Etchemendy and Bolzano on Logical Consequence

In a series of publications beginning in the 1980s, John Etchemendy has argued that the standard semantical account of logical consequence, due in its essentials to Alfred Tarski, is fundamentally mistaken. He argues that, while Tarski's definition requires us to classify the terms of a language as logical or non-logical, no such division is guaranteed to deliver the correct extension of our pre-theoretical or intuitive consequence relation. In addition, and perhaps more importantly, Tarski's account is claimed to be incapable of explaining an essential modal/epistemological feature of consequence, namely, its necessity and apriority.

Bernard Bolzano (1781–1848) is widely recognized as having anticipated Tarski's definition in his Wissenschaftslehre (or Theory of Science) of 1837. Because of the similarities between his account and Tarski's, Etchemendy's arguments have also been extended to cover Bolzano. The purpose of this article is to consider Bolzano's theory in the light of these criticisms. We argue that, due to important differences between Bolzano's and Tarski's theories, Etchemendy's objections do not apply immediately to Bolzano's account of consequence. Moreover, Bolzano's writings contain the elements of a detailed philosophical response to Etchemendy.     

Methodological Practice and Complementary Concepts of Logical Consequence: Tarski's Model-Theoretic Consequence and Corcoran's Information-Theoretic Consequence

This article discusses two coextensive concepts of logical consequence that are implicit in the two fundamental logical practices of establishing validity and invalidity for premise-conclusion arguments. The premises and conclusion of an argument have information content (they ‘say’ something), and they have subject matter (they are ‘about’ something). The asymmetry between establishing validity and establishing invalidity has long been noted: validity is established through an information-processing procedure exhibiting a step-by-step deduction of the conclusion from the premise-set. Invalidity is established by exhibiting a countermodel satisfying the premises but not the conclusion. The process of establishing validity focuses on information content; the process of establishing invalidity focuses on subject matter. Corcoran's information-theoretic concept of logical consequence corresponds to the former. Tarski's model-theoretic concept of logical consequence formulated in his famous 1936 no-countermodels definition corresponds to the latter. Both are found to be indispensable for understanding the rationale of the deductive method and each complements the other. This study discusses the ontic question of the nature of logical consequence and the epistemic question of the human capabilities presupposed by practical applications of these two concepts as they make validity and invalidity accessible to human knowledge.     

Logical consequence: A defense of Tarski

In his classic 1936 essay “On the Concept of Logical Consequence”, Alfred Tarski used the notion of satisfaction to give a semantic characterization of the logical properties. Tarski is generally credited with introducing the model-theoretic characterization of the logical properties familiar to us today. However, in his book, The Concept of Logical Consequence, Etchemendy argues that Tarski's account is inadequate for quite a number of reasons, and is actually incompatible with the standard model-theoretic account. Many of his criticisms are meant to apply to the model-theoretic account as well. In this paper, I discuss the following four critical charges that Etchemendy makes against Tarski and his account of the logical properties:

1. Tarski's account of logical consequence diverges from the standard model-theoretic account at points where the latter account gets it right.
2. Tarski's account cannot be brought into line with the model-theoretic account, because the two are fundamentally incompatible.
3. There are simple counterexamples (enumerated by Etchemendy) which show that Tarski's account is wrong.
4. Tarski committed a modal fallacy when arguing that his account captures our pre-theoretical concept of logical consequence, and so obscured an essential weakness of the account.
5. Tarski's account depends on there being a distinction between the “logical terms” and the “non-logical terms” of a language, but (according to Etchemendy) there are very simple (even first-order) languages for which no such distinction can be made. Etchemendy's critique raises historical and philosophical questions about important foundational work. However, Etchemendy is mistaken about each of these central criticisms. In the course of justifying that claim, I give a sustained explication and defense of Tarski's account. Moreover, since I will argue that Tarski's account and the model-theoretic account really do come to the same thing, my subsequent defense of Tarski's account against Etchemendy's other attacks doubles as a defense against criticisms that would apply equally to the familiar model-theoretic account of the logical properties.

     

On Bolzano's Concept of a Sum

Alongside his groundbreaking work in logic, Bernard Bolzano (1781–1848) made important contributions to ontology, notably with his theory of collections. Recent work has done much to elucidate Bolzano's conceptions, but his notion of a sum has proved stubbornly resistant to complete understanding. This paper offers a new interpretation of Bolzano's concept of a sum. I argue that, although Bolzano's presentation is defective, his conception is unexceptionable, and has important applications, notably in his work on the foundations of arithmetic.     

Empathetic Understanding and Deliberative Democracy

Epistemic democracy is standardly characterized in terms of “aiming at truth”. This presupposes a veritistic conception of epistemic value, according to which truth is the fundamental epistemic goal. I will raise an objection to the standard (veritistic) account of epistemic democracy, focusing specifically on deliberative democracy. I then propose a version of deliberative democracy that is grounded in non-veritistic epistemic goals. In particular, I argue that deliberation is valuable because it facilitates empathetic understanding. I claim that empathetic understanding is an epistemic good that doesn't have truth as its primary goal.     

Levels of unconsciousness and their formal structure

This brief essay replies to Carvalho's exposition of a formal approach to the concept of the unconscious which is originally due to Ignacio Matte Blanco (1908–1995), a psychoanalyst from Chile. It's a challenge – first because I have been largely unfamiliar with the details of Matte Blanco's approach, and second because the space available for this reply does not allow me to be as precise as Carvalho's essay no doubt deserves. I will start with some remarks about how I see Matte Blanco's system from a mathematical perspective and then try to relate it to some of the core features of Pauli's and Jung's thinking. I will conclude with a tentative proposal of how Matte Blanco's strata between full consciousness and most undifferentiated unconscious can be related to the tension between ontic and epistemic accounts.     

Problems for Logical Pluralism

I argue that Beall and Restall's logical pluralism fails. Beall–Restall pluralism is the claim that there are different, equally correct logical consequence relations in a single language. Their position fails for two, related, reasons: first, it relies on an unmotivated conception of the ‘settled core’ of consequence: they believe that truth-preservation, necessity, formality and normativity are ‘settled’ features of logical consequence and that any relation satisfying these criteria is a logical consequence relation. I consider historical evidence and argue that their position relies on an unmotivated conception of the settled features of logical consequence. There are many features that are just as settled but which are inconsistent with pluralism. Second, I argue that Beall–Restall pluralism fails to hold in a single language with a single selection of logical constants, which they require for the position to be distinct from Carnap's. I consider various ways in which Beall and Restall can resist this meaning variance, particularly for negation, but argue that the strongest way relies on an unmotivated conception of the settled features of the logical constants.     

Tarski ‐ a dilemma

Tarski's correspondence theory of truth (which he spells out in his semantic conception of truth) is open to two interpretations. This ambiguity in the theory has led philosophers to find support in it for metaphysical reali sm. In fact, Tarski's theory turns out to support a form of ontological relativism. In different passages Tarski himself gives support to each of these interpretations. The first interpretation leads to ontological relativism, while the second sacrifices the connection between language and the world. I clarify the dilemma that I see in having to choose between these two interpretations, explain how these interpretations have their source in different problems which occupied Tarski, and consider a possible solution to the dilemma. Finally, finding good reasons to claim that Tarski's theory is indeed a correspondence theory of truth, I argue in favour of the first interpretation with its relativistic implications.     

On Understanding Leśniewski

Tarski's manner of defining truth is generally considered highly significant. About why, there is less consensus. I argue first, that in his truth-definitions Tarski was trying to solve a set of philosophical problems; second, that he solved them successfully; third, that all of these that are simply problems about defining truth are as well or better solved by a simpler account of truth. But one of his crucial problems remains: to give an account of validity, one requires an account not just of truth but of truth under varying interpretations. Tarski's account has the merit of generalizing to this, to model theory and to abstract algebra.     

Epistemic Side Constraints and the Structure of Epistemic Normativity

In this paper, I develop the notion of an epistemic side constraint in order to overcome one of the main challenges to a goal‐based approach to the structure of epistemic normativity. I argue that the rationale for such side constraints can be found in the work of John Locke and that his argument is best understood as the epistemic analog to David Gauthier's argument as to the rationality of being moral.     

Discovery in complex adaptive systems

The distinction between ontological ground-truth phenomena and epistemic measurements of those phenomena is discussed and analyzed in the context of complex cognitive systems research. A common style of computational simulation is identified as a Dissect-the-Simulation motif. In this style, a model of cognition is designed and when it generally mimics some cognitive behavior, its own ontic processes (which are fully accessible because it is a simulation) are proposed as potential ontic processes inside actual human cognition. I propose here a second style of modeling, which might be called Measure-the-Simulation. In this style, simulated versions of coarse-grained epistemic measurements are performed on the model with the intent of discovering how those epistemic measurements themselves may transform the actual ontic data, and thus induce a variety of mis-categorizations of phenomena. When our epistemic measurements are better understood, such mis-categorizations can perhaps be avoided. As a proof of concept, Conway’s Game of Life is analyzed and measured with two different types of coarse-grained epistemic measures. Dramatic differences are identified in how a binary coarse-graining, versus a graded coarse-graining, transforms the discovery process for activity patterns on the lattice of this cellular automaton.     

Anti-Individualism, Content Preservation, and Discursive Justification

Most explorations of the epistemic implications of Semantic Anti‐Individualism (SAI) focus on issues of self‐knowledge (first‐person authority) and/or external‐world skepticism. Less explored has been SAI's implications for the epistemology of reasoning. In this paper I argue that SAI has some nontrivial implications on this score. I bring these out by reflecting on a problem first raised by Boghossian (1992) . Whereas Boghossian's main interest was in establishing the incompatibility of SAI and “the a priority of logical abilities” ( Boghossian 1992 : 22), I argue that Boghossian's argument is better interpreted as pointing to SAI's implications for the nature of discursive justification.     

The Proof of Utility and Equity in Mill's Utilitarianism

Bolzano incorporated Kant's distinction between intuitions and concepts into the doctrine of propositions by distinguishing between conceptual (Begriffssätze an sich) and intuitive propositions (Anschauungssätze an sich). An intuitive proposition contains at least one objective intuition, that is, a simple idea that represents exactly one object; a conceptual proposition contains no objective intuition. After Bolzano, philosophers dispensed with the distinction between conceptual and intuitive propositions. So why did Bolzano attach philosophical importance to it? I will argue that, ultimately, the value of the distinction lies in the fact that conceptual and intuitive truths have different objective grounds: if a conceptual truth is grounded at all, its ground is a conceptual truth. The difference in grounds between conceptual and intuitive truths motivates Bolzano's criticism of Kant's view that intuition plays the fundamental role in mathematics, a conceptual science by Bolzano's lights.     

Repugnant Accuracy

Accuracy‐first epistemology is an approach to formal epistemology which takes accuracy to be a measure of epistemic utility and attempts to vindicate norms of epistemic rationality by showing how conformity with them is beneficial. If accuracy‐first epistemology can actually vindicate any epistemic norms, it must adopt a plausible account of epistemic value. Any such account must avoid the epistemic version of Derek Parfit's “repugnant conclusion.” I argue that the only plausible way of doing so is to say that accurate credences in certain propositions have no, or almost no, epistemic value. I prove that this is incompatible with standard accuracy‐first arguments for probabilism, and argue that there is no way for accuracy‐first epistemology to show that all credences of all agents should be coherent.     

Radical internalism

In her paper “Radical Externalism”, Amia Srinivasan argues that externalism about epistemic justification should be preferred to internalism by those who hold a “radical” worldview (according to which pernicious ideology distorts our evidence and belief-forming processes). I share Srinivasan's radical worldview, but do not agree that externalism is the preferable approach in light of the worldview we share. Here I argue that cases informed by this worldview can intuitively support precisely the internalist view that Srinivasan challenges, offer two such cases, and explain away the externalist-friendly intuitions that Srinivasan's cases solicit. I then articulate and defend a “radical” internalism, arguing that internalists’ aversion to epistemic hubris and emphasis on subjecting one's beliefs to critical scrutiny are especially attractive in realistic cases involving multiple intersecting axes of oppression—that is, precisely the sort of case that permeates our social world. I also argue that externalism's lack of interest in action-guiding principles leaves it with little to offer us in the fight against epistemic oppression.     

Distant Peers

What is the nature of rational disagreement? A number of philosophers have recently addressed this question by examining how we should respond to epistemic conflict with a so‐called epistemic peer—that is, someone over whom you enjoy no epistemic advantage. Some say that you're rationally required to suspend judgment in these cases—thereby denying the very possibility of a certain kind of rational disagreement. Others say that it's permissible to retain your beliefs even in the face of epistemic conflict. By distinguishing between close peers and distant peers, I argue that it's rational to respond to different types of peers in different ways. I also argue that remote peers—a particularly distant kind of distant peer—provide us with an important lesson in epistemic humility.     

Deducing the Mind

Frank Jackson has argued that, in principle, all mental truths are deducible from all physical science truths: 'deducibility'. Jackson's defence of deducibility relies upon the method for producing naturalistic definitions of mental states championed in the analytical functionalism of himself, David Lewis, and others. Two arguments are presented. The first contends that the particular naturalistic definitions of analytical functionalism fail because they do not take account of the extraordinary kind of bodily animation displayed by human beings, which I argue is necessary to (at least one kind of) mentality; machines lacking (at least this one kind of) mentality can satisfy the naturalistic definitions of analytical functionalism. So Jackson's defence of deducibility fails as it stands. The second argument contends that no naturalistic conceptual analysis of the mental can be adequate, because understanding (certain) mental concepts requires a special kind of affective reaction here named 'personal response', while understanding naturalistic concepts does not require this- therefore no naturalistic analysis can ever capture our common-sense mental concepts. The upshot is that Jackson's defence of deducibility cannot be repaired. No defence of deducibility will work which relies upon the possibility of naturalistic conceptual analyses of mentality.     

Sourcing Women's Ecological Knowledge: The Worry of Epistemic Objectification

In this paper, I argue that although it is important to attend to injustices surrounding women's epistemic exclusions, it is equally important to attend to injustices surrounding women's epistemic inclusions. Partly in response to the historical exclusion of women's knowledge, there has been increasing effort among first‐world actors to seek out women's knowledge. This trend is apparent in efforts to mainstream gender in climate change negotiation. Here, one is told that women's superior knowledge about how to adapt to climate change makes them “poised to help solve and overcome this daunting challenge.” Pulling from the work of Miranda Fricker, I argue that such claims risk epistemically objectifying women. To illuminate the risk of women's epistemic objectification in climate change discourse, I offer a feminist analysis of current efforts to seek women's environmental knowledge, cautioning throughout that such efforts must reflect just epistemic relations.     

SOLVING THE PROBLEM OF LOGICAL OMNISCIENCE

This paper looks at three ways of addressing probabilism's implausible requirement of logical omniscience. The first and most common strategy says it's okay to require an ideally rational person to be logically omniscient. I argue that this view is indefensible on any interpretation of ‘ideally rational’. The second strategy says probabilism should be formulated not in terms of logically possible worlds but in terms of doxastically possible worlds, ways you think the world might be. I argue that, on the interpretation of this approach that lifts the requirement of certainty in all logical truths, the view becomes vacuous, issuing no requirements on rational believers at all. Finally, I develop and endorse a new solution to the problem. This view proposes dynamic norms for reasoning with credences. The solution is based on an old proposal of Ian Hacking's that says you're required to be sensitive to logical facts only when you know they are logical facts.     

On the nature and systematic role of evidence: Husserl as a proponent of mentalist evidentialism?

In this paper, I shall show that for Husserl, (a) evidence determines epistemic justification and (b) evidence is linked to originary givenness in the sense that one's ultimate evidence consists of one's originary presentive intuitions. This means that in contemporary analytic terminology, Husserl is a proponent of evidentialism and mentalism. Evidentialism and mentalism have been introduced into current debates by Earl Conee and Richard Feldman. Finally, I shall highlight that there is one significant difference between Husserl and Earl Conee and Richard Feldman. Although Conee and Feldman argue that the fundamental principles of epistemology are principles of best explanation, Husserl opts for phenomenological principles as the most fundamental epistemic principles. The main difference is that for Husserl, experiences gain their justificatory force by virtue of their phenomenal character, namely, their originary givenness.