Overview
Philosophy of Logic is a compact philosophical inquiry into the nature of logic rather than a formal textbook in proof technique. Its central concern is the relationship between logic, truth, and grammar. The book argues that logic is the product of two factors, truth and grammar, but it rejects the view that logical truths are true merely because of grammar, language, or linguistic convention. Logical truth is not a mere matter of words. Across its seven chapters, the book develops an account of logical form, truth-functional logic, quantification, the boundaries of logic, the challenge of “deviant” logics, and the ultimate ground of logical truth.
Meaning and Truth
The opening chapter distinguishes questions of truth from questions of meaning. Logic is concerned with truth, but not with all truths; it studies truth insofar as truth depends on logical structure. The chapter treats truth as a property of sentences and emphasizes the disquotational character of the truth predicate: to say that a sentence is true is, in the basic case, simply to affirm what the sentence says. This makes the truth predicate a device for talking about sentences rather than directly about the world, and it allows language to be turned upon itself.
The chapter also discusses the difference between using an expression and mentioning it, and the role of quotation in forming names of expressions. Meaning is approached through translation and synonymy rather than through abstract entities such as propositions. The discussion prepares the way for later chapters by separating the question “What does a sentence mean?” from the question “Is the sentence true?” and by showing why logic can focus on truth-preserving structure without relying on a mysterious realm of meanings.
Grammar
The second chapter develops a general theory of grammar. Grammar is treated as a finite specification of which strings count as grammatical, and grammatical categories are understood through patterns of substitutability and distribution. The chapter distinguishes grammaticality from meaningfulness: a string can be grammatically well formed and still be semantically odd or nonsensical. It also distinguishes surface grammar from logical grammar. Ordinary language has a grammatical structure, but logical analysis requires a sharper representation of the categories and constructions that matter for truth.
This chapter supplies the apparatus for identifying logical form. Logical structure is not simply read off the surface grammar of ordinary sentences; it depends on a disciplined grammatical analysis of terms, predicates, connectives, and quantifiers. At the same time, the chapter insists that logical form is still a kind of grammatical form. Logic is not divorced from language, even though logical truth is not reducible to mere linguistic convention.
Truth
The third chapter turns to truth-functional logic. It introduces truth values and truth-functional compounds, and it explains how the truth value of a compound sentence is determined by the truth values of its components. Negation, conjunction, disjunction, the conditional, and the biconditional are treated as truth functions. Truth tables are used to display the possible truth values of compound sentences, and the notion of a tautology is explained as a sentence that comes out true under every assignment of truth values to its components.
The chapter also discusses the material conditional and the sense in which ordinary “if … then” constructions can be represented truth-functionally. Truth-functionality is presented as a feature of the logical connectives: the truth value of a truth-functional compound depends only on the truth values of its parts, not on their meanings or subject matter. This gives the first layer of logic: a system of truth-functional validity.
Logical Truth
The fourth chapter extends the account from truth-functional tautology to quantification and logical truth more generally. Logical truth is characterized through logical form: a logical truth is a sentence that is true under all relevant interpretations or substitutions of its nonlogical vocabulary. Quantifiers, variables, open sentences, and satisfaction are introduced to explain how sentences involving “all” and “some” can be treated systematically. Logical implication is likewise explained in terms of truth under all interpretations.
The chapter distinguishes logical truth from mere grammaticality and from truth by definition. Logical truths are true in virtue of their logical structure—the arrangement of truth-functional connectives, quantifiers, variables, and identity—rather than in virtue of the specific subject matter of the nonlogical terms. This is the core of the book’s positive account: logical truth arises from the interplay of grammar and truth, but it is not merely a report about how words are used.
The Scope of Logic
The fifth chapter asks what belongs to logic. The core of logic is identified with truth-functional logic, quantification, and identity. These are the devices that generate the most general truth-preserving forms. Set theory and mathematics are not simply more of the same logic; set theory is a substantive mathematical theory rather than a mere extension of logical grammar. The chapter thus draws boundaries around logic and distinguishes logical constants from nonlogical vocabulary.
The discussion also considers possible extensions of logic and the question of how far the domain of logic should be pushed. The guiding idea is that logic is not coextensive with all rigorous reasoning or with all of mathematics. Its scope is fixed by the general logical vocabulary and by the forms of truth-preserving inference that depend on that vocabulary. This chapter reinforces the book’s opposition to the idea that logic is merely a matter of words: logic has a determinate subject matter, namely the most general forms of truth and inference.
Deviant Logics
The sixth chapter examines proposed alternatives to classical logic, often called deviant logics. Examples include intuitionistic logic, quantum logic, and many-valued logic. Intuitionism refuses to accept the law of excluded middle in certain contexts; quantum logic is motivated by apparent failures of distributivity in quantum phenomena; many-valued logics introduce additional truth values beyond truth and falsehood.
The book’s treatment is critical. Proposed deviations often change the meanings of the logical constants rather than refuting classical logic on its own terms. When a deviant system uses a connective with a different truth table or a different inferential role, it is not simply contradicting classical logic; it is using a different logical vocabulary. The chapter argues that the classical laws are not easily revised as if they were ordinary empirical hypotheses. Deviant logics may have their uses, but they do not show that classical logic is false or that logical truth is merely conventional.
The Ground of Logical Truth
The final chapter asks why logical truths are true. It rejects the doctrine that logical truths are true because of grammar alone or because of arbitrary linguistic conventions. Logical truth is indeed connected with grammar—it depends on the meanings of the logical constants and on the grammatical structure of sentences—but grammar by itself does not explain why those truths hold. The truth of logical truths is not exhausted by the fact that language has certain rules.
The book concludes that logic is grounded in truth and grammar together. Logical truths are true because of the most general features of logical structure and because of the way the logical vocabulary functions in relation to truth. They are not mere verbal stipulations, and they are not simply descriptions of how people happen to speak. Logic is a substantive discipline: it articulates the most general forms of truth-preserving discourse, and its truths are not reducible to linguistic convention.
The book’s account of truth is deliberately austere. It treats “true” as a predicate of sentences rather than of propositions or mental contents, and it explains the truth of a sentence by the equivalence between saying that the sentence is true and simply affirming the sentence. This does not make truth a linguistic convention; it makes truth a device that allows one to generalize over sentences. The discussion also acknowledges the need to distinguish a language from the metalanguage in which its truth predicate is defined, and it takes seriously the semantic paradoxes that arise when truth is allowed to apply to the language in which it is expressed.
Closely connected is the book’s attention to use and mention. Logical laws are stated in language and apply to sentences, so confusion between an expression and what it says can generate spurious problems. The treatment of grammar is similarly restrained: ordinary surface grammar is not a reliable guide to logical form, and logical analysis requires a perspicuous notation that makes truth-functional and quantificational structure explicit. This regimentation is a tool for isolating the forms relevant to inference, not a claim that ordinary language is inferior.
The account of logical truth is formulated in terms of substitution: a sentence is logically true when it is true and remains true under all substitutions for its nonlogical vocabulary. The logical constants are those expressions whose meanings sustain this invariance. This account explains why logical truth is more than grammatical well-formedness and less than all necessary or mathematical truth, and it avoids appealing to a realm of propositions or possible worlds. The book does not explain logical truth by appeal to analyticity; it treats logical truth as the clearer notion.
Throughout, the book opposes psychologism: logic is not a description of how people actually think, but a theory of the most general forms of truth-preserving discourse. Its significance is as a compact statement of a classical, truth-oriented philosophy of logic—one that accepts the linguistic and grammatical dimension of logic while refusing to collapse logical truth into convention, grammar, or psychology.
