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In showing that all representation of the world takes place through the representation of possible states of affairs in elementary propositions, Wittgenstein has begun to clarify both how one proposition occurs in another, and the nature and status of so-called logical truths. He has used his clarified understanding of the nature of logical portrayal to show that one proposition does not occur in another in the same way in which a name occurs in a proposition of which it is a constituent. That is to say, a molecular proposition does not have any content over and above what is contained in its atoms.

Tarski implicitly postulated that a certain pre-theoretical concept of logical consequence and his technical concept of logical consequence are co-extensional. This chapter makes explicit a few theses about logical consequence or logical truth that sound Tarskian somehow, including one that most deserves the name ‘Tarski's Thesis’. Some of these theses are probably true or close to true but weaker than Tarski's. Some are false but stronger than Tarski's. Tarski's Thesis plausibly postulated that a sentence of a classical language possibly extended with non-traditional extensional logical constants is logically true, if it is true in all classical interpretations of all its non-logical constants. But it is noted that this thesis turns out to be false on most conceptions of logical truth, for some sentences of a classical language extended with extensional logical constants are true in all classical interpretations of all its non-logical constants, but are not necessary.

This chapter argues that the new tracking view is superior to externalist rivals: process reliabilism, the safety view, and the relevant alternatives view. This is because of the generality problem, and treatments of reflective knowledge, lottery propositions, direction of fit with the world, the power property, and knowledge of logical and other necessary truths. A new view of logical truth is introduced, which is in keeping with the tracking view that knowledge is a matter of responsiveness to the way the world is.

Defends both the concepts of truth at a time and of truth simpliciter.

It rejects arguments against truth at a time, according to which this concept involves a confusion between propositions and propositional functions. It argues that tensed views of time should employ three valued logics, and that alleged problems with the latter can be overcome by distinguishing between factual truth and logical truth. Finally, the chapter defends the concept of truth simpliciter: Tensed views of time still require this concept so as to apply it to propositions involving atemporal entities.

The chapter first displays how Descartes and Leibniz offered contrasting theist approaches to the conflicts — Leibniz’ being in a broad sense Platonic. Theists, it argues, should hold that necessary truths never have non-divine ontology not both created if it begins to exist and sustained if continuing to exist. They should hold that God creates and sustains events much as He does non-events like tables and chairs, and that if a necessary truth has no ontology, God still explains its being true. The chapter also argues that by providing necessary truths’ ontologies, God makes them true, discussing identity-statements, truths about essences and attributes, mathematical truths, and logical truths, including truths of modal logic.

It is maintained that Quine had two arguments against quantified modal logic; one rooted in an opposition to the idea of an essential property; and the other rooted in an opposition to the idea that one might intelligibly quantify into opaque contexts. These arguments are critically examined and shown to lead to very different conclusions and considerations.

The highly general notion of structure lets us raise metaphysical questions about logic. Is it conjunction or disjunction that is most fundamental? (An uncomfortable question! ‐ fortunately we may answer “both”; the joint‐carving notions can contain some redundancy.) Do logical notions carve at the joints? (Surely yes, since they are indispensable in fundamental theories.) Do metalogical notions ‐ such as logical truth and logical consequence ‐ carve at the joints? (Probably not; unlike logical notions they are not needed in fundamental theories.) Is logic classical? (At the fundamental level, yes; but in nonfundamental languages perhaps we should say not, because of vagueness and the liar paradox.)

For Kant, logical truth arises from the structure of the discursive intellect (i.e., an intellect that relates to objects indirectly, by means of concepts). Discursive cognition necessarily involves application of the categories, so we know a priori that the world as experienced by the discursive knower will consist of objects-with-properties standing in ground-consequent relations. This means that logical truths count as (roughly) analytic in Kant's famous dichotomy of analytic/synthetic, but the analytic truths involved aren't trivially definitional, but deep, contentful truths uncovered by delicate ‘exposition’ that's subject to error and often incomplete. Furthermore, just as the a priori truths of geometry are true only of the world as experienced by discursive cognizers with our spatiotemporal forms of intuition, likewise the a priori truths of logic are true only of the world as experienced by any discursive cognizer whatsoever. Thus logic is also, in a sense, transcendentally ideal.

Modal operators are unneeded in fundamental inquiries, and so they probably do not carve at the joints. A reduction of modality is therefore demanded. A “Humean” reduction is proposed, according to which necessarily true propositions are the logical consequences of a more‐or‐less arbitrary list of propositions; the list includes mathematical truths, analytic truths, “laws of metaphysics”, “natural kind propositions”, and others. Although the Humean account is similar in some ways to old‐fashioned conventionalism, truth by convention plays no role in it.

Here the book turns to doing, rather than describing, Second Philosophy. In preparation for the philosophy of mathematics in Part IV, Part III takes up the question of the nature of logical truth. In this chapter, several naturalistic possibilities are surveyed and critiqued: psychologism, empiricism, conventionalism and analyticity. This sets the stage for a distinctive second-philosophical account.

This chapter provides shorter version of the previous chapter and develops some of its themes. It argues that the status of Quine’s arguments against quantifying into modal contexts varies depending upon whether a logical or a metaphysical modality is in question. Various ways of making sense of de re logical modality are distinguished.

Considers criteria of adequacy for a theory of truth. The semantics of the truth predicate is explicated, together with accounts of what the proximate and ultimate truth conditions of logically complex sentences are.

This chapter traces out some implications of this epistemological account. First, it is explained how the account developed in Chapter 10 implies that under favourable conditions, normative truths are knowable a priori; but they are a special case of the a priori, differing in important ways from other forms of a priori truths, such as logical and mathematical truths. The remainder of the chapter is devoted to a further problem: the existence of widespread and persistent disagreement about normative questions. It is argued that it can be rational to persist in one's normative belief, even if those who disagree with one's belief include thinkers who are equally intelligent, thoughtful, and well informed about the non-normative facts (i.e., thinkers who are one's ‘epistemic peers’). Contrary to what some philosophers might assume, this view is quite compatible with the realist conception of the normative that this book is designed to defend.

This chapter discusses the philosophical theories and presuppositions of applying possible worlds semantics in order to draw conclusions about matters involving what are called conceptual or broadly logical possibilities and necessities. Every purely logical truth is necessary in this sense, but the set of conceptually necessary truths includes much more: mathematical truths and analytic truths are also held to be necessary in this broadly logical sense. There are many different systems of modal logic, but the type of system that is generally believed to formalise correctly the logical features of this broadly logical sense of necessity is called S5. It is useful to have a specific version of an S5 quantificational modal logic at hand, in terms of which this book's philosophical investigations can be carried out.

How does a law of logic speak to thought? How, if at all, might the world speak to such a law's truth? Is there such a thing as things being other than it says? What does it say? This chapter explores these questions by developing an idea of Putnam's, as set out in his ‘Rethinking Logical Necessity’.

There are schools of logicians who claim that an argument is not valid unless the conclusion is relevant to the premises. In particular, relevance logicians reject the classical theses that anything follows from a contradiction and that a logical truth follows from everything. This chapter critically evaluates several different motivations for relevance logic, and several systems of relevance logic, finding them all wanting.

According to this second-philosophical account, rudimentary logic is contingent on certain very general structural features and is true only when and where they are present. (We tend to think logic truth is necessary because its outlines are so fundamental to our cognition; KF-structure comes built into our very notion of a possible world.) Whether or not it counts as a priori depends on one's account of a priority, but it does appear to reside in our innate or nearly innate cognitive structures; it requires no training, no particular experience, and will naturally seem self-evident or obvious to us. Rudimentary logic isn't empirical in a psychologistic or Quinean sense, but it could in principle be overturned empirically (quantum logic is not a successful example, pace Putnam), assuming our feeble human brains were up to the task of thinking in an alternative way. Finally, there seems little to recommend the idea that it is true by virtue of meaning (the contemporary version of analyticity), and even if it were, this wouldn't settle the empirical question of whether or not those meanings are applicable in a given situation.

Kant's two-level scheme allows him to say two things at once: speaking empirically, logic is objectively true (empirically real) because of the structure of the world (e.g., because it's made up of objects-with-properties, standing in ground-consequent relations); speaking transcendentally, logic is true because of the necessary structure of any discursive intellect (transcendentally ideal). To make use of these attractive ideas, the Second Philosopher needs to combine them on one level: as a first approximation, she proposes that a rudimentary logic is true of the world because of its structural features, that humans believe this logic because their cognitive apparatus allow them to detect those structural features, and humans are so-configured because the world is so-structured. This chapter spells out the structural features at work here, beginning from Kant's categories and modifying in light of Frege's work (to reach the notion of a ‘KF-structure’).

Chapter 6 re-presents the famous Benacerraf Dilemma, now extended from its original version in the context of mathematical truth and knowledge, to logical truth and knowledge, and then generalized to all kinds of a priori knowledge. More specifically, the chapter outlines and addresses five difficult philosophical problems, namely: (1) The Original Benacerraf Dilemma, which seems to entail that objective mathematical necessary truth, on the one hand, and rational human a priori knowledge of objective mathematical necessary truth, on the other hand, are mutually incompatible; (2) The Extended Benacerraf Dilemma, which smoothly extends The Original Benacerraf Dilemma from mathematics to logic; (3) The Generalized Benacerraf Dilemma, which further elaborates the shared deep structure of The Original and The Extended Dilemmas; (4) The Problem of the Epistemic Status of Rational Intuitions; and (5) The Problem of Objectivity.