Open theists deny that God knows future contingents. Most open theists justify this denial by adopting the position that there are no future contingent truths to be known. In this paper we examine some of the arguments put forward for this position in two recent articles in this journal, one by Dale Tuggy and one by Alan Rhoda, Gregory Boyd, and Thomas Belt. The arguments concern time, modality, and the semantics of ‘will’ statements. We explain why we find none (...) of these arguments persuasive. This wide road leads only to destruction. (shrink)

Most accounts of cognitive scaffolding focus on ways that external structure can support or augment an agent’s cognitive capacities. We call cases where the interests of the user are served benign scaffolding and argue for the possibility and reality of hostile scaffolding. This is scaffolding which depends on the same capacities of an agent to make cognitive use of external structure as in benign cases, but that undermines or exploits the user while serving the interests of another agent. We develop (...) criteria for scaffolding being hostile and show by reference to examples including the design features of electronic gambling machines and casino management systems that hostile scaffolding exists and can be highly effective. In cases where the scaffolding is deep and permits the offloading of significant cognitive work, hostile scaffolding exploitatively manipulates cognitive processing itself. Given the extent of human reliance on scaffolding this is an important and neglected vulnerability. [This is an updated version of the paper, added in February 2023.]. (shrink)

Knowledge is widely thought to entail belief. But Radford has claimed to offer a counterexample: the case of the unconfident examinee. And Myers-Schulz and Schwitzgebel have claimed empirical vindication of Radford. We argue, in defense of orthodoxy, that the unconfident examinee does indeed have belief, in the epistemically relevant sense of dispositional belief. We buttress this with empirical results showing that when the dispositional conception of belief is specifically elicited, people’s intuitions then conform with the view that knowledge entails (dispositional) (...) belief. (shrink)

The law views with suspicion statistical evidence, even evidence that is probabilistically on a par with direct, individual evidence that the law is in no way suspicious of. But it has proved remarkably hard to either justify this suspicion, or to debunk it. In this paper, we connect the discussion of statistical evidence to broader epistemological discussions of similar phenomena. We highlight Sensitivity – the requirement that a belief be counterfactually sensitive to the truth in a specific way – as (...) a way of epistemically explaining the legal suspicion towards statistical evidence. Still, we do not think of this as a satisfactory vindication of the reluctance to rely on statistical evidence. Knowledge – and Sensitivity, and indeed epistemology in general – are of little, if any, legal value. Instead, we tell an incentive-based story vindicating the suspicion towards statistical evidence. We conclude by showing that the epistemological story and the incentive-based story are closely and interestingly related, and by offering initial thoughts about the role of statistical evidence in morality. (shrink)

The starting point regarding consent has to be that it is both extremely important, and that it is often suspicious. In this article, the author tries to make sense of both of these claims, from a largely liberal perspective, tying consent, predictably, to the value of autonomy and distinguishing between autonomy as sovereignty and autonomy as nonalienation. The author then discusses adaptive preferences, claiming that they suffer from a rationality flaw but that it's not clear that this flaw matters morally (...) or politically. What matters is whether they suffer from an autonomy flaw. To answer this question, the author develops an account of autonomy failure, according to which a preference is nonautonomous if an injustice played an appropriate role in its causal history. The author then discusses the moral implications—and in an initial way, the political ones as well—of proclaiming a preference, or consent based on it, nonautonomous in this way. (shrink)

People are often offended by beliefs, expect apologies for beliefs, apologize for their own beliefs. In many mundane cases, people are morally criticized for their beliefs. Intuitively, then, beliefs seem to sometimes wrong people. Recently, the philosophical literature has picked up on this theme, and has started to discuss it under the heading of doxastic wrongdoing. In this paper we argue that despite the strength of such initial intuitions, at the end of the day they have to be rejected. If (...) it can be ever truthfully asserted that beliefs wrong, this is always derivative – beliefs wrong only in virtue of other things (like evidence-gathering actions) wronging. We distinguish between modest and ambitious doxastic wrongdoing theories (the former deny, while the latter accept, the possibility of a morally wrong yet epistemically permissible belief); we argue that each of these options faces insurmountable problems; and we offer partly debunking explanations of the intuitions purportedly supporting doxastic wrongdoing. (shrink)

Critics have argued that human-controlled avatar interactions fail to facilitate the kinds of expressivity and social understanding afforded by our physical bodies. We identify three claims meant to justify the supposed expressive limits of avatar interactions compared to our physical interactions. First, “The Limited Expressivity Claim”: avatars have a more limited expressive range than our physical bodies. Second, “The Inputted Expressivity Claim”: any expressive avatarial behaviour must be deliberately inputted by the user. Third, “The Decoding Claim”: users must infer or (...) figure out the expressive meaning of human-controlled avatars’ behaviour through cognitively onerous processes. With the aim of critically assessing all three claims, we analyze data collected through observations of and interviews with expert players of the avatar-based video game League of Legends. Focusing on Daniel Stern’s (2010) notion of vitality, we analyze the participants’ descriptions of seeing and interacting with other avatars during performance. Our analysis shows that the informants experience human-based avatarial interactions as qualitatively different than interactions with bots, that the informants see the movements of other players’ avatars as having different expressive styles, and that the informants actively use and manipulate this avatarial expressivity during performance. The results of our analysis, we argue, provide reasons for loosening or resisting the three claims concerning the limits of avatarial expressivity. (shrink)

Statistical evidence—say, that 95% of your co-workers badmouth each other—can never render resenting your colleague appropriate, in the way that other evidence (say, the testimony of a reliable friend) can. The problem of statistical resentment is to explain why. We put the problem of statistical resentment in several wider contexts: The context of the problem of statistical evidence in legal theory; the epistemological context—with problems like the lottery paradox for knowledge, epistemic impurism and doxastic wrongdoing; and the context of a (...) wider set of examples of responses and attitudes that seem not to be appropriately groundable in statistical evidence. Regrettably, we do not come up with a fully general, fully adequate, fully unified account of all the phenomena discussed. But we give reasons to believe that no such account is forthcoming, and we sketch a somewhat messier account that may be the best that can be had here. (shrink)

Political philosophers frequently claim that political ideals can provide normative guidance for unjust and otherwise nonideal circumstances. This is mistaken. This paper demonstrates that political ideals contribute nothing to our understanding of the normative principles we should satisfy amidst unjust or otherwise nonideal circumstances.

When do the folk think that material objects persist? Many metaphysicians have wanted a view which fits with folk intuitions, yet there is little agreement about what the folk intuit. I provide a range of empirical evidence which suggests that the folk operate with a teleological view of persistence: the folk tend to intuit that a material object survives alterations when its function is preserved. Given that the folk operate with a teleological view of persistence, I argue for a debunking (...) explanation of folk intuitions, concluding that metaphysicians should dismiss folk intuitions as tied into a benighted view of nature. (shrink)

In this paper, we develop an account of the justification thinkers have for employing certain basic belief-forming methods. The guiding idea is inspired by Reichenbach's work on induction. There are certain projects in which thinkers are rationally required to engage. Thinkers are epistemically justified in employing any belief-forming method such that "if it doesn't work, nothing will" for successfully engaging in such a project. We present a detailed account based on this intuitive thought and address objections to it. We conclude (...) by commenting on the implications that our account may have for other important epistemological issues and debates. (shrink)

I argue that according to Socrates in the Phaedo we should not merely evaluate bodily pleasures and desires as worthless or bad, but actively avoid them. We need to avoid them because they change our values and make us believe falsehoods. This change in values and acceptance of falsehoods undermines the soul’s proper activity, making virtue and happiness impossible for us. I situate this account of why we should avoid bodily pleasures within Plato’s project in the Phaedo of providing Pythagorean (...) and Orphic ideas with clearer meanings and better justifications. (shrink)

Philosophical Issues, Volume 31, Issue 1, Page 85-103, October 2021.

ABSTRACTIn a recent paper, Michael Pardo argues that the epistemic property that is legally relevant is the one called Safety, rather than Sensitivity. In the process, he argues against our Sensitivity-related account of statistical evidence. Here we revisit these issues, partly in order to respond to Pardo, and partly in order to make general claims about legal epistemology. We clarify our account, we show how it adequately deals with counterexamples and other worries, we raise suspicions about Safety's value here, and (...) we revisit our general skepticism about the role that epistemological considerations should play in determining legal policy. (shrink)

The late Middle Ages witnessed a recapitulation of medieval reflection on beauty. Jean Gerson is an important representative of these philosophical and theological contributions, although he has been largely neglected up to this time. A first dimension of his ideas on beauty is the incorporation of beauty (pulchrum) into the number of transcendentals, i.e., the concepts “convertible” with the notion of being (ens), that is, unity, truth, and goodness (unum, verum and bonum). This article revisits Monica Calma’s study on Gerson’s (...) theory of beauty and suggests new hypothetical sources that may have inspired this aspect of his thought. The second aspect emphasised here is Gerson’s classification of beauty, which entails some similarities to the one of Ulrich of Strasbourg, but also differs from it. Moreover, its incorporation of a division entirely devoted to artistic beauty is highly remarkable. (shrink)

Orthodoxy has it that knowledge is a composite of belief and non-mental factors. However, Timothy Williamson suggests that orthodoxy implies that the concept of belief is acquired before the concept of knowledge, whereas developmental data suggest the reverse. More recently, Jennifer Nagel reviews the psychological evidence, building a psychological case that the concept of knowledge emerges prior to belief. I assess the psychological state of the art and find support for the opposite conclusion. Overall the empirical evidence supports the orthodox (...) view that the concept of belief is prior to the concept of knowledge. (shrink)

Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...) logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)

eSports practice designates a unique set of activities tethered to competitive, virtual environments, or worlds. This correlation between eSports practitioner and virtual world, we argue, is inadequately accounted for solely in terms of something physical or intellectual. Instead, we favor a perspective on eSports practice to be analyzed as a perceptual and embodied phenomenon. In this article, we present the phenomenological approach and focus on the embodied sensations of eSports practitioners as they cope with and perceive within their virtual worlds. (...) By approaching eSports phenomenologically, we uncover ways in which its unique forms of virtual involvement overlap with as well as differentiate themselves from traditional structures of embodiment. (shrink)

Traditionally, the investigation of truth has been anchored in a priori reasoning. Cognitive science deviates from this tradition by adding empirical data on how people understand and use concepts. Building on psychophysics and machine learning methods, we introduce conceptual scaling, an approach to map people's understanding of abstract concepts. This approach, allows computing participant-specific conceptual maps from obtained ordinal comparison data, thereby quantifying perceived similarities among abstract concepts. Using this approach, we investigated individual's alignment with philosophical theories on truth and (...) the predictive capacity of conceptual maps. The obtained results indicated that, while people's understanding of truth is multifaceted and encapsulates notions of coherence and authenticity, alignment is best for the correspondence theory of truth. Furthermore, conceptual maps allowed predicting individual outcomes with an accuracy of roughly 70%. This research demonstrates that conceptual scaling offers accurate descriptions of individual's understanding of abstract concepts, behavioral predictions, and quantification of alignment with theoretical perspectives. (shrink)

This is a contribution to the symposium on Tim Scanlon’s Being Realistic about Reasons. We have two aims here: First, we ask for more details about Scanlon’s meta-metaphysical view, showing problems with salient clarifications. And second, we raise independent objections to the view – to its explanatory productivity, its distinctness, and the argumentative support it enjoys.

We provide an overview of the meta-ontological position known as "Quantifier Variance".

Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u′) from the universe U ] is dual to an "element". An element being in a subset is analogous to a partition π on U making a distinction, i.e., if u and u′ were in different blocks of π. Subset logic leads to finite (...) probability theory by taking the (Laplacian) probability as the normalized size of each subset-event of a finite universe. The analogous step in the logic of partitions is to assign to a partition the number of distinctions made by a partition normalized by the total number of ordered pairs |U|² from the finite universe. That yields a notion of "logical entropy" for partitions and a "logical information theory." The logical theory directly counts the (normalized) number of distinctions in a partition while Shannon's theory gives the average number of binary partitions needed to make those same distinctions. Thus the logical theory is seen as providing a conceptual underpinning for Shannon's theory based on the logical notion of "distinctions.". (shrink)

This chapter explores the relationship between ethical judgement writ large (as opposed to merely moral judgement) and motivation. We discuss arguments for and against views on which ethical judgement entails motivation, either alone or under conditions of rationality or normalcy, either at the individual or community level.

In this chapter, we argue that it’s possible to lose your faith in God by the actions of other people. In particular, we argue that spiritually violent religious trauma, where religious texts are used to shame a person into thinking themselves unworthy of God’s love, can cause a person to stop engaging in activities that sustain their faith in God, such as engaging in the worship of God. To do this, we provide an analysis of faith, worship, and love on (...) which to have faith in God is to have an attitude of worship to him; to have such an attitude of worship to God is to love him; and to love God is to desire union with him. We apply this analysis particularly to the case of LGBT Christians and their experience in the church today. (shrink)

Liberal-contractarian philosophies of justice see the unjust systems of slavery and autocracy in the past as being based on coercion—whereas the social order in modern democratic market societies is based on consent and contract. However, the ‘best’ case for slavery and autocracy in the past were consent-based contractarian arguments. Hence, our first task is to recover those ‘forgotten’ apologia for slavery and autocracy. To counter those consent-based arguments, the historical anti-slavery and democratic movements developed a theory of inalienable rights. Our (...) second task is to recover that theory and to consider several other applications of the theory. Finally, the liberal theories of justice expounded by John Rawls and by Robert Nozick are briefly examined from this perspective. (shrink)

According to the Good True Self (GTS) theory, if an action is deemed good, its psychological source is typically viewed as more reflective of its agent’s true self, of who the agent really is ‘deep down inside’; if the action is deemed bad, its psychological source is typically viewed as more external to its agent’s true self. In previous work, we discovered a related asymmetry in judgments of blame- and praiseworthiness with respect to the mitigating effect of moral ignorance via (...) childhood deprivation. Inspired by work motivating the GTS theory, we ran a new study to discover whether our asymmetry likewise reflected judgments about the true self. It did. However, it is unclear whether our results fit with the ‘good’ part of the GTS theory: some of our and others’ results suggest that, in certain contexts, wrong actions are taken to be more expressive of agents’ true selves than right ones. In this paper, we propose that our and others’ data can be explained by the hypothesis that we are inclined to judge as the GTS theory predicts when there is a readily available external explanation for an agent’s action. In short, we give people the benefit of the doubt. (shrink)

Political equality is in tension with political quality, and quality has recently been neglected. My thesis is that proper attention to the quality of democratic procedures and their outcomes requires that we accept substantive inequalities of political input in the interest of increasing input overall. Mainly, I hope to refute political egalitarianism, the view that justice or legitimacy requires substantive political equality, specifically equal availability of power or influence over collective choices that have legal force. I hope to show that (...) political egalitarianism exaggerates individual rights in the conduct of political procedures, and neglects the substantive justice of the decisions made through those procedures. Some unequal distributions of influence may better promote just decisions, and without reliance on any invidious comparisons such as the relative wisdom of the wealthy or the educated. (shrink)

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

Normative moral theories are frequently invoked to serve one of two distinct purposes: (1) explicate a criterion of rightness, or (2) provide an ethical decision-making procedure. Although a criterion of rightness provides a valuable theoretical ideal, proposed criteria rarely can be (nor are they intended to be) directly translated into a feasible decision-making procedure. This paper applies the computational framework of bounded rationality to moral decision-making to ask: how ought a bounded human agent make ethical decisions? We suggest agents ought (...) to follow moral maxims: principles that approximate rightness in many situations, but that can be overridden in specific, precisely describable circumstances. While this intuitive idea has been proposed many times before, we provide a precise model of how maxim consequentialism functions as an approximation to an act-consequentialist criterion of rightness, while maintaining the flexibility and defeasibility that has eluded most forms of rule consequentialism. Furthermore, while our overarching aim is to propose a new normative standard of moral decision-making, we demonstrate how maxim consequentialism can also function as a descriptive account of human behavior. We conclude by noting that different criteria of rightness may lead to different maxim-based ethics. (shrink)

Suppose justice depends on some very unlikely good behavior. In that case the true (or correct, or best) theory of justice might have no practical value. But then, what good would it be? I consider analogies with science and mathematics in order to test various ways of tying their the value of intellectual work to practice, though I argue that these fail. If their value, or that of some political theory, is not practical then what is good about them? As (...) for political theory, I consider the question of what would even count as an answer to this question, and I conclude with the tentative proposal that it is valuable to come to understand something that is, itself, important. (shrink)

Various philosophers discuss perlocutionary silencing, but none defend an account of perlocutionary silencing. This gap may exist because perlocutionary success depends on extralinguistic effects, whereas silencing interrupts speech, leaving theorists to rely on extemporary accounts when they discuss perlocutionary silencing. Consequently, scholars assume perlocutionary silencing occurs but neglect to explain how perlocutionary silencing harms speakers as speakers. In relation to that shortcoming, I defend a novel account of perlocutionary silencing. I argue that speakers experience perlocutionary silencing when they are illegitimately (...) deprived of perlocutionary influence on a conversation in which they are active participants, where perlocutionary influence on the conversation relates to speech-related perlocutionary goals meant to influence the conversation or conversational direction. Thus, this account grounds perlocutionary silencing in linguistic phenomena and characterizes perlocutionary silencing in a way that explains why those who experience perlocutionary silencing are harmed as speakers. Moreover, this account explains how perlocutionary silencing harms speakers as conversational participants in a way that cannot be captured by illocutionary or locutionary silencing, for a speaker may be perlocutionarily silenced despite illocutionary success. Consequently, the account explains why “All Lives Matter” silences Black Lives Matter and “Not All Men” silences women sharing experiences of sexual harassment. (shrink)

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to more definite (...) states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this paper (...) is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. (shrink)

This article addresses three main questions: What causes cognitive overload in the workplace? What analytical framework should be used to understand how agents interact with their work environments? How can environments be restructured to improve the cognitive workflow of agents? Four primary causes of overload are identified: too much tasking and interruption, and inadequate workplace infrastructure to help reduce the need for planning, monitoring, reminding, reclassifying information, etc… The first step in reducing the cognitive impact of these causes is to (...) enrich classical frameworks for understanding work environments, such as Newell and Simon’s notion of a task environment, by recognizing that our actual workplace is a superposition of many specific environments – activity spaces – which we slip between. Each has its own cost structure arising from the tools and resources available, including the cognitive strategies and interpretational frameworks of individual agents. These cognitive factors are significant, affecting how easy or difficult it is to perform an action, such as finding a specific paper in a “mess” desk. A few simple examples show how work environments can be redesigned and how restructuring can alter the cost structure of activity spaces. (shrink)

We argue that genuine modal realism can be extended, rather than modified, so as to allow for the possibility of nothing concrete, a possibility we term ‘metaphysical nihilism’. The issue should be important to the genuine modal realist because, not only is metaphysical nihilism itself intuitively plausible, but also it is supported by an argument with pre-theoretically credible premises, namely, the subtraction argument. Given the soundness of the subtraction argument, we show that there are two ways that the genuine modal (...) realist can accommodate metaphysical nihilism: (i) by allowing for worlds containing only spatiotemporal points and (ii) by allowing for a world containing nothing but the null individual. On methodological grounds, we argue that the genuine modal realist should reject the former way but embrace the latter way. (shrink)

Holism in interwar Germany provides an excellent example for social and political in- fluences on scientific developments. Deeply impressed by the ubiquitous invocation of a cultural crisis, biologists, physicians, and psychologists presented holistic accounts as an alternative to the “mechanistic worldview” of the nineteenth century. Although the ideological background of these accounts is often blatantly obvious, many holistic scientists did not content themselves with a general opposition to a mechanistic worldview but aimed at a rational foundation of their holistic projects. (...) This article will discuss the work of Kurt Goldstein, who is known for both his groundbreaking contributions to neuropsychology and his holistic philosophy of human nature. By focusing on Goldstein’s neurolinguistic research, I want to reconstruct the empirical foundations of his holistic program without ignoring its cultural background. In this sense, Goldstein’s work provides a case study for the formation of a scientific theory through the complex interplay between specific empirical evidences and the general cultural developments of the Weimar Republic. (shrink)

Zetetic norms govern our acts of inquiry. Epistemic norms govern our beliefs and acts of belief formation. Recently, Jane Friedman (2020) has defended that we should think of these norms as conforming a single normative domain: epistemology should take a zetetic turn. Though this unification project implies a substantive re-elaboration of our traditional epistemic norms, Friedman argues that the reasons supporting the turn are robust enough to warrant its revisionary implications. In this paper, I suggest we should read Friedman’s proposal (...) as a dilemma. Either we believe the zetetic turn is well-motivated and undertake the task of looking for the proper revision of our traditional epistemic norms, or we take the revisionary implications of the turn to be unacceptable, in which case our challenge is to show why a zetetic epistemology is not a well-motivated project after all. After presenting this dilemma, I make a case for endorsing its second horn by presenting a two-pronged argument against Friedman’s project. First, I show that the revisionary implications of the zetetic turn are more far-reaching than expected. Second, I defend that the most persuasive reasons for endorsing the turn are not strong enough to support it. Taken together, these considerations speak against accepting the zetetic turn and the revisionary implications that come with it. (shrink)

The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite set--just as the usual logical notion of probability based on the Boolean logic (...) of subsets is the normalized counting measure of the subsets (events). Thus logical entropy is a measure on the set of ordered pairs, and all the compound notions of entropy (join entropy, conditional entropy, and mutual information) arise in the usual way from the measure (e.g., the inclusion-exclusion principle)--just like the corresponding notions of probability. The usual Shannon entropy of a partition is developed by replacing the normalized count of distinctions (dits) by the average number of binary partitions (bits) necessary to make all the distinctions of the partition. (shrink)

I argue that the technique Socrates describes in the Meno at 86e-87c allows him to make progress without definitions, even while accepting that definitions are necessary for knowledge. Some contend that the technique involves provisionally accepting a claim. I argue, instead, that it provides a secure biconditional that one can use to reduce the question one cares care about to a new question that one thinks will be easier to answer.