Jeremy Goodman

The Preface Paradox is often discussed for its implications for rational belief. Much less discussed is a variant of the Preface Paradox for knowledge. In this paper, I argue that the most plausible closure-friendly resolution to the Preface Paradox for Knowledge is to say that in any given context, we do not know much. I call this view “Socraticism”. I argue that Socraticism is the most plausible view on two accounts—(1) this view is compatible with the claim that most of our knowledge ascriptions are true, and (2) provided that (1) is true, the costs of accepting Socraticism are much less than the costs of accepting any other resolution to the Paradox. I argue for (1) in Section 2 by developing a question-sensitive contextualist model for knowledge that shows how Socraticism is compatible with the claim that most of our knowledge ascriptions are true. I also argue how this contextualist model can achieve this result where other contextualist models fail. I then consider other closure-friendly solutions to the paradox in Section 3 and show how accepting those solutions forces us to give up a number of plausible epistemic principles.

Contingentists—who hold that it is contingent what there is—are divided on the claim that having a property or standing in a relation requires being something. This claim can be formulated as a natural schematic principle of higher-order modal logic. On this formulation, I argue that contingentists who are also higher-order contingentists—and so hold that it is contingent what propositions, properties and relations there are—should reject the claim. Moreover, I argue that given higher-order contingentism, having a property or standing in a relation does not even require possibly being something.

The 'content view', in slogan form, is 'Perceptual experiences have representational content'. I explain why the content view should be reformulated to remove any reference to 'experiences'. I then argue, against Bill Brewer, Charles Travis and others, that the content view is true. One corollary of the discussion is that the content of perception is relatively thin (confined, in the visual case, to roughly the output of 'mid-level' vision). Finally, I argue (briefly) that the opponents of the content view are partially vindicated, because perceptual error is due to false belief.

We argue that all comparative expressions in natural language obey a principle that we call Comparability: if x and y are at least as F as themselves, then either x is at least as F as y or y is at least as F as x. This principle has been widely rejected among philosophers, especially by ethicists, and its falsity has been claimed to have important normative implications. We argue that Comparability is needed to explain the goodness of several patterns of inference that seem manifestly valid, that the purported failures of Comparability would have absurd consequences, and that the influential arguments against Comparability are less compelling than they may have initially seemed.

This article presents a new interpretation of the great Ming dynasty philosopher Wang Yangming’s celebrated doctrine of the “unity of knowledge and action”. Wang held that action was not unified with all knowledge, but only with an elevated form of knowledge, which he sometimes called “genuine knowledge”. I argue for a new interpretation of this notion, according to which genuine knowledge requires freedom from a form of doxastic conflict. I propose that, in Wang’s view, a person is free from this form of doxastic conflict if and only if they are acting virtuously.

Suppose you’d like to believe that p, whether or not it’s true. What can you do to help? A natural initial thought is that you could engage in Intentionally Biased Inquiry : you could look into whether p, but do so in a way that you expect to predominantly yield evidence in favour of p. This paper hopes to do two things. The first is to argue that this initial thought is mistaken: intentionally biased inquiry is impossible. The second is to show that reflections on intentionally biased inquiry strongly support a controversial ‘access’ principle which states that, for all p, if p is part of our evidence, then that p is part of our evidence is itself part of our evidence.

In explaining the notion of a fundamental property or relation, metaphysicians will often draw an analogy with languages. The fundamental properties and relations stand to reality as the primitive predicates and relations stand to a language: the smallest set of vocabulary God would need in order to write the “book of the world.” This paper attempts to make good on this metaphor. To that end, a modality is introduced that, put informally, stands to propositions as logical truth stands to sentences. The resulting theory, formulated in higher-order logic, also vindicates the Humean idea that fundamental properties and relations are freely recombinable and a variant of the structural idea that propositions can be decomposed into their fundamental constituents via logical operations. Indeed, it is seen that, although these ideas are seemingly distinct, they are not independent, and fall out of a natural and general theory about the granularity of reality.

This three-part chapter explores a higher-order logic we call ‘Classicism’, which extends a minimal classical higher-order logic with further axioms which guarantee that provable coextensiveness is sufficient for identity. The first part presents several different ways of axiomatizing this theory and makes the case for its naturalness. The second part discusses two kinds of extensions of Classicism: some which take the view in the direction of coarseness of grain (whose endpoint is the maximally coarse-grained view that coextensiveness is sufficient for identity), and some which take the view in the direction of fineness of grain (whose endpoint is the maximally fine-grained theory containing all distinctness claims compatible with Classicism). The third part introduces some techniques for constructing models of Classicism, and uses them to prove the consistency of many of the extensions of Classicism introduced in the second part.

We develop a theory of necessity operators within a version of higher-order logic that is neutral about how fine-grained reality is. The theory is axiomatized in terms of the primitive of *being a necessity*, and we show how the central notions in the philosophy of modality can be recovered from it. Various questions are formulated and settled within the framework, including questions about the ordering of necessities under strength, the existence of broadest necessities satisfying various logical conditions, and questions about their logical behaviour. We also wield the framework to probe the conditions under which a logicist account of necessities is possible, in which the theory is completely reducible to logic.

Can conjunctive propositions be identical without their conjuncts being identical? Can universally quantified propositions be identical without their instances being identical? On a common conception of propositions, on which they inherit the logical structure of the sentences which express them, the answer is negative both times. Here, it will be shown that such a negative answer to both questions is inconsistent, assuming a standard type-theoretic formalization of theorizing about propositions. The result is not specific to conjunction and universal quantification, but applies to any binary operator and propositional quantifier. It is also shown that the result essentially arises out of giving a negative answer to both questions, as each negative answer is consistent by itself.

This paper presents a puzzle involving embedded attitude reports. We resolve the puzzle by arguing that attitude verbs take restricted readings: in some environments the denotation of attitude verbs can be restricted by a given proposition. For example, when these verbs are embedded in the consequent of a conditional, they can be restricted by the proposition expressed by the conditional’s antecedent. We formulate and motivate two conditions on the availability of verb restrictions: a constraint that ties the content of restrictions to the “dynamic effects” of sentential connectives and a constraint that limits the availability of restriction effects to present tense verbs with first-person subjects. However, we also present some cases that make trouble for these conditions, and outline some possible ways of modifying the view to account for the recalcitrant data. We conclude with a brief discussion of some of the connections between our semantics for attitude verbs and issues concerning epistemic modals and theories of knowledge.

This paper defends the view, put roughly, that to think that p is to guess that p is the answer to the question at hand, and that to think that p rationally is for one’s guess to that question to be in a certain sense non-arbitrary. Some theses that will be argued for along the way include: that thinking is question-sensitive and, correspondingly, that ‘thinks’ is context-sensitive; that it can be rational to think that p while having arbitrarily low credence that p; that, nonetheless, rational thinking is closed under entailment; that thinking does not supervene on credence; and that in many cases what one thinks on certain matters is, in a very literal sense, a choice. Finally, since there are strong reasons to believe that thinking just is believing, there are strong reasons to think that all this goes for belief as well.

Most philosophers have largely downplayed any relevance of multiple meanings of the folk concept of truth in the empirical domain. However, confusions about what truth is have surged in political and everyday discourse. In order to resolve these confusions, we argue that we need a more accurate picture of how the term ‘true’ is in fact used. Our experimental studies reveal that the use of ‘true’ shows substantial variance within the empirical domain, indicating that ‘true’ is ambiguous between a correspondence and a coherence reading. We then explore the consequences of these results for the project of re-engineering truth.

Current views of metaphysical ground suggest that a true conjunction is immediately grounded in its conjuncts, and only its conjuncts. Similar principles are suggested for disjunction and universal quantification. Here, it is shown that these principles are jointly inconsistent: They require that there is a distinct truth for any plurality of truths. By a variant of Cantor’s Theorem, such a fine-grained individuation of truths is inconsistent. This shows that the notion of grounding is either not in good standing, or that natural assumptions about it need to be revised.

Is the fact that our universe contains fine-tuned life evidence that we live in a multiverse? Ian Hacking and Roger White influentially argue that it is not. We approach this question through a systematic framework for self-locating epistemology. As it turns out, leading approaches to self-locating evidence agree that the fact that our own universe contains fine-tuned life indeed confirms the existence of a multiverse. This convergence is no accident: we present two theorems showing that, in this setting, any updating rule that satisfies a few reasonable conditions will have the same feature. The conclusion that fine-tuned life provides evidence for a multiverse is hard to escape.

According to the structured theory of propositions, if two sentences express the same proposition, then they have the same syntactic structure, with corresponding syntactic constituents expressing the same entities. A number of philosophers have recently focused attention on a powerful argument against this theory, based on a result by Bertrand Russell, which shows that the theory of structured propositions is inconsistent in higher order-logic. This paper explores a response to this argument, which involves restricting the scope of the claim that propositions are structured, so that it does not hold for all propositions whatsoever, but only for those which are expressible using closed sentences of a given formal language. We call this restricted principle Closed Structure, and show that it is consistent in classical higher-order logic. As a schematic principle, the strength of Closed Structure is dependent on the chosen language. For its consistency to be philosophically significant, it also needs to be consistent in every extension of the language which the theorist of structured propositions is apt to accept. But, we go on to show, Closed Structure is in fact inconsistent in a very natural extension of the standard language of higher-order logic, which adds resources for plural talk of propositions. We conclude that this particular strategy of restricting the scope of the claim that propositions are structured is not a compelling response to the argument based on Russell’s result, though we note that for some applications, for instance to propositional attitudes, a restricted thesis in the vicinity may hold some promise.

The iterative conception of set is typically considered to provide the intuitive underpinnings for ZFCU (ZFC+Urelements). It is an easy theorem of ZFCU that all sets have a definite cardinality. But the iterative conception seems to be entirely consistent with the existence of “wide” sets, sets (of, in particular, urelements) that are larger than any cardinal. This paper diagnoses the source of the apparent disconnect here and proposes modifications of the Replacement and Powerset axioms so as to allow for the existence of wide sets. Drawing upon Cantor’s notion of the absolute infinite, the paper argues that the modifications are warranted and preserve a robust iterative conception of set. The resulting theory is proved consistent relative to ZFC + “there exists an inaccessible cardinal number.”

Predictive algorithms are playing an increasingly prominent role in society, being used to predict recidivism, loan repayment, job performance, and so on. With this increasing influence has come an increasing concern with the ways in which they might be unfair or biased against individuals in virtue of their race, gender, or, more generally, their group membership. Many purported criteria of algorithmic fairness concern statistical relationships between the algorithm’s predictions and the actual outcomes, for instance requiring that the rate of false positives be equal across the relevant groups. We might seek to ensure that algorithms satisfy all of these purported fairness criteria. But a series of impossibility results shows that this is impossible, unless base rates are equal across the relevant groups. What are we to make of these pessimistic results? I argue that none of the purported criteria, except for a calibration criterion, are necessary conditions for fairness, on the grounds that they can all be simultaneously violated by a manifestly fair and uniquely optimal predictive algorithm, even when base rates are equal. I conclude with some general reflections on algorithmic fairness.

I observe that the “concept-generator” theory of Percus and Sauerland (2003), Anand (2006), and Charlow and Sharvit (2014) does not predict an intuitive true interpretation of the sentence “Plato did not believe that Hesperus was Phosphorus”. In response, I present a simple theory of attitude reports which employs a fine-grained semantics for names, according to which names which intuitively name the same thing may have distinct compositional semantic values. This simple theory solves the problem with the concept-generator theory, but, as I go on to show, it has problems of its own. I present three examples which the concept-generator theory can accommodate, but the simple fine-grained theory cannot. These examples motivate the full theory of the paper, which combines the basic ideas behind the concept-generator theory with a fine-grained semantics for names. The examples themselves are of interest independently of my theory: two of them constrain the original concept-generator theory more tightly than previously discussed examples had.

Many psychologists studying lay belief attribution and behavior explanation cite Donald Davidson in support of their assumption that people construe beliefs as inner causes. But Davidson’s influential argument is unsound; there are no objective grounds for the intuition that the folk construe beliefs as inner causes that produce behavior. Indeed, recent experimental work by Ian Apperly, Bertram Malle, Henry Wellman, and Tania Lombrozo provides an empirical framework that accords well with Gilbert Ryle’s alternative thesis that the folk construe beliefs as patterns of living that contextualize behavior.

Do people tend to be overconfident? Many think so. They’ve run studies on whether people are calibrated: whether their average confidence in their opinions matches the proportion of those opinions that are true. Under certain conditions, people are systematically ‘over-calibrated’—for example, of the opinions they’re 80% confident in, only 60% are true. From this empirical over-calibration, it’s inferred that people are irrationally overconfident. My question: When and why is this inference warranted? Answering it requires articulating a general connection between being rational and being right—something extant studies have not done. I show how to do so using the notion of deference. This provides a theoretical foundation for calibration research, but also reveals a flaw: the connection between being rational and being right is much weaker than is standardly assumed, since rational people can often be expected to be miscalibrated. Thus we can’t test whether people are overconfident by simply testing whether they are over-calibrated; instead, we must try to predict the rational deviations from calibration, and then compare those predictions to people’s performance. I show how this can be done—and that doing so complicates the interpretation of robust empirical effects.

This paper considers how counterfactuals should be evaluated on the assumption that determinism is true. I argue against Lewis's influential view that the actual laws of nature would have been false if something had happened that never actually happened, and in favour of the competing view that history would have been different all the way back. I argue that we can do adequate justice to our ordinary practice of relying on a wide range of historical truths in evaluating counterfactuals by saying that, in typical cases, history would have been only *very slightly* different until shortly before the relevant time. The paper also draws some connections between the puzzle about counterfactuals under determinism and the debate about whether determinism entails that no-one can ever do otherwise than they in fact do.