carnap (1891-1970), culminating in his ‘Logical Foundations of Probability’ (1950). Carnap’s idea was that the measure necessitated would be the proportion of logically possible states of affairs in which the theory and the evidence both hold, compared ti the number in which the evidence itself holds that the probability of a preposition, relative to some evidence, is a proportion of the range of possibilities under which the proposition is true, compared to the total range of possibilities left by the evidence. The difficulty with the theory lies in identifying sets of possibilities so that they admit of measurement. It therefore demands that we can put a measure on the ‘range’ of possibilities consistent with theory and evidence, compared with the range consistent with the evidence alone.
Among the obstacles the enterprise meets, is the fact that while evidence covers only a finite range of data, the hypotheses of science may cover an infinite range. In addition, confirmation proves to vary with the language in which the science is couched, and the Carnapian programme has difficulty in separating genuinely confirming variety of evidence from less compelling repetition of the same experiment. Confirmation also proved to be susceptible to acute paradoxes. Finally, scientific judgement seems to depend on such intangible factors as the problems facing rival theories, and most workers have come to stress instead the historically situated scene of what would appear as a plausible distinction of a scientific knowledge at a given time.
Arose to the paradox of which when a set of apparent incontrovertible premises is given to unacceptable or contradictory conclusions. To solve a paradox will involve showing either that there is a hidden flaw in the premises, or that the reasoning is erroneous, or that the apparently unacceptable conclusion can, in fact, be tolerated. Paradoxes are therefore important in philosophy, for until one is solved it shows that there is something about our reasoning and our concepts that we do not understand. What is more, and somewhat loosely, a paradox is a compelling argument from unacceptable premises to an unacceptable conclusion: More strictly speaking, a paradox is specified to be a sentence that is true if and only if it is false. A characterized objection lesson of it would be: ‘The displayed sentence is false.’
Seeing that this sentence is false if true is easy, and true if false, a paradox, in either of the senses distinguished, presents an important philosophical challenger. Epistemologists are especially concerned with various paradoxes having to do with knowledge and belief. In other words, for example, the Knower paradox is an argument that begins with apparently impeccable premisses about the concepts of knowledge and inference and derives an explicit contradiction. The origin of the reasoning is the ‘surprise examination paradox’: A teacher announces that there will be a surprise examination next week. A clever student argues that this is impossible. ‘The test cannot be on Friday, the last day of the week, because it would not be a surprise. We would know the day of the test on Thursday evening. This means we can also rule out Thursday. For after we learn that no test has been given by Wednesday, we would know the test is on Thursday or Friday -and would already know that it s not on Friday and would already know that it is not on Friday by the previous reasoning. The remaining days can be eliminated in the same manner’.
This puzzle has over a dozen variants. The first was probably invented by the Swedish mathematician Lennard Ekbon in 1943. Although the first few commentators regarded the reverse elimination argument as cogent, every writer on the subject since 1950 agrees that the argument is unsound. The controversy has been over the proper diagnosis of the flaw.
Initial analyses of the subject’s argument tried to lay the blame on a simple equivocation. Their failure led to more sophisticated diagnoses. The general format has been an assimilation to better-known paradoxes. One tradition casts the surprise examination paradox as a self-referential problem, as fundamentally akin to the Liar, the paradox of the Knower, or Gödel’s incompleteness theorem. That in of itself, says enough that Kaplan and Montague (1960) distilled the following ‘self-referential’ paradox, the Knower. Consider the sentence:
(S) The negation of this sentence is known (to be true).
Suppose that (S) is true. Then its negation is known and hence true. However, if its negation is true, then (S) must be false. Therefore (s) is false, or what is the name, the negation of (S) is true.
This paradox and its accompanying reasoning are strongly reminiscent of the Lair Paradox that (in one version) begins by considering a sentence ‘This sentence is false’ and derives a contradiction. Versions of both arguments using axiomatic formulations of arithmetic and Gödel-numbers to achieve the effect of self-reference yields important meta-theorems about what can be expressed in such systems. Roughly these are to the effect that no predicates definable in the formalized arithmetic can have the properties we demand of truth (Tarski’s Theorem) or of knowledge (Montague, 1963).
These meta-theorems still leave ‘us; with the problem that if we suppose that we add of these formalized languages predicates intended to express the concept of knowledge (or truth) and inference-as one mighty does if a logic of these concepts is desired. Then the sentence expressing the leading principles of the Knower Paradox will be true.
Explicitly, the assumption about knowledge and inferences are:
(1) If sentences ‘A’ are known, then ‘a.’
(2) (1) is known?
To give an absolutely explicit t derivation of the paradox by applying these principles to (S), we must add (contingent) assumptions to the effect that certain inferences have been done. Still, as we go through the argument of the Knower, these inferences are done. Even if we can somehow restrict such principles and construct a consistent formal logic of knowledge and inference, the paradoxical argument as expressed in the natural language still demands some explanation.
The usual proposals for dealing with the Liar often have their analogues for the Knower, e.g., that there is something wrong with a self-reference or that knowledge (or truth) is properly a predicate of propositions and not of sentences. The relies that show that some of these are not adequate are often parallel to those for the Liar paradox. In addition, on e c an try here what seems to be an adequate solution for the Surprise Examination Paradox, namely the observation that ‘new knowledge can drive out knowledge’, but this does not seem to work on the Knower (Anderson, 1983).
There are a number of paradoxes of the Liar family. The simplest example is the sentence ‘This sentence is false’, which must be false if it is true, and true if it is false. One suggestion is that the sentence fails to say anything, but sentences that fail to say anything are at least not true. In fact case, we consider to sentences ‘This sentence is not true’, which, if it fails to say anything is not true, and hence (this kind of reasoning is sometimes called the strengthened Liar). Other versions of the Liar introduce pairs of sentences, as in a slogan on the front of a T-shirt saying ‘This sentence on the back of this T-shirt is false’, and one on the back saying ‘The sentence on the front of this T-shirt is true’. It is clear that each sentence individually is well formed, and was it not for the other, might have said something true. So any attempts to dismiss the paradox by sating that the sentence involved are meaningless will face problems.
Even so, the two approaches that have some hope of adequately dealing with this paradox is ‘hierarchy’ solutions and ‘truth-value gap’ solutions. According to the first, knowledge is structured into ‘levels’. It is argued that there be one-coherent notion expressed by the verb; knows’, but rather a whole series of notions: knows0. knows, and so on (perhaps into transfinite), stated ion terms of predicate expressing such ‘ramified’ concepts and properly restricted, (1)-(3) lead to no contradictions. The main objections to this procedure are that the meaning of these levels has not been adequately explained and that the idea of such subscripts, even implicit, in a natural language is highly counterintuitive the ‘truth-value gap’ solution takes sentences such as (S) to lack truth-value. They are neither true nor false, but they do not express propositions. This defeats a crucial step in the reasoning used in the derivation of the paradoxes. Kripler (1986) has developed this approach in connection with the Liar and Asher and Kamp (1986) has worked out some details of a parallel solution to the Knower. The principal objection is that ‘strengthened’ or ‘super’ versions of the paradoxes tend to reappear when the solution itself is stated.
Since the paradoxical deduction uses only the properties (1)-(3) and since the argument is formally valid, any notions that satisfy these conditions will lead to a paradox. Thus, Grim (1988) notes that this may be read as ‘is known by an omniscient God’ and concludes that there is no coherent single notion of omniscience. Thomason (1980) observes that with some different conditions, analogous reasoning about belief can lead to paradoxical consequence.
Overall, it looks as if we should conclude that knowledge and truth are ultimately intrinsically ‘stratified’ concepts. It would seem that wee must simply accept the fact that these (and similar) concepts cannot be assigned of any-one fixed, finite or infinite. Still, the meaning of this idea certainly needs further clarification.
Its paradox arises when a set of apparently incontrovertible premises gives unacceptable or contradictory conclusions, to solve a paradox will involve showing either that there is a hidden flaw in the premises, or that the reasoning is erroneous, or that the apparently unacceptable conclusion can, in fact, be tolerated. Paradoxes are therefore important in philosophy, for until one is solved its show that there is something about our reasoning and our concepts that we do not understand. Famous families of paradoxes include the ‘semantic paradoxes’ and ‘Zeno’s paradoxes. Art the beginning of the 20th century, paradox and other set-theoretical paradoxes led to the complete overhaul of the foundations of set theory, while the ’Sorites paradox’ has lead to the investigations of the semantics of vagueness and fuzzy logics.
It is, however, to what extent can analysis be informative? This is the question that gives a riser to what philosophers has traditionally called ‘the’ paradox of analysis. Thus, consider the following proposition:
(1) To be an instance of knowledge is to be an instance of justified true belief not essentially grounded in any falsehood.
(1) if true, illustrates an important type of philosophical analysis. For convenience of exposition, I will assume (1) is a correct analysis. The paradox arises from the fact that if the concept of justified true belief not been essentially grounded in any falsification is the analysand of the concept of knowledge, it would seem that they are the same concept and hence that:
(2) To be an instance of knowledge is to be as an instance of.
knowledge and would have to be the same propositions as (1). But then how can (1) be informative when (2) is not? This is what is called the first paradox of analysis. Classical writings’ on analysis suggests a second paradoxical analysis (Moore, 1942).
brother is to be a male sibling. If (3) is true, it would seem that the concept of being a brother would have to be the same concept as the concept of being a male sibling and tat:
(4) An analysis of the concept of being a brother is that to be a brother is to be a brother
would also have to be true and in fact, would have to be the same proposition as (3?). Yet (3) is true and (4) is false.
Both these paradoxes rest upon the assumptions that analysis is a relation between concepts, than one involving entity of other sorts, such as linguistic expressions, and tat in a true analysis, analysand and analysandum are the same concept. Both these assumptions are explicit in Moore, but some of Moore’s remarks hint at a solution to that of another statement of an analysis is a statement partly about the concept involved and partly about the verbal expressions used to express it. He says he thinks a solution of this sort is bound to be right, but fails to suggest one because he cannot see a way in which the analysis can be even partly about the expression (Moore, 1942).
Elsewhere, of such ways, as a solution to the second paradox, to which is explicating (3) as:
(5) An analysis is given by saying that the verbal expression ‘÷ is a brother’ expresses the same concept as is expressed by the conjunction of the verbal expressions ‘÷ is male’ when used to express the concept of being male and ‘÷ is a sibling’ when used to express the concept of being a sibling. (Ackerman, 1990).
An important point about (5) is as follows. Stripped of its philosophical jargon (‘analysis’, ‘concept’, ‘÷ is a . . . ‘), (5) seems to state the sort of information generally stated in a definition of the verbal expression ‘brother’ in terms of the verbal expressions ‘male’ and ‘sibling’, where this definition is designed to draw upon listeners’ antecedent understanding of the verbal expression ‘male’ and ‘sibling’, and thus, to tell listeners what the verbal expression ‘brother’ really means, instead of merely providing the information that two verbal expressions are synonymous without specifying the meaning of either one. Thus, its solution to the second paradox seems to make the sort of analysis tat gives rise to this paradox matter of specifying the meaning of a verbal expression in terms of separate verbal expressions already understood and saying how the meanings of these separate, already-understood verbal expressions are combined. This corresponds to Moore’s intuitive requirement that an analysis should both specify the constituent concepts of the analysandum and tell how they are combined, but is this all there is to philosophical analysis?
To answer this question, we must note that, in addition too there being two paradoxes of analysis, there is two types of analyses that are relevant here. (There are also other types of analysis, such as reformatory analysis, where the analysands are intended to improve on and replace the analysandum. But since reformatory analysis involves no commitment to conceptual identity between analysand and analysandum, reformatory analysis does not generate a paradox of analysis and so will not concern ‘us’ here.) One way to recognize the difference between the two types of analysis concerning ‘us’ here is to focus on the difference between the two paradoxes. This can be done by means of the Frége-inspired sense-individuation condition, which is the condition that two expressions have the same sense if and only if they can be interchangeably ‘salva veritate’ whenever used in propositional attitude context. If the expressions for the analysands and the analysandum in (1) met this condition, (1) and (2) would not raise the first paradox, but the second paradox arises regardless of whether the expression for the analysand and the analysandum meet this condition. The second paradox is a matter of the failure of such expressions to be interchangeable salva veritate in sentences involving such contexts as ‘an analysis is given thereof. Thus, a solution (such as the one offered) that is aimed only at such contexts can solve the second paradox. This is clearly false for the first paradox, however, which will apply to all pairs of propositions expressed by sentences in which expressions for pairs of analysands and anslysantia raising the first paradox is interchangeable. For example, consider the following proposition:
(6) Mary knows that some cats tail.
It is possible for John to believe (6) without believing:
(7) Mary has justified true belief, not essentially grounded in any falsehood, that some cats lack tails.
Yet this possibility clearly does not mean that the proposition that Mary knows that some casts lack tails is partly about language.
One approach to the first paradox is to argue that, despite the apparent epistemic inequivalence of (1) and (2), the concept of justified true belief not essentially grounded in any falsehood is still identical with the concept of knowledge (Sosa, 1983). Another approach is to argue that in the sort of analysis raising the first paradox, the analysand and analysandum is concepts that are different but that bear a special epistemic relation to each other. Elsewhere, the development is such an approach and suggestion that this analysand-analysandum relation has the following facets.
(a) The analysand and analysandum are necessarily coextensive, i.e., necessarily every instance of one is an instance of the other.
(b) The analysand and analysandum are knowable theoretical to be coextensive.
© The analysandum is simpler than the analysands a condition whose necessity is recognized in classical writings on analysis, such as, Langford, 1942.
(d) The analysand do not have the analysandum as a constituent.
Condition (d) rules out circularity. But since many valuable quasi-analyses are partly circular, e.g., knowledge is justified true belief supported by known reasons not essentially grounded in any falsehood, it seems best to distinguish between full analysis, from that of (d) is a necessary condition, and partial analysis, for which it is not.
These conditions, while necessary, are clearly insufficient. The basic problem is that they apply too many pairs of concepts that do not seem closely enough related epistemologically to count as analysand and analysandum. , such as the concept of being 6 and the concept of the fourth root of 1296. Accordingly, its solution upon what actually seems epistemologically distinctive about analyses of the sort under consideration, which is a certain way they can be justified. This is by the philosophical example-and-counterexample method, which is in a general term that goes as follows. ‘J’ investigates the analysis of K’s concept ‘Q’ (where ‘K’ can but need not be identical to ‘J’ by setting ‘K’ a series of armchair thought experiments, i.e., presenting ‘K’ with a series of simple described hypothetical test cases and asking ‘K’ questions of the form ‘If such-and-such where the case would this count as a case of Q? ‘J’ then contrasts the descriptions of the cases to which; K’ answers affirmatively with the description of the cases to which ‘K’ does not, and ‘J’ generalizes upon these descriptions to arrive at the concepts (if possible not including the analysandum) and their mode of combination that constitute the analysand of K’‘s concept ‘Q’. Since ‘J’ need not be identical with ‘K’, there is no requirement that ‘K’ himself be able to perform this generalization, to recognize its result as correct, or even to understand he analysand that is its result. This is reminiscent of Walton’s observation that one can simply recognize a bird as a swallow without realizing just what feature of the bird (beak, wing configurations, etc.) form the basis of this recognition. (The philosophical significance of this way of recognizing is discussed in Walton, 1972) ‘K’ answers the questions based solely on whether the described hypothetical cases just strike him as cases of ‘Q’. ‘J’ observes certain strictures in formulating the cases and questions. He makes the cases as simple as possible, to minimize the possibility of confusion and to minimize the likelihood that ‘K’ will draw upon his philosophical theories (or quasi-philosophical, a rudimentary notion if he is unsophisticated philosophically) in answering the questions. For this conflicting result, the conflict should ‘other things being equal’ be resolved in favour of the simpler case. ‘J’ makes the series of described cases wide-ranging and varied, with the aim of having it be a complete series, where a series is complete if and only if no case that is omitted in such that, if included, it would change the analysis arrived at. ‘J’ does not, of course, use as a test-case description anything complicated and general enough to express the analysand. There is no requirement that the described hypothetical test cases be formulated only in terms of what can be observed. Moreover, using described hypothetical situations as test cases enables ‘J’ to frame the questions in such a way as to rule out extraneous background assumption to a degree, thus, even if ‘K’ correctly believes that all and only P’s are R’s, the question of whether the concepts of P, R, or both enter the analysand of his concept ‘Q’ can be investigated by asking him such questions as ‘Suppose (even if it seems preposterous to you) that you were to find out that there was a ‘P’ that was not an ‘R’. Would you still consider it a case of Q?
Taking all this into account, the fifth necessary condition for this sort of analysand-analysandum relations is as follows:
(e) If ‘S’ is the analysand of ‘Q’, the proposition that necessarily all and only instances of ‘S’ are instances of ‘Q’ can be justified by generalizing from intuition about the correct answers to questions of the sort indicated about a varied and wide-ranging series of simple described hypothetical situations. It so does occur of antinomy, when we are able to argue for, or demonstrate, both a proposition and its contradiction, roughly speaking, a contradiction of a proposition ‘p’ is one that can be expressed in form ‘not-p’, or, if ‘p’ can be expressed in the form ‘not-q’, then a contradiction is one that can be expressed in the form ‘q’. Thus, e.g., if ‘p is 2 + 1 = 4, then 2 + 1 4 is the contradictory of ‘p’, for 2 + 1 4 can be expressed in the form not (2 + 1 = 4). If ‘p’ is 2 + 1 4, then 2 + 1-4 is a contradictory of ‘p’, since 2 + 1 4 can be expressed in the form not (2 + 1 = 4). This is, mutually, but contradictory propositions can be expressed in the form, ‘r’, ‘not-r’. The Principle of Contradiction says that mutually contradictory propositions cannot both be true and cannot both be false. Thus, by this principle, since if ‘p’ is true, ‘not-p’ is false, no proposition ‘p’ can be at once true and false (otherwise both ‘p’ and its contradictories would be false?). In particular, for any predicate ‘p’ and object ‘÷’, it cannot be that ‘p’; is at once true of ‘÷’ and false of ÷? This is the classical formulation of the principle of contradiction, but it is nonetheless, that wherein, we cannot now fault either demonstrates. We would eventually hope to be able ‘to solve the antinomy’ by managing, through careful thinking and analysis, eventually to fault either or both demonstrations.
Many paradoxes are as an easy source of antinomies, for example, Zeno gave some famously lets say, logical-cum-mathematical arguments that might be interpreted as demonstrating that motion is impossible. But our eyes as it was, demonstrate motion (exhibit moving things) all the time. Where did Zeno go wrong? Where do our eyes go wrong? If we cannot readily answer at least one of these questions, then we are in antinomy. In the ‘Critique of Pure Reason,’ Kant gave demonstrations of the same kind -in the Zeno example they were obviously not the same kind of both, e.g., that the world has a beginning in time and space, and that the world has no beginning in time or space. He argues that both demonstrations are at fault because they proceed on the basis of ‘pure reason’ unconditioned by sense experience.
At this point, we display attributes to the theory of experience, as it is not possible to define in an illuminating way, however, we know what experiences are through acquaintances with some of our own, e.g., visual experiences of as afterimage, a feeling of physical nausea or a tactile experience of an abrasive surface (which might be caused by an actual surface -rough or smooth, or which might be part of a dream, or the product of a vivid sensory imagination). The essential feature of experience is it feels a certain way -that there is something that it is like to have it. We may refer to this feature of an experience as its ‘character’.
Another core feature of the sorts of experiences with which this may be of a concern, is that they have representational ‘content’. (Unless otherwise indicated, ‘experience’ will be reserved for their ‘contentual representations’.) The most obvious cases of experiences with content are sense experiences of the kind normally involved in perception. We may describe such experiences by mentioning their sensory modalities ad their contents, e.g., a gustatory experience (modality) of chocolate ice cream (content), but do so more commonly by means of perceptual verbs combined with noun phrases specifying their contents, as in ‘Macbeth saw a dagger’. This is, however, ambiguous between the perceptual claim ‘There was a (material) dagger in the world that Macbeth perceived visually’ and ‘Macbeth had a visual experience of a dagger’ (the reading with which we are concerned, as it is afforded by our imagination, or perhaps, experiencing mentally hallucinogenic imagery).
As in the case of other mental states and events with content, it is important to distinguish between the properties that and experience ‘represents’ and the properties that it ‘possesses’. To talk of the representational properties of an experience is to say something about its content, not to attribute those properties to the experience itself. Like every other experience, a visual; experience of a non-shaped square, of which is a mental event, and it is therefore not itself irregular or is it square, even though it represents those properties. It is, perhaps, fleeting, pleasant or unusual, even though it does not represent those properties. An experience may represent a property that it possesses, and it may even do so in virtue of a rapidly changing (complex) experience representing something as changing rapidly. However, this is the exception and not the rule.
Which properties can be [directly] represented in sense experience is subject to debate. Traditionalists include only properties whose presence could not be doubted by a subject having appropriate experiences, e.g., colour and shape in the case of visual experience, and apparent shape, surface texture, hardness, etc., in the case of tactile experience. This view is natural to anyone who has an egocentric, Cartesian perspective in epistemology, and who wishes for pure data in experiences to serve as logically certain foundations for knowledge, especially to the immediate objects of perceptual awareness in or of sense-data, such categorized of colour patches and shapes, which are usually supposed distinct from surfaces of physical objectivity. Qualities of sense-data are supposed to be distinct from physical qualities because their perception is more relative to conditions, more certain, and more immediate, and because sense-data is private and cannot appear other than they are they are objects that change in our perceptual field when conditions of perception change. Physical objects remain constant.
Others who do not think that this wish can be satisfied, and who are more impressed with the role of experience in providing animisms with ecologically significant information about the world around them, claim that sense experiences represent properties, characteristic and kinds that are much richer and much more wide-ranging than the traditional sensory qualities. We do not see only colours and shapes, they tell ‘us’, but also earth, water, men, women and fire: We do not smell only odours, but also food and filth. There is no space here to examine the factors relevantly responsible to their choice of situational alternatives. Yet, this suggests that character and content are not really distinct, and there is a close tie between them. For one thing, the relative complexity of the character of sense experience places limitations upon its possible content, e.g., a tactile experience of something touching one’s left ear is just too simple to carry the same amount of content as typically convincing to an every day, visual experience. Moreover, the content of a sense experience of a given character depends on the normal causes of appropriately similar experiences, e.g., the sort of gustatory experience that we have when eating chocolate would be not represented as chocolate unless it was normally caused by chocolate. Granting a contingent ties between the character of an experience and its possible causal origins, once, again follows that its possible content is limited by its character.
Character and content are none the less irreducibly different, for the following reasons. (a) There are experiences that completely lack content, e.g., certain bodily pleasures. (b) Not every aspect of the character of an experience with content is relevant to that content, e.g., the unpleasantness of an aural experience of chalk squeaking on a board may have no representational significance. © Experiences in different modalities may overlap in content without a parallel overlap in character, e.g., visual and tactile experiences of circularity feel completely different. (d) The content of an experience with a given character may vary according to the background of the subject, e.g., a certain content ‘singing bird’ only after the subject has learned something about birds.
According to the act/object analysis of experience (which is a special case of the act/object analysis of consciousness), every experience involves an object of experience even if it has no material object. Two main lines of argument may be offered in support of this view, one ‘phenomenological’ and the other ‘semantic’.
In an outline, the phenomenological argument is as follows. Whenever we have an experience, even if nothing beyond the experience answers to it, we seem to be presented with something through the experience (which is itself diaphanous). The object of the experience is whatever is so presented to ‘us’-is that it is an individual thing, an event, or a state of affairs.
The semantic argument is that objects of experience are required in order to make sense of certain features of our talk about experience, including, in particular, the following. (i) Simple attributions of experience, e.g., ‘Rod is experiencing an oddity that is not really square but in appearance it seems more than likely a square’, this seems to be relational. (ii) We appear to refer to objects of experience and to attribute properties to them, e.g., ‘The after-image that John experienced was certainly odd’. (iii) We appear to quantify ov er objects of experience, e.g., ‘Macbeth saw something that his wife did not see’.
The act/object analysis faces several problems concerning the status of objects of experiences. Currently the most common view is that they are sense-data -private mental entities that actually posses the traditional sensory qualities represented by the experiences of which they are the objects. But the very idea of an essentially private entity is suspect. Moreover, since an experience may apparently represent something as having a determinable property, e.g., redness, without representing it as having any subordinate determinate property, e.g., any specific shade of red, a sense-datum may actually have a determinate property subordinate to it. Even more disturbing is that sense-data may have contradictory properties, since experiences can have contradictory contents. A case in point is the waterfall illusion: If you stare at a waterfall for a minute and then immediately fixate on a nearby rock, you are likely to have an experience of the rock’s moving upward while it remains in the same place. The sense-data theorist must either deny that there are such experiences or admit contradictory objects.
These problems can be avoided by treating objects of experience as properties. This, however, fails to do justice to the appearances, for experience seems not to present ‘us’ with properties embodied in individuals. The view that objects of experience is Meinongian objects accommodate this point. It is also attractive in as far as (1) it allows experiences to represent properties other than traditional sensory qualities, and (2) it allows for the identification of objects of experience and objects of perception in the case of experiences that constitute perception.
According to the act/object analysis of experience, every experience with content involves an object of experience to which the subject is related by an act of awareness (the event of experiencing that object). This is meant to apply not only to perceptions, which have material objects (whatever is perceived), but also to experiences like hallucinations and dream experiences, which do not. Such experiences none the less appear to represent something, and their objects are supposed to be whatever it is that they represent. Act/object theorists may differ on the nature of objects of experience, which have been treated as properties. Meinongian objects (which may not exist or have any form of being), and, more commonly private mental entities with sensory qualities. (The term ‘sense-data’ is now usually applied to the latter, but has also been used as a general term for objects of sense experiences, as in the work of G. E. Moore) Act/object theorists may also differ on the relationship between objects of experience and objects of perception. In terms of perception (of which we are ‘indirectly aware’) are always distinct from objects of experience (of which we are ‘directly aware’). Meinongian, however, may treat objects of perception as existing objects of experience. But sense-datum theorists must either deny that there are such experiences or admit contradictory objects. Still, most philosophers will feel that the Meinongian’s acceptance of impossible objects is too high a price to pay for these benefits.
A general problem for the act/object analysis is that the question of whether two subjects are experiencing one and the same thing (as opposed to having exactly similar experiences) appears to have an answer only on the assumption that the experiences concerned are perceptions with material objects. But in terms of the act/object analysis the question must have an answer even when this condition is not satisfied. (The answer is always negative on the sense-datum theory; it could be positive on other versions of the act/object analysis, depending on the facts of the case.)
In view of the above problems, the case for the act/object analysis should be reassessed. The phenomenological argument is not, on reflection, convincing, for it is easy enough to grant that any experience appears to present ‘us’ with an object without accepting that it actually does. The semantic argument is more impressive, but is none the less answerable. The seemingly relational structure of attributions of experience is a challenge dealt with below in connection with the adverbial theory. Apparent reference to and quantification over objects of experience can be handled by analysing them as reference to experiences themselves and quantification over experiences tacitly typed according to content. Thus, ‘The after-image that John experienced was colourfully appealing’ becomes ‘John’s after-image experience was an experience of colour’, and ‘Macbeth saw something that his wife did not see’ becomes ‘Macbeth had a visual experience that his wife did not have’.
Pure cognitivism attempts to avoid the problems facing the act/object analysis by reducing experiences to cognitive events or associated disposition, e.g., Susy’s experience of a rough surface beneath her hand might be identified with the event of her acquiring the belief that there is a rough surface beneath her hand, or, if she does not acquire this belief, with a disposition to acquire it that has somehow been blocked.
This position has attractions. It does full justice to the cognitive contents of experience, and to the important role of experience as a source of belief acquisition. It would also help clear the way for a naturalistic theory of mind, since there seems to be some prospect of a physicalist/functionalist account of belief and other intentional states. But pure cognitivism is completely undermined by its failure to accommodate the fact that experiences have a felt character that cannot be reduced to their content, as aforementioned.
The adverbial theory is an attempt to undermine the act/object analysis by suggesting a semantic account of attributions of experience that does not require objects of experience. Unfortunately, the oddities of explicit adverbializations of such statements have driven off potential supporters of the theory. Furthermore, the theory remains largely undeveloped, and attempted refutations have traded on this. It may, however, be founded on sound basis intuitions, and there is reason to believe that an effective development of the theory (which is merely hinting at) is possible.
The relevant intuitions are (1) that when we say that someone is experiencing ‘an A’, or has an experience ‘of an A’, we are using this content-expression to specify the type of thing that the experience is especially apt to fit, (2) that doing this is a matter of saying something about the experience itself (and maybe about the normal causes of like experiences), and (3) that it is no-good of reasons to posit of its position to presuppose that of any involvements, is that its descriptions of an object in which the experience is. Thus the effective role of the content-expression in a statement of experience is to modify the verb it compliments, not to introduce a special type of object.
Perhaps, the most important criticism of the adverbial theory is the ‘many property problem’, according to which the theory does not have the resources to distinguish between, e.g.,
(1) Frank has an experience of a brown triangle
and:
(2) Frank has an experience of brown and an experience of a triangle.
Which is entailed by (1) but does not entail it. The act/object analysis can easily accommodate the difference between (1) and (2) by claiming that the truth of (1) requires a single object of experience that is both brown and triangular, while that of the (2) allows for the possibility of two objects of experience, one brown and the other triangular, however, (1) is equivalent to:
(1*) Frank has an experience of something’s being both brown and triangular.
And (2) is equivalent to:
(2*) Frank has an experience of something’s being brown and an experience of something’s being triangular,
and the difference between these can be explained quite simply in terms of logical scope without invoking objects of experience. The Adverbialists may use this to answer the many-property problem by arguing that the phrase ‘a brown triangle’ in (1) does the same work as the clause ‘something’s being both brown and triangular’ in (1*). This is perfectly compatible with the view that it also has the ‘adverbial’ function of modifying the verb ‘has an experience of’, for it specifies the experience more narrowly just by giving a necessary condition for the satisfaction of the experience (the condition being that there are something both brown and triangular before Frank).
A final position that should be mentioned is the state theory, according to which a sense experience of an ‘A’ is an occurrent, non-relational state of the kind that the subject would be in when perceiving an ‘A’. Suitably qualified, this claim is no doubt true, but its significance is subject to debate. Here it is enough to remark that the claim is compatible with both pure cognitivism and the adverbial theory, and that state theorists are probably best advised to adopt adverbials as a means of developing their intuitions.
Yet, clarifying sense-data, if taken literally, is that which is given by the senses. But in response to the question of what exactly is so given, sense-data theories posit private showings in the consciousness of the subject. In the case of vision this would be a kind of inner picture show which itself only indirectly represents aspects of the external world that has in and of itself a worldly representation. The view has been widely rejected as implying that we really only see extremely thin coloured pictures interposed between our mind’s eye and reality. Modern approaches to perception tend to reject any conception of the eye as a camera or lense, simply responsible for producing private images, and stress the active life of the subject in and of the world, as the determinant of experience.
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