Strict Finitism and the Happy Sorites

Call an argument a ‘happy sorites’ if it is a sorites argument with true premises and a false conclusion. It is a striking fact that although most philosophers working on the sorites paradox find it at prima facie highly compelling that the premises of the sorites paradox are true and its conclusion false, few (if any) of the standard theories on the issue ultimately allow for happy sorites arguments. There is one philosophical view, however, that appears to allow for at least some happy sorites arguments: strict finitism in the philosophy of mathematics. My aim in this paper is to explore to what extent this appearance is accurate. As we shall see, this question is far from trivial. In particular, I will discuss two arguments that threaten to show that strict finitism cannot consistently accept happy sorites arguments, but I will argue that (given reasonable assumptions on strict finitistic logic) these arguments can ultimately be avoided, and the view can indeed allow for happy sorites arguments.     

If Abortion,then Infanticide

Our contention is that all of the major arguments for abortion are also arguments for permitting infanticide. One cannot distinguish the fetus from the infant in terms of a morally significant intrinsic property, nor are they morally discernible in terms of standing in different relationships to others. The logic of our position is that if such arguments justify abortion, then they also justify infanticide. If we are right that infanticide is not justified, then such arguments will fail to justify abortion. We respond to those philosophers who accept infanticide by putting forth a novel account of how the mindless can be wronged which serves to distinguish morally significant potential from morally irrelevant potential. This allows our account to avoid the standard objection that many entities possess a potential for personhood which we are intuitively under no obligation to further or protect.     

Radical Interpretation and Logical Pluralism

I examine Quine’s and Davidson’s arguments to the effect that classical logic is the one and only correct logic. This conclusion is drawn from their views on radical translation and interpretation, respectively. I focus on the latter, but I first address, independently, Quine’s argument to the effect that the ‘deviant’ logician, who departs from classical logic, is merely changing the subject. Regarding logical pluralism, the question is whether there is more than one correct logic. I argue that bivalence may be subject matter dependent, but that distribution and the law of excluded middle can probably not be dropped whilst maintaining the standard meanings of the connectives. In discussing the ramifications of the indeterminacy of interpretation, I ask whether it forces Davidsonian interpreters to adopt Dummett’s epistemic conception of truth vis-à-vis their interpretations. And, if so, does this cohere with their attributing a nonepistemic notion of truth to their interpretees? This would be a form of logical pluralism. In addition, I discuss Davidson’s arguments against conceptual schemes. Schemes incommensurable with our own could be construed as wholesale deviant logics, or so I argue. And, if so, their possibility would yield, in turn, the possibility of a radical logical pluralism. I also address Davidson’s application of Tarski’s definition of truth.

     

The Individuation of Actions

I argue against a view of the individuation of actions endorsed most notably by Hornsby and Davidson. This is the view that in, for example, Anscombe's case of the pumping man, we have a single action which can be described, variously, as a pumping, a poisoning and so on. I argue that, even in the area of the standard arguments against this view, such as that based on the logic of 'by' and the argument from temporal dimensions, the case against the Davidson-Hornsby view has not been made as strong as it ought to have been. I show how those standard arguments can be strengthened; and I argue that the principal considerations adduced in support of the view do not in fact lend it the support that they have been widely thought to lend it. I conclude that the view should be rejected.     

Why should we abandon the mental logic hypothesis?

Two hypotheses on deductive reasoning are under development: mental logic and mental models. It is often accepted that there are overwhelming arguments to reject the mental logic hypothesis. I revise these arguments and claim that they are either not conclusive, or point at problems which are troublesome for the mental model hypothesis as well.     

An erotetic approach to explanation by specification

In earlier publications of the first author it was shown that intentional explanation of actions, functional explanation of biological traits and causal explanation of abnormal events share a common structure. They are called explanation by specification (of a goal, a biological function, an abnormal causal factor, respectively) as opposed to explanation by subsumption under a law. Explanation by specification is guided by a schematic train of thought, of which the argumentative steps not concerning questions were already shown to be logically valid (elementary) arguments.Independently, the second author developed a new, inferential approach to erotetic logic, the logic of questions. In this approach arguments resulting in questions, with declarative sentences and/or other questions as premises, are analyzed, and validity of such arguments is defined.In the present paper it is shown that all four kinds of erotetic argumentative steps occurring in the train of thought of explanation by specification are valid arguments in the sense of inferential erotetic logic. Hence, in view of the fact that the other argumentative steps were already shown to be valid, it may be concluded that the logical structure of explanation by specification can be as well-established as that of explanation by nomological subsumption. Moreover, explanation by specification provides some illustrations of the applicability of erotetic logic in everyday life and some empirical sciences.     

基于论证型式应用的论证挖掘

本文旨在为构建一种以论证型式为基础的方法,用以帮助非形式逻辑的学生分析自然语言对话的文本,并识别出其中所出现的常见论证类型。他们在这一过程中时常会错误地辨识论证类型,而本文将表明所发展的这种方法对于学习非形式逻辑的学生们是非常有帮助的。另外,对于那些可用于构建一种有用的论证识别方法的理论资源,本文对其最新发展动态进行了考察,并且也概览了当前人工智能领域中所发展的自动论证挖掘工具。     

Context and consequence. An intercontextual substructural logic

Some apparently valid arguments crucially rely on context change. To take a kind of example first discussed by Frege, ‘Tomorrow, it’ll be sunny’ taken on a day seems to entail ‘Today, it’s sunny’ taken on the next day, but the first sentence taken on a day sadly does not seem to entail the second sentence taken on the second next day. Mid-argument context change has not been accounted for by the tradition that has extensively studied the distinctive logical properties of context-dependent languages, for that tradition has focussed on arguments whose premises and conclusions are taken at the same context. I first argue for the desiderability of having a logic that accounts for mid-argument context change and I explain how one can informally understand such context change in a standard framework in which the relation of logical consequence holds among sentences. I then propose a family of simple temporal “intercontextual” logics that adequately model the validity of certain arguments in which the context changes. In particular, such logics validate the apparently valid argument in the Fregean example. The logics lack many traditional structural properties (reflexivity, contraction, commutativity etc.) as a consequence of the logical significance acquired by the sequence structure of premises and conclusions. The logics are however strong enough to capture in the form of logical truths all the valid arguments of both classical logic and Kaplan-style “intracontextual” logic. Finally, I extend the framework by introducing new operations into the object language, such as intercontextual conjunction, disjunction and implication, which, contrary to intracontextual conjunction, disjunction and implication, perfectly match the metalinguistic, intercontextual notions of premise combination, conclusion combination and logical consequence by representing their respective two operands as taken at different contexts.     

Ideal Worlds — Wishful Thinking in Deontic Logic

The ideal world semantics of standard deontic logic identifies our obligations with how we would act in an ideal world. However, to act as if one lived in an ideal world is bad moral advice, associated with wishful thinking rather than well-considered moral deliberation. Ideal world semantics gives rise to implausible logical principles, and the metaphysical arguments that have been put forward in its favour turn out to be based on a too limited view of truth-functional representation. It is argued that ideal world semantics should be given up in favour of other, more plausible uses of possible worlds for modelling normative subject-matter.     

Argumentation Without Arguments

A well-known ambiguity in the term ‘argument’ is that of argument as an inferential structure and argument as a kind of dialogue. In the first sense, an argument is a structure with a conclusion supported by one or more grounds, which may or may not be supported by further grounds. Rules for the construction and criteria for the quality of arguments in this sense are a matter of logic. In the second sense, arguments have been studied as a form of dialogical interaction, in which human or artificial agents aim to resolve a conflict of opinion by verbal means. Rules for conducting such dialogues and criteria for their quality are part of dialogue theory. Usually, formal accounts of argumentation dialogues in logic and artificial intelligence presuppose an argument-based logic. That is, the ways in which dialogue participants support and attack claims are modelled as the construction of explicit arguments and counterarguments (in the inferential sense). However, in this paper formal models of argumentation dialogues are discussed that do not presuppose arguments as inferential structures. The motivation for such models is that there are forms of inference that are not most naturally cast in the form of arguments (such as abduction, statistical reasoning and coherence-based reasoning) but that can still be the subject of argumentative dialogue. Some recent work in artificial intelligence is discussed which embeds non-argumentative inference in an argumentative dialogue system, and some general observations are drawn from this discussion.     

On the Special Logic Thesis in Chinese Philosophy

I address the problem of whether philosophy can be international by its claim to represent rationality, hence universality. I argue in favor of this claim by focusing on the special logic thesis in Chinese philosophy. This thesis holds that a different type of logic must be used when studying the Chinese texts. I argue at length against the special logic thesis by examining the problem of human nature in the Confucian philosophers Mencius, Hsün Tzu and Kao Tzu. I show how their arguments can be reconstructed as inductive analogical arguments and as deductive argument. I then broaden the notion of the logic of argumentation into a discussion of metaphysical anti-essentialism and underdetermination in order to resolve the problem of human nature and also to show how the same types of logical analysis (more generally construed) can be applied to the arguments from these Confucian philosophers. Under my treatment, Kao Tzu, somewhat surprisingly, turns out to provide the most insight.     

Psychologism and Metalogic

This paper examines two arguments againstpsychologism advanced by Frege andHusserl. The first argument says that thelaws of logic cannot be justified by thelaws of psychology, because the formerand a priori and certain, but the latterare probable only. The second argumentpoints out that the status of logicallaws as universal principles of thinking isnot intelligible on the psychologisticinterpretation of logic. The author tries toshow how to examine both arguments bymetalogical devices.     

Structure and pragmatics in informal argument: circularity and question-begging

Most everyday arguments are informal, as contrasted with the formal arguments of logic and mathematics. Whereas formal argument is well understood, the nature of informal argument is more elusive. A recent study by Rips (2002) provides further evidence regarding the roles of structure and pragmatics in informal argument.     

Some Artificial Intelligence Tools for Argument Evaluation: An Introduction

Even though tools for identifying and analyzing arguments are now in wide use in the field of argumentation studies, so far there is a paucity of resources for evaluating real arguments, aside from using deductive logic or Bayesian rules that apply to inductive arguments. In this paper it is shown that recent developments in artificial intelligence in the area of computational systems for modeling defeasible argumentation reveal a different approach that is currently making interesting progress. It is shown how these systems provide the general outlines for a system of argument evaluation that can be applied to legal arguments as well as everyday conversational arguments to assist a user to evaluate an argument.     

The Early Formation of Modal Logic and its Significance: A Historical Note on Quine,Carnap, and a Bit of Church

The aim of the paper is to show that W. V. O. Quine's animadversions against modal logic did not get the same attention that is considered to be the case nowadays. The community of logicians focused solely on the technical aspects of C. I. Lewis’ systems and did not take Quine's arguments and remarks seriously—or at least seriously enough to respond. In order to assess Quine's place in the history, however, his relation to Carnap is considered since their notorious break was about the status of extensionality and modal logic (and analyticity was much more of a second issue). Since much of the works about the history of analytic philosophy is centered on the relationship of Quine and Carnap, their break about modality deserves much more attention—it also sheds some light on why should anyone wonder about Quine's early arguments against modal logic. The paper ends with some further considerations regarding the early formation of modal logic and hitherto unconsidered problematic issues.     

Some Comments on Ian Rumfitt’s Bilateralism

Ian Rumfitt has proposed systems of bilateral logic for primitive speech acts of assertion and denial, with the purpose of ‘exploring the possibility of specifying the classically intended senses for the connectives in terms of their deductive use’ (Rumfitt Mind109, 781–823 (4): 810f). Rumfitt formalises two systems of bilateral logic and gives two arguments for their classical nature. I assess both arguments and conclude that only one system satisfies the meaning-theoretical requirements Rumfitt imposes in his arguments. I then formalise an intuitionist system of bilateral logic which also meets those requirements. Thus Rumfitt cannot claim that only classical bilateral rules of inference succeed in imparting a coherent sense onto the connectives. My system can be extended to classical logic by adding the intuitionistically unacceptable half of a structural rule Rumfitt uses to codify the relation between assertion and denial. Thus there is a clear sense in which, in the bilateral framework, the difference between classicism and intuitionism is not one of the rules of inference governing negation, but rather one of the relation between assertion and denial.     

Supervenience arguments under relaxed assumptions

When it comes to evaluating reductive hypotheses in metaphysics, supervenience arguments are the tools of the trade. Jaegwon Kim and Frank Jackson have argued, respectively, that strong and global supervenience are sufficient for reduction, and others have argued that supervenience theses stand in need of the kind of explanation that reductive hypotheses are particularly suited to provide. Simon Blackburn’s arguments about what he claims are the specifically problematic features of the supervenience of the moral on the natural have also been influential. But most discussions of these arguments have proceeded under the strong and restrictive assumptions of the S5 modal logic. In this paper we aim to remedy that defect, by illustrating in an accessible way what happens to these arguments under relaxed assumptions and why. The occasion is recent work by Ralph Wedgwood, who seeks to defend non-reductive accounts of moral and mental properties together with strong supervenience, but to evade both the arguments of Kim and Jackson and the explanatory challenge by accepting only the weaker, B, modal logic. In addition to drawing general lessons about what happens to supervenience arguments under relaxed assumptions, our goal is therefore to shed some light on both the virtues and costs of Wedgwood’s proposal.     

I—What is the Normative Role of Logic?

The paper tries to spell out a connection between deductive logic and rationality, against Harman's arguments that there is no such connection, and also against the thought that any such connection would preclude rational change in logic. One might not need to connect logic to rationality if one could view logic as the science of what preserves truth by a certain kind of necessity (or by necessity plus logical form); but the paper points out a serious obstacle to any such view.     

Reassessing logical hylomorphism and the demarcation of logical constants

The paper investigates the propriety of applying the form versus matter distinction to arguments and to logic in general. Its main point is that many of the currently pervasive views on form and matter with respect to logic rest on several substantive and even contentious assumptions which are nevertheless uncritically accepted. Indeed, many of the issues raised by the application of this distinction to arguments seem to be related to a questionable combination of different presuppositions and expectations; this holds in particular of the vexed issue of demarcating the class of logical constants. I begin with a characterization of currently widespread views on form and matter in logic, which I refer to as ‘logical hylomorphism as we know it’—LHAWKI, for short—and argue that the hylomorphism underlying LHAWKI is mereological. Next, I sketch an overview of the historical developments leading from Aristotelian, non-mereological metaphysical hylomorphism to mereological logical hylomorphism (LHAWKI). I conclude with a reassessment of the prospects for the combination of hylomorphism and logic, arguing in particular that LHAWKI is not the only and certainly not the most suitable version of logical hylomorphism. In particular, this implies that the project of demarcating the class of logical constants as a means to define the scope and nature of logic rests on highly problematic assumptions.     

Profiles of Dialogue for Evaluating Arguments from Ignorance

This investigation uses the technique of the profile of dialogue as a tool for the evaluation of arguments from ignorance (also called lack-of-evidence arguments, negative evidence, ad ignorantiam arguments and ex silentio arguments). Such arguments have traditionally been classified as fallacies by the logic textbooks, but recent research has shown that in many cases they can be used reasonably. A profile of dialogue is a connected sequence of moves and countermoves in a conversational exchange of a type that is goal-directed and can be represented in a normative model of dialogue. Selected case studies are used to probe special features of using the profile technique as applied to arguments from ignorance of a kind that occur frequently in everyday conversational exchanges. One of these special features is the use of Gricean implicature. Another is the need to use negative profiles of argument.