We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the "determination rule", so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization of the different types of dependency relations defined in database theory. Specifically, we define determination as a relation between schemata (...) of first order logic that have two kinds of free variables: (1) object variables and (2) what we call "polar" variables, which hold the place of truth values. Determination rules facilitate sound rule inference and valid conclusions projected by analogy from single instances, without implying what the conclusion should be prior to an inspection of the instance. They also provide a way to specify what information is sufficiently relevant to decide a question, prior to knowledge of the answer to the question. (shrink)

This paper defines the form of prior knowledge that is required for sound inferences by analogy and single-instance generalizations, in both logical and probabilistic reasoning. In the logical case, the first order determination rule defined in Davies (1985) is shown to solve both the justification and non-redundancy problems for analogical inference. The statistical analogue of determination that is put forward is termed 'uniformity'. Based on the semantics of determination and uniformity, a third notion of "relevance" is defined, both (...) logically and probabilistically. The statistical relevance of one function in determining another is put forward as a way of defining the value of information: The statistical relevance of a function F to a function G is the absolute value of the change in one's information about the value of G afforded by specifying the value of F. This theory provides normative justifications for conclusions projected by analogy from one case to another, and for generalization from an instance to a rule. The soundness of such conclusions, in either the logical or the probabilistic case, can be identified with the extent to which the corresponding criteria (determination and uniformity) actually hold for the features being related. (shrink)

In this essay we collect and put together a number of ideas relevant to the under- standing of the phenomenon of creativity, confining our considerations mostly to the domain of cognitive psychology while we will, on a few occasions, hint at neuropsy- chological underpinnings as well. In this, we will mostly focus on creativity in science, since creativity in other domains of human endeavor have common links with scientific creativity while differing in numerous other specific respects. We begin by briefly (...) introducing a few basic notions relating to cognition, among which the notion of ‘concepts’ is of basic relevance. The myriads of concepts lodged in our mind constitute a ‘conceptual space’ of an enormously complex structure, where con- cepts are correlated by beliefs that are themselves made up of concepts and are as- sociated with emotions. The conceptual space, moreover, is perpetually in a state of dynamic evolution that is once again of a complex nature. A major component of the dynamic evolution is made up of incessant acts of inference, where an inference occurs essentially by means of a succession of correlations among concepts set up with beliefs and heuristics, the latter being beliefs of a special kind, namely, ones relatively free of emotional associations and possessed of a relatively greater degree of justification. Beliefs, along with heuristics, have been described as the ‘mind’s software’, and con- stitute important cognitive components of the self-linked psychological resources of an individual. The self is the psychological engine driving all our mental and physical activity, and is in a state of ceaseless dynamics resulting from one’s most intimate ex- periences of the world accumulating in the course of one’s journey through life. Many of our psychological resources are of a dual character, having both a self-linked and a shared character, the latter being held in common with larger groups of people and imbibed from cultural inputs. We focus on the privately held self-linked beliefs of an individual, since these are presumably of central relevance in making possible inductive inferences – ones in which there arises a fundamental need of adopting a choice or making a decision. Beliefs, decisions, and inferences, all have the common link to the self of an individual and, in this, are fundamentally analogous to free will, where all of these have an aspect of non-determinism inherent in them. Creativity involves a major restructuring of the conceptual space where a sustained inferential process eventually links remote conceptual domains, thereby opening up the possibility of a large number of new correlations between remote concepts by a cascading process. Since the process of inductive inference depends crucially on de- cisions at critical junctures of the inferential chain, it becomes necessary to examine the basic mechanism underlying the making of decisions. In the framework that we attempt to build up for the understanding of scientific creativity, this role of decision making in the inferential process assumes central relevance. With this background in place, we briefly sketch the affect theory of decisions. Affect is an innate system of response to perceptual inputs received either from the exter- nal world or from the internal physiological and psychological environment whereby a positive or negative valence gets associated with a perceptual input. Almost every sit- uation faced by an individual, even one experienced tacitly, i.e., without overt aware-ness, elicits an affective response from him, carrying a positive or negative valence that underlies all sorts of decision making, including ones carried out unconsciously in inferential processes. Referring to the process of inferential exploration of the conceptual space that gener- ates the possibility of correlations being established between remote conceptual do- mains, such exploration is guided and steered at every stage by the affect system, analogous to the way a complex computer program proceeds through junctures where the program ascertains whether specified conditions are met with by way of generating appropriate numerical values – for instance, the program takes different routes, depending on whether some particular numerical value turns out to be positive or negative. The valence generated by the affect system in the process of adoption of a choice plays a similar role which therefore is of crucial relevance in inferential processes, especially in the exploration of the conceptual space where remote domains need to be linked up – the affect system produces a response along a single value dimension, resembling a number with a sign and a magnitude. While the affect system plays a guiding role in the exploration of the conceptual space, the process of exploration itself consists of the establishment of correlations between concepts by means of beliefs and heuristics, the self-linked ones among the latter having a special role in making possible the inferential journey along alternative routes whenever the shared rules of inference become inadequate. A successful access to a remote conceptual domain, necessary for the creative solution of a standing problem or anomaly – one that could not be solved within the limited domain hitherto accessed – requires a phase of relatively slow cumulative search and then, at some stage, a rapid cascading process when a solution is in sight. Representing the conceptual space in the form of a complex network, the overall process can be likened to one of self-organized criticality commonly observed in the dynamical evolution of complex systems. In order that inferential access to remote domains may actually be possible, it is necessary that restrictions on the exploration process – necessary for setting the context in ordinary instances of inductive inference – be relaxed and a relatively free exploration in a larger conceptual terrain be made possible. This is achieved by the mind going into the default mode, where external constraints – ones imposed by shared beliefs and modes of exploration – are made inoperative. While explaining all these various aspects of the creative process, we underline the supremely important role that analogy plays in it. Broadly speaking, analogy is in the nature of a heuristic, establishing correlations between concepts. However, analo- gies are very special in that these are particularly effective in establishing correlations among remote concepts, since analogy works without regard to the contiguity of the concepts in the conceptual space. In establishing links between concepts, analogies have the power to light up entire terrains in the conceptual space when a rapid cas- cading of fresh correlations becomes possible. The creative process occurs within the mind of a single individual or of a few closely collaborating individuals, but is then continued by an entire epistemic community, eventually resulting in a conceptual revolution. Such conceptual revolutions make pos- sible the radical revision of scientific theories whereby the scope of an extant theory is broadened and a new theoretical framework makes its appearance. The emerging theory is characterized by a certain degree of incommensurability when compared with the earlier one – a feature that may appear strange at first sight. But incommen- surability does not mean incompatibility and the apparently contrary features of the relation between the successive theories may be traced to the multi-layered structureof the conceptual space where concepts are correlated not by means of single links but by multiple ones, thereby generating multiple layers of correlation, among which some are retained and some created afresh in a conceptual restructuring. We conclude with the observation that creativity occurs on all scales. Analogous to correlations being set up across domains in the conceptual space and new domains being generated, processes with similar features can occur within the confines of a domain where a new layer of inferential links may be generated, connecting up sub- domains. In this context, insight can be looked upon as an instance of creativity within the confines of a domain of a relatively limited extent. (shrink)

Homeostatic property clusters (HPCs) are offered as a way of understanding natural kinds, especially biological species. I review the HPC approach and then discuss an objection by Ereshefsky and Matthen, to the effect that an HPC qua cluster seems ill-fitted as a description of a polymorphic species. The standard response by champions of the HPC approach is to say that all members of a polymorphic species have things in common, namely dispositions or conditional properties. I argue that this response fails. (...) Instances of an HPC kind need not all be similar in their exhibited properties. Instead, HPCs should instead be understood as unified by the underlying causal mechanism that maintains them. The causal mechanism can both produce and explain some systematic differences between a kind’s members. An HPC kind is best understood not as a single cluster of properties maintained in stasis by causal forces, but as a complex of related property clusters kept in relation by an underlying causal process. This approach requires recognizing that taxonomic systems serve both explanatory and inductive purposes. (shrink)

Aristotle said that induction (epagōgē) is a proceeding from particulars to a universal, and the definition has been conventional ever since. But there is an ambiguity here. Induction in the Scholastic and the (so-called) Humean tradition has presumed that Aristotle meant going from particular statements to universal statements. But the alternate view, namely that Aristotle meant going from particular things to universal ideas, prevailed all through antiquity and then again from the time of Francis Bacon until the mid-nineteenth (...) century. Recent scholarship is so steeped in the first-mentioned tradition that we have virtually forgotten the other. In this essay McCaskey seeks to recover that alternate tradition, a tradition whose leading theoreticians were William Whewell, Francis Bacon, Socrates, and in fact Aristotle himself. The examination is both historical and philosophical. The first part of the essay fills out the history. The latter part examines the most mature of the philosophies in the Socratic tradition, specifically Bacon’s and Whewell’s. After tracing out this tradition, McCaskey shows how this alternate view of induction is indeed employed in science, as exemplified by several instances taken from actual scientific practice. In this manner, McCaskey proposes to us that the Humean problem of induction is merely an artifact of a bad conception of induction and that a return to the Socratic conception might be warranted. (shrink)

Under what conditions does machine learning (ML) model opacity inhibit the possibility of explaining and understanding phenomena? In this article, I argue that nonepistemic values give shape to the ML opacity problem even if we keep researcher interests fixed. Treating ML models as an instance of doing model-based science to explain and understand phenomena reveals that there is (i) an external opacity problem, where the presence of inductive risk imposes higher standards on externally validating models, and (ii) an internal (...) opacity problem, where greater inductive risk demands a higher level of transparency regarding the inferences the model makes. (shrink)

As our epistemic ambitions grow, the common and scientific endeavours are becoming increasingly dependent on Machine Learning (ML). The field rests on a single experimental paradigm, which consists of splitting the available data into a training and testing set and using the latter to measure how well the trained ML model generalises to unseen samples. If the model reaches acceptable accuracy, an a posteriori contract comes into effect between humans and the model, supposedly allowing its deployment to target environments. (...) Yet the latter part of the contract depends on human inductive predictions or generalisations, which infer a uniformity between the trained ML model and the targets. The paper asks how we justify the contract between human and machine learning. It is argued that the justification becomes a pressing issue when we use ML to reach ‘elsewheres’ in space and time or deploy ML models in non-benign environments. The paper argues that the only viable version of the contract can be based on optimality (instead of on reliability which cannot be justified without circularity) and aligns this position with Schurz’s optimality justification. It is shown that when dealing with inaccessible/unstable ground-truths (‘elsewheres’ and non-benign targets), the optimality justification undergoes a slight change, which should reflect critically on our epistemic ambitions. Therefore, the study of ML robustness should involve not only heuristics that lead to acceptable accuracies on testing sets. The justification of human inductive predictions or generalisations about the uniformity between ML models and targets should be included as well. Without it, the assumptions about inductive risk minimisation in ML are not addressed in full. (shrink)

The orthodox view about sensitivity and induction has it that beliefs formed via induction are insensitive. Since inductive knowledge is highly plausible, this problem is usually regarded as a reductio argument against sensitivity accounts of knowledge. Some adherents of sensitivity defend sensitivity against this objection, for example by considering backtracking interpretations of counterfactuals. All these extant views about sensitivity and induction have to be revised, since the problem of sensitivity and induction is a different one. Regardless (...) of whether we allow backtracking interpretations of counterfactuals, some instances of induction yield insensitive beliefs whereas others yield sensitive ones. These results are too heterogenous for providing a plausible sensitivity-account of inductive knowledge. Induction remains a serious problem for sensitivity accounts of knowledge. (shrink)

We are often justified in acting on the basis of evidential confirmation. I argue that such evidence supports belief in non-quantificational generic generalizations, rather than universally quantified generalizations. I show how this account supports, rather than undermines, a Bayesian account of confirmation. Induction from confirming instances of a generalization to belief in the corresponding generic is part of a reasoning instinct that is typically (but not always) correct, and allows us to approximate the predictions that formal epistemology would make.

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

An extract from Williams' The Ground of Induction (1947): "The sober amateur who takes the time to follow recent philosophical discussion will hardly resist the impression that much of it, in its dread of superstition and dogmatic reaction, has been oriented purposely toward skepticism: that a conclusion is admired in proportion as it is skeptical; that a jejune argument for skepticism will be admitted where a scrupulous defense of knowledge is derided or ignored; that an affirmative theory is a (...) mere annoyance to be stamped down as quickly as possible to a normal level of denial and defeat. It is an age which most admires the man who, as somebody has said, 'has a difficulty for every solution'. Whether or not this judgment is fair, however, it is safe to say, with Whitehead, that 'the theory of induction is the despair of philosophy - and yet all our activities are based upon it'. [A.N. Whitehead, Science and the Modern World (New York, 1925, p. 35] So prodigious a theoretical contretemps cannot remain a tempest in the professors' teapot. The news that no foundation is discoverable for the procedures of empirical intelligence, and still more the proclaimed discovery that there is no foundation, and still more the complacency which recommends that we reconcile ourselves to the lack, condemn the problem as a 'pseudoproblem', and proceed by irrational faith or pragmatic postulate, will slowly shatter civilized life and thought, to a degree which will make the modernist's loss of confidence in Christian supernaturalism, so often cited as the ultimate in spiritual cataclysms, seem a minor vicissitude. The demand that rational man adjust himself to a somewhat bleaker universe than he once hoped for is only one large and picturesque instance of the sort of re-orientation which inductive intelligence, in its very nature,continually imposes, and well within the proved capacities of human reason and good-will.. (shrink)

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

Within ordinary ---unitary--- quantum mechanics there exist global protocols that allow to verify that no definite event ---an outcome to which a probability can be associated--- occurs. Instead, states that start in a coherent superposition over possible outcomes always remain as a superposition. We show that, when taking into account fundamental errors in measuring length and time intervals, that have been put forward as a consequence of a conjunction of quantum mechanical and general relativity arguments, there are instances in which (...) such global protocols no longer allow to distinguish whether the state is in a superposition or not. All predictions become identical as if one of the outcomes occurs, with probability determined by the state. We use this as a criteria to define events, as put forward in the Montevideo Interpretation of Quantum Mechanics. We analyze in detail the occurrence of events in the paradigmatic case of a particle in a superposition of two different locations. We argue that our approach provides a consistent single-world picture of the universe, thus allowing an economical way out of the limitations imposed by a recent theorem by Frauchiger and Renner showing that having a self-consistent single-world description of the universe is incompatible with quantum theory. In fact, the main observation of this paper may be stated as follows: If quantum mechanics is extended to include gravitational effects to a QG theory, then QG, S, and C are satisfied. (shrink)

Medical diagnosis has been traditionally recognized as a privileged field of application for so called probabilistic induction. Consequently, the Bayesian theorem, which mathematically formalizes this form of inference, has been seen as the most adequate tool for quantifying the uncertainty surrounding the diagnosis by providing probabilities of different diagnostic hypotheses, given symptomatic or laboratory data. On the other side, it has also been remarked that differential diagnosis rather works by exclusion, e.g. by modus tollens, i.e. deductively. By drawing on (...) a case history, this paper aims at clarifying some points on the issue. Namely: 1) Medical diagnosis does not represent, strictly speaking, a form of induction, but a type, of what in Peircean terms should be called ‘abduction’ (identifying a case as the token of a specific type); 2) in performing the single diagnostic steps, however, different inferential methods are used for both inductive and deductive nature: modus tollens, hypothetical-deductive method, abduction; 3) Bayes’ theorem is a probabilized form of abduction which uses mathematics in order to justify the degree of confidence which can be entertained on a hypothesis given the available evidence; 4) although theoretically irreconcilable, in practice, both the hypothetical- deductive method and the Bayesian one, are used in the same diagnosis with no serious compromise for its correctness; 5) Medical diagnosis, especially differential diagnosis, also uses a kind of “probabilistic modus tollens”, in that, signs (symptoms or laboratory data) are taken as strong evidence for a given hypothesis not to be true: the focus is not on hypothesis confirmation, but instead on its refutation [Pr (¬ H/E1, E2, …, En)]. Especially at the beginning of a complicated case, odds are between the hypothesis that is potentially being excluded and a vague “other”. This procedure has the advantage of providing a clue of what evidence to look for and to eventually reduce the set of candidate hypotheses if conclusive negative evidence is found. 6) Bayes’ theorem in the hypothesis-confirmation form can more faithfully, although idealistically, represent the medical diagnosis when the diagnostic itinerary has come to a reduced set of plausible hypotheses after a process of progressive elimination of candidate hypotheses; 7) Bayes’ theorem is however indispensable in the case of litigation in order to assess doctor’s responsibility for medical error by taking into account the weight of the evidence at his disposal. (shrink)

The idea of the uniformity of nature, as a solution to the problem of induction, has at least two contemporary versions: natural kinds and natural necessity. Then there are at least three alternative ontological ideas addressing the problem of induction. In this paper, I articulate how these ideas are used to justify the practice of inductive inference, and compare them, in terms of their applicability, to see whether each of them is preferred in addressing the problem of (...) class='Hi'>induction. Given the variety of contexts in which inductive inferences are made, from natural science to social science and to everyday thinking, I suggest that no singular idea is absolutely preferred, and a proper strategy is probably to welcome the plurality of ideas helpful to induction, and to take pragmatic considerations into account, in order to judge in every single case. (shrink)

In this paper I wish to connect the recent debate in the philosophy of quantum mechanics concerning the nature of the wave function to the historical debate in the philosophy of science regarding the tenability of scientific realism. Being realist about quantum mechanics is particularly challenging when focusing on the wave function. According to the wave function ontology approach, the wave function is a concrete physical entity. In contrast, according to an alternative viewpoint, namely the primitive ontology approach, the wave (...) function does not represent physical entities. In this paper, I argue that the primitive ontology approach can naturally be interpreted as an instance of the so-called ‘explanationism’ realism, which has been proposed as a response to the pessimistic-meta induction argument against scientific realism. If my arguments are sound, then one could conclude that: (1) contrarily to what is commonly though, if explanationism realism is a good response to the pessimistic-meta induction argument, it can be straightforwardly extended also to the quantum domain; (2) the primitive ontology approach is in better shape than the wave function ontology approach in resisting the pessimistic-meta induction argument against scientific realism. (shrink)

The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The (...) relevant mathematical structure is Hilbert arithmetic in a wide sense, in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem. (shrink)

There is a straightforward view of perception that has not received adequate consideration because it requires us to rethink basic assumptions about the objects of perception. In this paper, I develop a novel account of these objects—the sensible qualities—which makes room for the straightforward view. I defend two primary claims. First, I argue that qualities like color and shape are “ontologically flexible” kinds. That is, their real definitions allow for both physical objects and mental entities to be colored or shaped. (...) Second, a single instance of these qualities can be attributed to more than one entity. Just as we attribute the same instance of a material property to a statue and to the clay that constitutes it, single instances of sensible qualities should be attributed both to the physical objects perceived and to the perceptual states that have those instances as their objects. (shrink)

In this paper, I argue against what I call “natural realism” about social kinds, the view according to which social categories have natural boundaries, independent of our thought. First, I draw a distinction between two different types of entity realism, one being about the existence of the entity, “ontological realism”, and the other one being about the direct mind-independence of the entity, “natural realism”. After endorsing ontological realism, I present the natural realist argument according to which there would be certain (...) social kinds, such as economic recessions and racism, even if we had no clue about their existence and nature. I claim that the argument fails insofar it mistakes the single instances for the kinds themselves. I then argue against natural realism by showing how the vagueness characterizing the boundaries of social kinds puts the realist in front of a dilemma: either she accepts the vagueness of these boundaries as ontic, a metaphysically problematic thesis, or she accepts that most or all social kinds remain unknown, an epistemologically problematic thesis. Thus, I argue that antirealism, according to which social kinds are constructed, is a better alternative to the realist account. (shrink)

This paper is about knowledge construction in music listening. It argues for an experiential approach to music cognition, stressing the dynamic-vectorial field of meaning rather than the symbolic field. Starting from the conceptual framework of deixis and indexical devices, it elaborates on the concept of pointing as a heuristic guide for sense-making which allows the listener to conceive of perceptual elements in terms of salience, valence and semantical weight. As such, the act of (mental) pointing can be predicative, either in (...) a nominalistic or processual way, giving a description of the temporal evolution of a situation as against episodic nominalizations that refer to just one single instance of the process. The latter, especially, are characterized by distancing and polarization between the listener and the music, allowing him/her to deal with the music also at a level of mental imagery and to construct a mental or cognitive map of its unfolding. (shrink)

Peter Godfrey-Smith writes in the section 3.3 “The Ravens Problem” of his book “Theory and Reality” [chapter “Induction and Confirmation”]: “First, the logical empiricists were concerned to deal with the case where generalizations cover an infinite number of instances. In that case, as we see each raven we are not reducing the number of ways in which the hypothesis might fail”. Infinite sets and finite sets have different properties and follow different rules. For example: let’s call “bag X” a (...) specific bag that contains 90 marbles; the generalization A “All marbles in bag X are red” covers a finite number of instances. By contrast, the generalization AE “All things that are not red are not marbles in bag X” covers an infinite number of instances. The propositions A and AE are logically equivalent, but there is an asymmetry due to the fact that A can only have a finite number of instances (since the set of the marbles contained in bag X is a finite set). Because of the aforementioned asymmetry, even though A and AE are logically equivalent propositions, it is wrong to equate an instance of A with an instance of AE. Another example involving a finite set: let’s call “barrique X” a certain 205-liter (54.1553 US gal) barrique. In the following generalization, the expression "all minerals" should not be understood as "all types of minerals", but should be understood literally as "all minerals". B “All minerals are in barrique X”. BE “All objects that are not in barrique X are not minerals”. Of course, a 205-litre barrique cannot contain an infinite number of minerals; the set of objects contained in barrique X is a finite set: therefore in the generalization B we refer to a set that is assumed to be an infinite set (the set of minerals) and to a set (the finite set of minerals contained in barrique X) that is not assumed to be an infinite set. By contrast, in the generalization BE we refer to two sets that are assumed to be infinite sets (the set of all objects that are not contained in barrique X and the set of all objects that are not minerals). Therefore, although B and BE are logically equivalent propositions, an instance of BE cannot be equivalent to an instance of B. Now, let’s analyze the following generalizations. C “All the elements of the set of ravens are elements of the set of black ravens”. CE “All the things that are not elements of the set of black ravens are not elements of the set of ravens”. It is assumed that the number of ravens is infinite, but it is not assumed that the number of black ravens is infinite: that the number of black ravens is infinite is only a hypothesis (for which confirmation is sought), it cannot be assumed as true that the number of black ravens is infinite. Therefore, in the generalization C we refer to a set that is assumed to be an infinite set (the set of ravens) and to a set (the set of black ravens) that is not assumed to be an infinite set. By contrast, in the generalization CE we refer to two sets that are assumed to be infinite sets (the set of all objects that are not elements of the set of black ravens and the set of all objects that are not elements of the set of ravens). Someone could argue that in the generalizations C “All the elements of the set of ravens are elements of the set of black ravens” and CE “All the things that are not elements of the set of black ravens are not elements of the set of ravens” only the set of ravens is assumed to be infinite: but even in this case an asymmetry would remain because C “ All the elements of the set of ravens are elements of the set of black ravens” refers to a set (the set of ravens) that is assumed to be an infinite set and to a set (the set of black ravens) that is not assumed to be infinite; by contrast, CE “All the things that are not elements of the set of black ravens are not elements of the set of ravens” in this case would refer to two sets that are not assumed to be infinite sets. Because of the aforementioned asymmetries, an instance of C cannot be equivalent to an instance of CE. -/- -/- . (shrink)

Inductively defined structures are ubiquitous in mathematics; their specification is unambiguous and their properties are powerful. All fields of mathematical logic feature these structures prominently: the formula of a language, the set of theorems, the natural numbers, the primitive recursive functions, the constructive number classes and segments of the cumulative hierarchy of sets. -/- This dissertation gives a mathematical characterization of a species of inductively defined structures, called accessible domains, which include all of the above examples except the set of (...) theorems. The concept of an accessible domain comes from Wilfried Sieg's analysis of proof-theoretic practices, starting with his dissertation. In particular, he noticed the special epistemological character of elements of an accessible domain: they can always be uniquely identified with their build-up. Generally, the unique build-up of elements justifies the principles of induction and recursion. -/- I use category theory to give an abstract characterization of accessible domains. I claim that accessible domains are all instances of initial algebras for endofunctors. Grounded in the historical roots of Sieg's discussions, this dissertation shows how the properties of initial algebras for endofunctors and accessible domains coincide in a satisfying and natural way. -/- Filling out this characterization, I show how important examples of accessible domains fit into this broad characterization. I first characterize some accessible domains by relatively simple functors (e.g. finite, polynomial, those that preserve certain colimits) where we can see how iterating the functor can produce the accessible domain. Then I describe accessible domains that result from more involved specifications (e.g. ordinals and segments of the cumulative hierarchies associated with CZF, IZF, and ZF) by relying heavily on algebraic set theory. I end with a discussion of some of the methodological features of category theory in particular that helped characterize accessible domains. (shrink)

Imagine two urns, each with a thousand beads - in one all the beads are blue while in the other only one of the thousand is blue. If one of these urns is pushed forward (based on the toss of a fair coin) and the single bead then randomly drawn from it is blue, we must infer that it is a thousand times more probable that the urn pushed forward is the purely blue one. The hypothesis that this was (...) instead the urn with only one blue bead would require that the occurrence of the evidence, the blue bead being drawn, was something improbable - and it is improbable that something improbable is what has occurred. Next consider an example of only one urn with no prior description. By the same reasoning as above, if all the first beads randomly drawn are blue, it is becoming more and more probable that the beads in the urn are generally blue. (Otherwise something improbable would be happening in another colour not appearing; and what’s improbable is improbable.) It is therefore probable also that the next bead drawn will be blue. This is induction. As Hume would have said, we could not know a priori, given this evidence, that the next bead will be blue. But, as he overlooked, we can know a priori, given this evidence, that it is probable that the next bead will be blue. In neither urn example has the belief regarding the beads been formed as a Humean habit of expectation after many observations of beads. (In the first case there is only one observation. The second could be modified to have all the beads drawn out at once.) Rather the belief is a product of a priori reasoning about probability. Next imagine that a coin has been tossed a thousand times and landed heads every time. There was a fair and a loaded coin. According to the same reasoning, it is overwhelmingly more probable that the coin used was the loaded one. For that the fair coin had so landed is most improbable. The hypothesis that there is no external world makes the orderliness in my current experience improbable - much like getting all heads with a fair coin. (Uncaused sensation would most probably be chaotic.) The most probable hypothesis is that of things like those we believe in causing this orderliness - as the coin’s being loaded would have caused all heads. The hypothesis that my experience has been made to take this pattern by a Cartesian malicious demon or by scientists controlling my brain in a vat can only falsely seem to make the character of the experience probable by sneaking in an inherently improbable ad hoc specification that this sort of pattern of experience was that which they were aiming at producing - like an ad hoc specification that the fair coin was one that by chance landed heads all thousand times. We may thus reject such hypotheses as improbable. So this is the problem of induction solved and scepticism answered through a priori reasoning. (shrink)

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

The paper takes a novel approach to a classic problem—Hempel’s Raven Paradox. A standard approach to it supposes the solution to consist in bringing our inductive logic into “reflective equilibrium” with our intuitive judgements about which inductive inferences we should license. This approach leaves the intuitions as a kind of black box and takes it on faith that, whatever the structure of the intuitions inside that box might be, it is one for which we can construct an isomorphic formal edifice, (...) a system of inductive logic. By popping open the box we can see whether that faith is misplaced. I aim, therefore, to characterize our pre-theoretical, intuitive understanding of generalizations like “ravens are black” and argue that, intuitively, we take them to mean, for instance: “ravens are black by some indeterminate yet characteristic means.” I motivate and explicate this formulation and bring it to bear on Hempel’s Problem. (shrink)

This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick (...) out a point on a continuum, for instance using a roulette wheel or by flipping a countable infinity of fair coins, it follows, given the axioms of ZFC, that there are many different cardinalities between countable infinity and the cardinality of the continuum. (shrink)

The applicability of Bayesian conditionalization in setting one’s posterior probability for a proposition, α, is limited to cases where the value of a corresponding prior probability, PPRI(α|∧E), is available, where ∧E represents one’s complete body of evidence. In order to extend probability updating to cases where the prior probabilities needed for Bayesian conditionalization are unavailable, I introduce an inference schema, defeasible conditionalization, which allows one to update one’s personal probability in a proposition by conditioning on a proposition that represents a (...) proper subset of one’s complete body of evidence. While defeasible conditionalization has wider applicability than standard Bayesian conditionalization (since it may be used when the value of a relevant prior probability, PPRI(α|∧E), is unavailable), there are circumstances under which some instances of defeasible conditionalization are unreasonable. To address this difficulty, I outline the conditions under which instances of defeasible conditionalization are defeated. To conclude the article, I suggest that the prescriptions of direct inference and statistical induction can be encoded within the proposed system of probability updating, by the selection of intuitively reasonable prior probabilities. (shrink)

I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. -/- There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is (...) countably infinite, then the property of being a tautology is \Pi^1_1-complete. But third, it is only granted the assumption of countability that the class of tautologies is \Sigma_1-definable in set theory. -/- Wittgenstein famously urges that logical relationships must show themselves in the structure of signs. He also urges that the size of the universe cannot be prejudged. The results of this paper indicate that there is no single way in which logical relationships could be held to make themselves manifest in signs, which does not prejudge the number of objects. (shrink)

We characterize those identities and independencies which hold for all probability functions on a unary language satisfying the Principle of Atom Exchangeability. We then show that if this is strengthen to the requirement that Johnson's Sufficientness Principle holds, thus giving Carnap's Continuum of inductive methods for languages with at least two predicates, then new and somewhat inexplicable identities and independencies emerge, the latter even in the case of Carnap's Continuum for the language with just a single predicate.

There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as the length of the shortest program producing it [1]. The second, Shannon information, takes events as belonging to ensembles and quantifies the information resulting from observing the given event in terms of the number of alternate events that have been ruled out [2]. The third, statistical learning (...) theory, has introduced measures of capacity that control (in part) the expected risk of classifiers [3]. These capacities quantify the expectations regarding future data that learning algorithms embed into classifiers. Solomonoff and Hutter have applied algorithmic information to prove remarkable results on universal induction. Shannon information provides the mathematical foundation for communication and coding theory. However, both approaches have shortcomings. Algorithmic information is not computable, severely limiting its practical usefulness. Shannon information refers to ensembles rather than actual events: it makes no sense to compute the Shannon information of a single string – or rather, there are many answers to this question depending on how a related ensemble is constructed. Although there are asymptotic results linking algorithmic and Shannon information, it is unsatisfying that there is such a large gap – a difference in kind – between the two measures. This note describes a new method of quantifying information, effective information, that links algorithmic information to Shannon information, and also links both to capacities arising in statistical learning theory [4, 5]. After introducing the measure, we show that it provides a non-universal analog of Kolmogorov complexity. We then apply it to derive basic capacities in statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. A nice byproduct of our approach is an interpretation of the explanatory power of a learning algorithm in terms of the number of hypotheses it falsifies [6], counted in two different ways for the two capacities. We also discuss how effective information relates to information gain, Shannon and mutual information. (shrink)

In Tulving’s initial characterization, episodic memory was one of multiple memory systems. It was postulated, in pursuit of explanatory depth, as displaying proprietary operations, representations, and substrates such as to explain a range of cognitive, behavioural, and experiential phenomena. Yet the subsequent development of this research program has, paradoxically, introduced surprising doubts about the nature, and indeed existence, of episodic memory. On dominant versions of the ‘common system’ view, on which a single simulation system underlies both remembering and imagining, (...) there are no processes unique to memory to support robust generalizations with inductive potential. Eliminativism about episodic memory seems to follow from the claim that it has no dedicated neurocognitive system of its own. After identifying this under-noticed threat, we push back against modern eliminativists by surveying recent evidence that still indicates specialized mechanisms, computations, and representations that are distinctly mnemic in character. We argue that contemporary realists about episodic memory can retain lessons of the common system approach while resisting the further move to eliminativism. (shrink)

The standard rule of single privative modification replaces privative modifiers by Boolean negation. This rule is valid, for sure, but also simplistic. If an individual a instantiates the privatively modified property (MF) then it is true that a instantiates the property of not being an F, but the rule fails to express the fact that the properties (MF) and F have something in common. We replace Boolean negation by property negation, enabling us to operate on contrary rather than contradictory (...) properties. To this end, we apply our theory of intensional essentialism, which operates on properties (intensions) rather than their extensions. We argue that each property F is necessarily associated with an essence, which is the set of the so-called requisites of F that jointly define F. Privation deprives F of some but not all of its requisites, replacing them by their contradictories. We show that properties formed from iterated privatives, such as being an imaginary fake banknote, give rise to a trifurcation of cases between returning to the original root property or to a property contrary to it or being semantically undecidable for want of further information. In order to determine which of the three forks the bearers of particular instances of multiply modified properties land upon we must examine the requisites, both of unmodified and modified properties. Requisites underpin our presuppositional theory of positive predication. Whereas privation is about being deprived of certain properties, the assignment of requisites to properties makes positive predication possible, which is the predication of properties the bearers must have because they have a certain property formed by means of privation. (shrink)

Plato's _Republic_ divided subsequent study of justice in two, as a virtue of people and of institutions. Here, the start of a reunification is attempted. Justice is first understood personally as the virtuous mean between arrogance and servility, where just people properly respect themselves and others. Because justice requires that like cases be treated alike and self-respect is a special instance of respect generally, justice requires a single standard for self and others. In understanding justice in terms of (...) respect, structural analogies become apparent between “recognition” and “appraisal” respect, on the one hand, and Rawls' two principles of justice on the other. The present view is then compared to “social egalitarian” theories of justice and the essay concludes with a discussion of how mercy is related to justice and an explanation of why just people always look for reasons to mitigate blame and punishment but never to aggravate them. (shrink)

Logical and philosophical literature provides different classifications of reasoning. In the Polish literature on the subject, for instance, there are three popular ones accepted by representatives of the Lvov-Warsaw School: Jan Łukasiewicz, Tadeusz Czeżowski and Kazimierz Ajdukiewicz (Ajdukiewicz in Logika pragmatyczna [Pragmatic Logic]. PWN, Warsaw (1965, 2nd ed. 1974). Translated as: Pragmatic Logic. Reidel & PWN, Dordrecht, 1975). The author of this paper, having modified those classifications, distinguished the following types of reasoning: (1) deductive and (2) non-deductive, and additionally (...) two types of them in each of the two, depending on the manner of combining their premises with the conclusion through the relation of classical logical entailment. Consequently, the four types of reasoning: unilateral deductive (incl. its sub-types: deductive inference and proof), bilateral deductive (incl. complete induction), and reductive (incl. the sub-types: explanation and verification), logically nonvaluable (incl. inference by analogy, statistic inference), correspond to four operators of derivability. They are defined formally on the ground of Tarski’s axiomatic theory of deductive systems, by means of the consequence operation _Cn_ (Tarski in Monatshefte Math Phys 37:361–404, 1930a, C R Soc Sci Lett Vars 23:22–29, 1930b). Also, certain metalogical properties of these operators are given, as well as their relations with Tarski’s consequence operations \(Cn^+\) ( \(Cn^+ = Cn\) ) and dual consequences \(Cn^{-1}\) (Słupecki in Zeszyty Naukowe Uniwersytetu Wrocławskiego Seria B Nr 3:33–40, 1959, Słupecki et al. in Stud Log 29:76–123, 1971, Wybraniec-Skardowska, in: Wybraniec-Skardowska, Bryll (eds) Z badań nad teorią zdań odrzuconych [Studies in the Theory of Rejected Propositions], Series B, Studia i Monografie, Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Opole, 1969), and \(Cn^-\) (Wójcicki in Bull Sect Log 2(2):54–57, 1973)). (shrink)

Localism is the view that the unit of evaluation in the scientific realism debate is a single scientific discipline, sub-discipline, or claim, whereas individualism is the view that the unit of evaluation is a single scientific theory. Localism is compatible, while individualism is not, with a local pessimistic induction and a local selective induction. Asay presents several arguments to support localism and undercut globalism, according to which the unit of evaluation is the set of all scientific (...) disciplines. I argue that some of his arguments clash with localism as well as with globalism and support individualism, and that individualism goes hand in hand, while localism does not, with the basic rule of how to evaluate an argument. (shrink)

In addressing the question of what mental health is we might proceed as if there is a single phenomenon – mental health – denoted by a single overarching concept. The task, then, is to provide an informative analysis of this concept which applies to all and only instances of mental health, and which illuminates what it is to be mentally healthy. In contrast, mental health pluralism is the idea that there are multiple mental health phenomena denoted by multiple (...) concepts of mental health. Analysis and illumination of mental health may still be possible, but there isn’t a single phenomenon or concept to be analysed in addressing the question of what mental health is. The question of pluralism has been overlooked in the philosophy of mental health. The discussion to follow is an attempt to get us to take mental health pluralism seriously. To that end, in this essay I have three primary goals: (1) to give a precise account of what mental health pluralism is, (2) to show that the question of pluralism should not be neglected in debate about what mental health is, and (3) to argue for mental health pluralism. I also draw out some implications of this discussion for philosophy, science, and psychotherapy. (shrink)

The main thesis of this paper is that when we trust the results of scientific research, that trust is inevitably directed at least in part at collective bodies rather than at single researchers, and that accordingly, reasonable assessments of epistemic trustworthiness in science must attend to these collective bodies. In order to support this claim, I start by invoking the collaborative nature of most of today’s scientific research. I argue that the trustworthiness of a collaborative research group does not (...) supervene on the trustworthiness of its individual members and point out some specific problems for the assessment of epistemic trustworthiness that arise from the specific nature of today’s collaborative research. Next, I argue that the social diffusion of trustworthiness goes even further; we always also need an assessment of the trustworthiness of the respective research community as a whole. Communities, I claim, play an essential role in the epistemic quality management of science. To see why this role is indispensible, we have to appreciate the full complexity of determining what is desirable in a method of inquiry. The relevant features of a method include three different dimensions: the reliability of positive results, the reliability of negative results, and the method’s power. Every methodological choice involves a trade-off between these three dimensions. The right balance between them (the “distribution of inductive risks”, or DIR) depends on value judgments about the costs of false results and the benefits of correct ones. Conventional methodological standards of research communities impose constraints on admissible DIR and thereby harmonize the implicit value judgments. Trusting that the research community has set the limitations on DIR in a suitable way is thus always part of placing our trust in a scientific result. (shrink)

Consider a set of shuffled observations drawn from a fixed probability distribution over some instance domain. What enables learning of inductive generalizations which proceed from such a set of observations? The scenario is worthwhile because it epistemically characterizes most of machine learning. This kind of learning from observations is also inverse and ill-posed. What reduces the non-uniqueness of its result and, thus, its problematic epistemic justification, which stems from a one-to-many relation between the observations and many learnable generalizations? The (...) paper argues that this role belongs to any complexity regularization which satisfies Norton’s Material Theory of Induction (MTI) by localizing the inductive risk to facts in the given domain. A prime example of the localization is the Lottery Ticket Hypothesis (LTH) about overparameterized neural networks. The explanation of MTI’s role in complexity regularization of neural networks is provided by analyzing the stability of Empirical Risk Minimization (ERM), an inductive rule that controls the learning process and leads to an inductive generalization on the given set of observations. In cases where ERM might become asymptotically unstable, making the justification of the generalization by uniform convergence unavailable, LTH and MTI can be used to define a local stability. A priori, overparameterized neural networks are such cases and the combination of LTH and MTI can block ERM’s trivialization caused by equalizing the strengths of its inductive support for risk minimization. We bring closer the investigation of generalization in artificial neural networks and the study of inductive inference and show the division of labor between MTI and the optimality justifications (developed by Gerhard Schurz) in machine learning. (shrink)

A Wittgensteinian Way with Paradoxes examines how some of the classic philosophical paradoxes that have so puzzled philosophers over the centuries can be dissolved. Read argues that paradoxes such as the Sorites, Russell’s Paradox and the paradoxes of time travel do not, in fact, need to be solved. Rather, using a resolute Wittgensteinian ‘therapeutic’ method, the book explores how virtually all apparent philosophical paradoxes can be diagnosed and dissolved through examining their conditions of arising; to loosen their grip and therapeutically (...) liberate those philosophers suffering from them (including oneself). The book contrasts such paradoxes with real, ‘lived paradoxes’: paradoxes that are genuinely experienced outside of the philosopher’s study, in everyday life. Thus Read explores instances of lived paradox (such as paradoxes of self-hatred and of denial of other humans’ humanity) and the harm they can cause, psychically, morally or politically. These lived paradoxes, he argues, sometimes cannot be dissolved using a Wittgensteinian treatment. Moreover, in some cases they do not need to be: for some, such as the paradoxical practices of Zen Buddhism (and indeed of Wittgenstein himself), can in fact be beneficial. The book shows how, once philosophers’ paradoxes have been exorcized, real lived paradoxes can be given their due. (shrink)

In view of the philosophical problems that vex the debate on situated affectivity, it can seem wise to focus on simple cases. Accordingly, theorists often single out scenarios in which an individual employs a device in order to enhance their emotional experience, or to achieve new kinds of experience altogether, such as playing an instrument, going to the movies or sporting a fancy handbag. I argue that this narrow focus on cases that fit a ‘user/resource model’ tends to channel (...) attention away from more complex and also more problematic instances of situated affectivity. Among these are scenarios in which a social domain draws individuals into certain modes of affective interaction, often by way of attunement and habituation to affective styles and interaction patterns that are normative in the domain in question. This can lead to a phenomenon that is not so much ‘mind extension’ than ‘mind invasion’: affectivity is dynamically framed and modulated from without, often contrary to the prior orientations of the individuals in question. As an example, I discuss affective patterns prevalent in today’s corporate workplace. I claim that workplace affect sometimes contributes to what is effectively a ‘hack’ of employees’ subjectivity. (shrink)

The United States Fish and Wildlife Service in Alaska, USA, conducted a species status assessment for a petition to list the Alexander Archipelago wolf (Canis lupus ligoni) under the Endangered Species Act in 2020-2022. This federal undertaking could not be adequately prepared without including the knowledge of Indigenous People who have a deep cultural connection with the subspecies. Our objective is to communicate the authoritative expertise and voice of the Indigenous People who partnered on the project by demonstrating how their (...) knowledge contributed to the species status assessment. The Indigenous knowledge applied in the assessment is the cultural and intellectual property of those who have shared it. We employed rapid appraisal research to expeditiously develop a preliminary and qualitative understanding of Indigenous People's cultural and ecological knowledge of Alexander Archipelago wolves. We used semi-directed interviewing and inductive coding from grounded theory for text analysis. Indigenous knowledge contributed to the agency's understanding of the Alexander Archipelago wolf in Southeast Alaska and helped the agency with their classification decision. Indigenous research partners explained the rich cultural significance and position of wolves in Tlingit society and described human–wolf relationships and ecological interactions. The agency used a single-species assessment approach based in species ecology and conservation biology, whereas the Indigenous wolf experts applied a multi-species, community ecology approach based in a sociocultural context of balance and respect. The Indigenous wolf experts successfully addressed knowledge gaps identified by the agency. The partners were challenged by a short regulatory timeframe that did not allow for comprehensive study of Indigenous knowledge and constrained review and feedback by Indigenous experts. The United States Fish and Wildlife Service learned that its assessment framework was not designed to account for an Indigenous worldview. To level the playing field, the agency and Indigenous experts should discuss how to co-develop an assessment framework that equitably applies both perspectives. (shrink)

How does good combine with bad? Most creatures are neither so blessed as to only enjoy good nor so cursed as to only suffer bad. Rather, the good and bad they receive throughout their lives combine to produce their overall quality of life. But it’s not just whole lives that have combined good and bad. Many stretches within contain both positive and negative occurrences whose value is joined to form the overall quality of that span of time. In a (...) class='Hi'>single morning someone might wake up, brush their teeth, stub their toe groggily lumbering down the stairs, and have a sip of coffee that’s tasty but so hot they burn their tongue. These events are good and bad for them to various degrees, and their value comes together to form an overall value for them of that morning. A single moment, even, can have combined value from distinct pockets of good and bad that occur simultaneously. The tastiness of the coffee is good, but the pain of the heat is bad. They combine to form an overall value of the sipping moment – negative if the pain outweighed the flavor. Thus, wellbeing and illbeing combine. But how? How can someone rightly chastise themselves for sipping the overly hot coffee when it was, in fact, good because it was tasty? To pose the question starkly, a life can be bad, even so bad to not be worth living, and yet it can have many instances of good, where these goods are, in themselves, pure of any negativity. But how can good make something bad? (shrink)

We show that true colors as defined by Chevreul (1839) produce unsuspected simultaneous brightness induction effects on their immediate grey backgrounds when these are placed on a darker (black) general background surrounding two spatially separated configurations. Assimilation and apparent contrast may occur in one and the same stimulus display. We examined the possible link between these effects and the perceived depth of the color patterns which induce them as a function of their luminance contrast. Patterns of square-shaped inducers of (...) a single color (red, green, blue, yellow, or grey) were placed on background fields of a lighter and a darker grey, presented on a darker screen. Inducers were always darker on one side of the display and brighter on the other in a given trial. The intensity of the grey backgrounds varied between trials only. This permitted generating four inducer luminance contrasts, presented in random order, for each color. Background fields were either spatially separated or consisted of a single grey field on the black screen. Experiments were run under three environmental conditions: dark-adaptation, daylight, and rod-saturation after exposure to bright light. In a first task, we measured probabilities of contrast, assimilation, and no effect in a three-alternative forced-choice procedure (background appears brighter on the ‘left’, on the ‘right’ or the ‘same’). Visual adaptation and inducer contrast had no significant influence on the induction effects produced by colored inducers. Achromatic inducers produced significantly stronger contrast effects after dark-adaptation, and significantly stronger assimilation in daylight conditions. Grouping two backgrounds into a single one was found to significantly decrease probabilities of apparent contrast. Under the same conditions, we measured probabilities of the inducers to be perceived as nearer to the observer inducers. These, as predicted by Chevreul’s law of contrast, were determined by the luminance contrast of the inducers only, with significantly higher probabilities of brighter inducers to be seen as nearer, and a marked asymmetry between effects produced by inducers of opposite sign. Implications of these findings for theories which attempt to link simultaneous induction effects to the relative depth of object surfaces in the visual field are discussed. (shrink)

Answering a question formulated by Halbach (2009), I show that a disquotational truth theory, which takes as axioms all positive substitutions of the sentential T-schema, together with all instances of induction in the language with the truth predicate, is conservative over its syntactical base.

Philosophical treatments of natural kinds are embedded in two distinct projects. I call these the philosophy of science approach and the philosophy of language approach. Each is characterized by its own set of philosophical questions, concerns, and assumptions. The kinds studied in the philosophy of science approach are projectible categories that can ground inductive inferences and scientific explanation. The kinds studied in the philosophy of language approach are the referential objects of a special linguistic category—natural kind terms—thought to refer directly. (...) Philosophers may hope for a unified account addresses both sets of concerns. This paper argues that this cannot be done successfully. No single account can satisfy both the semantic objectives of the philosophy of language approach and the explanatory projects of the philosophy of science approach. After analyzing where the tensions arise, I make recommendations about assumptions and projects that are best abandoned, those that should be retained, and those that should go their separate ways. I also recommend adopting the disambiguating terminology of “scientific kinds” and “natural kinds” for the different notions of kinds developed in these different approaches. (shrink)

This paper examines the issue of what the self is by reviewing neuropsychological research,which converges on the idea that the self may be more complex and differentiated than previous treatments of the topic have suggested. Although some aspects of self-knowledge such as episodic recollection may be compromised in individuals, other aspects—for instance, semantic trait summaries—appear largely intact. Taken together, these findings support the idea that the self is not a single, unified entity. Rather, it is a set of (...) interrelated, functionally independent systems. Implications for understanding the self in various areas of psychological research—e.g., neuroimaging, autism, amnesia, Alzheimer’s disease, and mirror self-recognition—are discussed in brief. (shrink)

The functionalist approach to kinds has suffered recently due to its association with law-based approaches to induction and explanation. Philosophers of science increasingly view nomological approaches as inappropriate for the special sciences like psychology and biology, which has led to a surge of interest in approaches to natural kinds that are more obviously compatible with mechanistic and model-based methods, especially homeostatic property cluster theory. But can the functionalist approach to kinds be weaned off its dependency on laws? Dan Weiskopf (...) has recently offered a reboot of the functionalist program by replacing its nomological commitments with a model-based approach more closely derived from practice in psychology. Roughly, Weiskopf holds that the natural kinds of psychology will be the functional properties that feature in many empirically successful cognitive models, and that those properties need not be localized to parts of an underlying mechanism. I here skeptically examine the three modeling practices that Weiskopf thinks introduce such non-localizable properties: fictionalization, reification, and functional abstraction. In each case, I argue that recognizing functional properties introduced by these practices as autonomous kinds comes at clear cost to those explanations’ counterfactual explanatory power. At each step, a tempting functionalist response is parochialism: to hold that the false or omitted counterfactuals fall outside the modeler’s explanatory aims, and so should not be counted against functional kinds. I conclude by noting the dangers this attitude poses to scientific disagreement, inviting functionalists to better articulate how the individuation conditions for functional kinds might outstrip the perspective of a single modeler. (shrink)

Some philosophers search for the mark of the cognitive: a set of individually necessary and jointly sufficient conditions identifying all instances of cognition. They claim that the mark of the cognitive is needed to steer the development of cognitive science on the right path. Here, I argue that, at least at present, it cannot be provided. First (§2), I identify some of the factors motivating the search for a mark of the cognitive, each yielding a desideratum the mark is supposed (...) to satisfy (§2.1). I then (§2.2) highlight a number of tensions in the literature on the mark of the cognitive, suggesting they’re best resolved by distinguishing two distinct programs. The first program (§3) is that of identifying a mark of the cognitive capturing our everyday notion of cognition. I argue that such a program is bound to fail for a number of reasons: it is not clear whether such an everyday notion exists; and even if it existed, it would not be able to spell out individually necessary and jointly sufficient conditions for cognition; and even if it were able to spell them out, these conditions won’t satisfy the desiderata a mark of the cognitive should satisfy. The second program is that of identifying a mark of the cognitive spelling out a genuine scientific kind. But the current state of fragmentation of cognitive science, and the fact that it is splintered in a myriad of different research traditions, prevent us from identifying such a kind. And we have no reason to think that these various research traditions will converge, allowing us to identify a single mark. Or so, at least, I will argue in (§4). I then conclude the paper (§5) deflecting an intuitive objection, and exploring some of the consequences of the thesis I have defended. (shrink)

According to buck-passers about art, such as Dominic Lopes, every work of art belongs to some art. I distinguish two versions of the buck-passing theory of art—what I call the double-buck-passers’ (DBP) view and the single-buck-passers’ (SBP) view—and point out that Lopes’s view is an instance of the latter. Then I argue the SBP view faces a dilemma, each horn of which leads to trouble. In doing so, I explore uncharted territory: the implications of vagueness for theories of (...) art. I conclude that buck-passers should not be single-buck-passers. (shrink)

In recent years, theorists have debated how we introduce new social objects and kinds into the world. Searle, for instance, proposes that they are introduced by collective acceptance of a constitutive rule; Millikan and Elder that they are the products of reproduction processes; Thomasson that they result from creator intentions and subsequent intentional reproduction; and so on. In this chapter, I argue against the idea that there is a single generic method or set of requirements for doing so. (...) Instead, there is a variety of what I call “anchoring schemas,” or methods by which new social kinds are generated. Not only are social kinds a diverse lot, but the metaphysical explanation for their being the kinds they are is diverse as well. I explain the idea of anchoring and present examples of social kinds that are similar to one another but that are anchored in different ways. I also respond to Millikan’s argument that there is only one kind of “glue” that is “sticky enough” for holding together kinds. I argue that no anchoring schema will work in all environments. It is a contingent matter which schemas are successful for anchoring new social kinds, and an anchoring schema need only be “sticky enough” for practical purposes in a given environment. (shrink)