The chapter is an overview of Indian logic, with a general introduction followed by specialized sections on four different schools: Nyāya logic, Buddhist logic, Jaina logic, and Navya-Nyāya logic.
Indicative Conditionals
The chapter is an introduction to logical treatments of indicative conditionals, comparing truth-functional, non-truth-functional, and suppositional approaches. Some of the topics discussed are truth conditions, conditional belief, assertability, and issues with compounds of conditionals.
Logic and Natural Language
Logicians have always found inspiration for new research in the ordinary language that is used on a daily basis and acquired naturally in childhood. Whereas the logical issues in the foundations of mathematics motivated the development of mathematical logic with its emphasis on notions of proof, validity, axiomatization, decidability, consistency, and completeness, the logical analysis of natural language motivated the development of philosophical logic with its emphasis on semantic notions of presupposition, entailment, modality, conditionals, and intensionality. The relation between research programs in both mathematical and philosophical logic and natural language syntax and semantics as branches of theoretical linguistics has increased in importance throughout the last fifty years. This chapter reviews the development of one particularly interesting and lively area of interaction between formal logic and linguistics—the semantics of natural language. Research in this emergent field has proved fruitful for the development of empirically, cognitively adequate models of reasoning with partial information, sharing or exchanging information, dynamic interpretation in context, belief revision and other cognitive processes.
Truth
The concept of truth serves in logic not only as an instrument but also as an object of study. Eubulides of Miletus (fl. fourth century BCE), a Megarian logician, discovered the paradox known as ‘the Liar,’ and, ever since his discovery, logicians down the ages – Aristotle and Chrysippus, John Buridan and William Heytesbury, and Alfred Tarski and Saul Kripke, to mention just a few – have tried to understand the puzzling behavior of the concept of truth.
The Form of Truth: Hegel’s Philosophical Logic
This book is a consideration of Hegel’s view on logic and basic logical concepts such as truth, form, validity, and contradiction, and aims to assess this view’s relevance for contemporary philosophical logic. The literature on Hegel’s logic is fairly rich. The attention to contemporary philosophical logic places the present research closer to those works interested in the link between Hegel’s thought and analytical philosophy, Koch 2014, Brandom 2014, 1-15, Pippin 2016, Moyar 2017, Quante & Mooren 2018 among others). In this context, one particularity of this book consists in focusing on something that has been generally underrated in the literature: the idea that, for Hegel as well as for Aristotle and many other authors, logic is the study of the forms of truth, i.e. the forms that our thought can assume in searching for truth. In this light, Hegel’s thinking about logic is a fundamental reference point for anyone interested in a philosophical foundation of logic.
Privilege and Position: Formal Tools for Standpoint Epistemology
How does being a woman affect one’s epistemic life? What about being black? Or queer? Standpoint theorists argue that such social positions can give rise to otherwise unavailable epistemic privilege. “Epistemic privilege” is a murky concept, however. Critics of standpoint theory argue that the view is offered without a clear explanation of how standpoints confer their benefits, what those benefits are, or why social positions are particularly apt to produce them. But this need not be so. This article articulates a minimal version of standpoint epistemology that avoids these criticisms and supports the normative goals of its feminist forerunners. With this foundation, we develop a formal model in which to explore standpoint epistemology using neighborhood semantics for modal logic.
Inner and Outer Truth
Kit Fine and Robert Adams have independently introduced a distinction between two ways in which a proposition might be true with respect to a world. A proposition is true at a world if it correctly represents the world. A proposition is true in a world, if it exists in that world and correctly represents it. In this paper, I clarify this distinction between outer and inner truth, defend it against recent charges of unintelligibly and argue that outer truth tracks counterfactual possibility while inner truth tracks counter-actual possibility. This connection allows us to clarify the relationship between possibility, possible actuality and the thesis of serious actualism, which is the thesis that nothing could have had a property without existing. I show that this undermines serious actualists’ scruples against reading sentences like `Even if Socrates had not existed, he might have’ as expressing true and genuinely de re propositions about Socrates. More generally, the connection I draw provides the serious actualist with a justification for treating actually existing but contingent objects differently from how he treats merely possible objects
Proxy ”Actualism”
Bernard Linsky and Edward Zalta have recently proposed a new form of actualism. I characterize the general form of their view and the motivations behind it. I argue that it is not quite new – it bears interesting similarities to Alvin Plantinga’s view – and that it definitely isn’t actualist.
Two Axes of Actualism
Actualists routinely characterize their view by means of the slogan, “Everything is actual.” They say that there aren’t any things that exist but do not actually exist—there aren’t any “mere possibilia.” If there are any things that deserve the label ‘possible world’, they are just actually existing entities of some kind—maximally consistent sets of sentences, or maximal uninstantiated properties, or maximal possible states of affairs, or something along those lines. Possibilists, in contrast, do think that there are mere possibilia, that there are things that are not actual. They think that more exists than what actually exists. All I have done so far, though, is rephrase the slogan in various ways. To say that everything is actual is precisely to say that there are no things that do not actually exist, which is precisely to say that there are no mere possibilia, and which is also precisely to say that we cannot sep- arately quantify over what exists and what is actual. These claims all amount to the same thing. But what is that, exactly? What on earth does it mean to say that everything is actual, that there are no mere possibilia, and so on? What does the actualist slogan really come to? I think the literature is far from clear on this point, and that people work themselves into unnecessary muddles because of it. Indeed, certain confusions that I shall discuss in the first half of this article seem to be on the rise. It is high time to lay out the issues and the choice points as clearly as possible. There are two primary choices to be made; there are two axes along which versions of actualism can vary. One choice has to do with how to treat claims about things that merely could exist. The other choice has to do with the modal status of the view and of how we should think about the “actual” in actualism. I make no claim that the positions I will eventually endorse are star- tlingly new. I think that most people will agree with the decisions I make at both choice points and will in fact find some bits of this essay obvious. But not everyone agrees with my decisions, and it has been my experience that people differ remarkably about which bits they find obvious—a fact I find rather telling. My goal, then, is to show that the two axes are there and to clarify the consequences of the choices.
The Methodological is Political: What’s the Matter with ‘Analytic Feminism’?
A core insight of some important second wave feminist writings is that, in order to qualify as truly ‘feminist’, a movement has to be politically radical. For example, there is a powerful articulation of this theme, to mention one noteworthy site, in the work of bell hooks. A guiding preoccupation of hooks’ thought, as far back as the early eighties, is to underline the pernicious and intellectually flawed character of the supposedly ‘feminist’ postures of ‘bourgeois white women’ in the U.S. whose efforts are directed toward the politically superficial goal of claiming the social privileges of bourgeois white men. hooks shows that there is no way to ‘overcome barriers that separate women from one another’ without ‘confronting the reality of racism’. She describes how the forms of gender-based subordination experienced by privileged white women are inextricable from racist and classist social mechanisms that elevate these women above women who are non-white and poor, and how the sexist obstacles that poor and non-white women encounter are in turn permeated by racism and classism. hooks concludes that if ‘feminism’ is to be dedicated to identifying and resisting sexist oppression, it needs to – in her words – ‘direct our attention to systems of domination and the interrelatedness of sex, race and class oppression.