36.3946, Reviews: Logic for Everyone: Jason Decker (2025)

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Subject: 36.3946, Reviews: Logic for Everyone: Jason Decker (2025)

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Date: 22-Dec-2025
From: Chara Vlachaki [charavl.88 at gmail.com]
Subject: Jason Decker (2025)


Book announced at https://linguistlist.org/issues/36-1601

Title: Logic for Everyone
Subtitle: From Proof to Paradox
Publication Year: 20250417

Publisher: Cambridge University Press
           http://www.cambridge.org/linguistics
Book URL:
https://www.cambridge.org/highereducation/books/logic-for-everyone/48CC430FEB5FD512D19A774CCD963F7B#overview

Author(s): Jason Decker

Reviewer: Chara Vlachaki

When you have finished your review, please go to
https://linguistlist.org/reviews/submit and click the button under
this book title.
SUMMARY
“Logic for Everyone: From Proof to Paradox” (henceforth, “Logic for
Everyone”), written by Jason Decker (2025), Professor of Philosophy
and Cognitive Science in Carleton College, is an academic textbook
designed for undergraduate students who seek a rigorous yet accessible
introduction to formal logic. It can also be intended for a broader
interdisciplinary audience, particularly those in philosophy,
linguistics, cognitive science, computer science, and mathematics, who
have more philosophical interests.
Decker’s engaging approach to key principles of logic does not assume
any prior formal training as he uses scaffolding to gradually
introduce complex concepts and paradoxes. The book is divided into
three parts, and each chapter includes clear, succinct definitions,
summaries, engaging examples, a suggested bibliography for further
reading and a series of practice exercises ranging from formal proof
drills to open-ended essays. The chapters are structured flexibly
giving potential instructors the opportunity to tailor their teaching
to a single or a two-part module throughout a course according to the
cohort’s prior knowledge and needs.
“Logic for Everyone” spans over twenty three chapters, which are
grouped into three main parts: foundations of propositional logic
(Chapters 1-9), quantified logic and formal semantics (Chapters
10-20), and paradoxes and next steps in the study of logic (Chapters
21-23).
Chapters 1-9: Propositional Logic
The first part begins with a discussion on propositional logic (PL)
and offers a meticulous introduction to classical logic and its
foundational concepts. Chapter 1 focuses on the basics of classical
logic and transitions to the structure of arguments in terms of
inductive and deductive reasoning. It highlights the difficulty caused
by ambiguity and vagueness. Chapter 2 deals with atomic and complex
sentences focusing on truth functions (Boolean connectives) and truth
tables. Chapter 3 explores key semantic concepts in logic, i.e.
tautologies, contradiction, and contingency. At this stage, Decker
introduces the principle of explosion, according to which, any
argument with contradictory premises can be deductively valid. Chapter
4 discusses the formal rules of inference for the Boolean operators
and the limitations of truth tables before revisiting the principle of
explosion. Chapter 5 explores further the limitations of PL in
capturing the nuances of natural language and introduces Grice’s
pragmatic theory (1957, 1975) in order to bring to light the pragmatic
aspects of language that PL tends to ignore. Chapter 6 presents the
distinction between indicative and subjunctive conditionals based on
their truth-conditions. This chapter sets the stage for a more
in-depth exploration of conditionals in Chapter 7, where Gricean
pragmatics is mentioned again to explore the extent to which context
and speaker intention influence the truth value of conditionals.
Chapter 8 investigates the underlying structure of logical arguments
especially in terms of indicative conditionals and examines the role
of semantic theory in clarifying logical inference. The last chapter
of Part I, Chapter 9, assesses the expressive power of PL by
introducing the concept of truth-functional completeness, according to
which a language is truth-functionally complete if and only if it can
express every possible truth function. The chapter explores universal
truth functions, such as the Sheffer function, and looks into system
completeness and system soundness to examine the deductive system
suited to the Sheffer function.
Chapter 10-20: Quantified Logic
The second part shifts from Propositional Logic to Quantified Logic
(QL), and Chapter 10 examines the influence of Aristotelian
Categorical Logic on contemporary classical Logic. Decker identifies
the problem of empty categories in categorical syllogisms and moves
forward to the need for quantifiers and variables to express
propositions. Chapter 11 introduces the formal syntax and semantics of
QL including the structure of well-formed formulas, the role of
variables, constants, predicates, and quantifiers, the distinction
between free and bound variables, and the truth conditions for
quantified statements. Decker emphasises the importance of precision
and how QL allows for a finer grain of detail than PL. Chapter 12
discusses formal semantics for both PL and QL. This chapter congeals
the connection between syntax, i.e. form, and semantics, i.e.
propositional meaning, and stresses that grasping both is a
prerequisite in order to understand Logic. Chapter 13 inspects the
semantics of definite and indefinite descriptions, such as ‘the man
with the hat’ and ‘a man with a hat’ respectively, as basic structures
of English and alludes to a debate started by Bertrand Russell (1919),
who proposed his Description Theory of Names to resolve ambiguities
and paradoxes in natural language. Decker argues that Russell’s theory
cannot account for complex cases and draws on Heim (1982), who views
indefinite descriptions as variables. Building on earlier chapters, in
Chapter 14, Decker explores the natural deduction system for QL. He
presents introduction and elimination rules for each quantifier and
explains how their rules interact with the structure of formal proofs.
Chapter 15 acknowledges the complexity of QL in comparison to PL and
functions as a tool for students to become more confident in
navigating QL. It provides heuristics for selecting proof strategies,
advice on how to avoid common pitfalls by introducing rules of thumb,
and examples of multi-step proofs involving quantifiers.
Chapter 16 explores reference failure, a phenomenon where terms fail
to refer to any object in the domain. Decker revisits Russell’s theory
of descriptions in light of reference failure by recounting the
dispute between Russell and Meinong (1904), and then moves to Kripke’s
theory (1980), the causal-historical theory of reference. This chapter
also explores reference failure in relation to negative and positive
free logic. The semantic tableaux device for evaluating logical
validity and logical truth in both PL and QL is introduced in Chapter
17. Decker weighs the strengths and limitations of the device and
concludes that it is a valuable addition to one’s logical toolkit.
Chapter 18 addresses the two foundational properties of logical
systems, i.e. soundness and completeness, and the extent to which
adding or subtracting rules from QL can impede these two properties.
Additionally, this chapter includes a discussion on Gödel’s
incompleteness theorems (1931) and the inspiration Gödel drew from
Russell’s paradox and the liar paradox. Chapter 19 explores the shift
from extensional (truth-based) to intentional (meaning-based)
semantics and discusses Frege’s (1982) distinction between sense and
reference, the limitation of extensional logic in capturing modal and
propositional attitudes and the need for intentional logic to handle
meaning beyond truth conditions. Part II ends with Chapter 20, in
which Church’s lambda calculus (1941), a formal system for
representing functions and meaning in logic is introduced. The chapter
examines the extent to which lambda expressions can be applied to the
logic of truth functions. Lambda calculus is then added to QL to
explore Montague’s Grammar (1970). The applications of the system in
compositional semantics and computational logic are also discussed in
relation to hyperintentionality.
Chapters 21-23: From Utopia to Dystopia [to… ?]
Part III introduces the reader to ordinary natural language reasoning
in terms of paradoxes. Chapter 21 discusses the Sorites Paradox and
explores political, social and ethical implications of the reasoning
behind the paradox since Decker argues that the paradox is more common
than we think. In this chapter, Decker also introduces three-valued
logic in an attempt to deal with vagueness and moves on to
infinite-valued logic by critically evaluating Łukasiewicz's version.
Chapter 22 examines self-reference and focuses on the Liar Paradox.
Decker deliberates whether challenging bivalent or trivalent logic as
strategies addresses this paradox. Unfortunately, trivalent logic
leads to the revenge of the liar. Following the failure to find a
compelling solution to both the liar and revenge paradoxes, Decker
dives into the surface of dialetheism and its potential connections to
Buddhist logic. The final chapter of the book, Chapter 23, reflects on
further avenues in the study of logic. For instance, we can extend
classical logic by adding quantifiers (first-order or second-order),
and introducing new logical operators. Other steps include metalogic
and nonclassical logics as well as studying the role of logic in
philosophy, linguistics, mathematics, and computer science.
EVALUATION
In this well-written academic textbook, Jason Decker has succeeded in
introducing undergraduates and logic-enthusiasts to formal logic. The
book is structured in a cohesive, progressive arc, reflecting a wisely
scaffolded learning journey designed for students across disciplines,
who can easily navigate between chapters and parts.. In Part I, Decker
succeeds in presenting the foundations of Propositional Logic,
achieving a remarkable balance between clarity, accessibility, and
conceptual depth. The same approach continues in Part II, where he
critically examines QL and introduces tools such as semantic tableaux
and natural deduction rules to handle logical truth, validity and
equivalence. The progressive arc culminates in Part III where Decker
explores paradoxes and the philosophical limits of formal systems.
Additionally, each chapter includes very clear and succinct
definitions that are highlighted in separate grey scale boxes.
Apart from scaffolding, the book is also successful pedagogically
because of its clear writing, cross-disciplinary connections and the
sections of suggested bibliography and practice exercises at the end
of each chapter, make the textbook suitable to the intended audience,
bridging theory and practice. Often Decker recommends further readings
that expand beyond logic, in order to provide a holistic perspective
on the issue he wants to cover. For example, in Chapter 5 he discusses
Grice and logic and suggests Sperber and Wilson’s Relevance Theory
(1995) as a framework which was inspired by Grice’s work. Decker
excels at his use of examples, analogies, and step-by-step
walkthroughs, which make the material significantly approachable for
novice readers. For example in Chapter 1, he demonstrates the
structure of an argument through the example of an upset Karen who
wants to speak to your manager. In the same chapter, the analogy of
the guitar amplifier is a really good way to introduce inductive
reasoning and how the premises probablify the conclusion. Furthermore,
Decker’s early reflection on the limits of classical logic adds
intellectual profundity and foreshadows the later content, encouraging
his readership to question the assumptions of classical logic,
especially in the chapters on conditionals (Ch. 6 and 7), reference
failure (Ch. 16) and paradoxes (Ch. 21 and 22). In addition to
promoting critical thinking, the book offers strategic guidance with
chapters like the one on QL Proof strategies (Ch. 15) and semantic
tableaux (Ch. 17), which serve as practical tools for mastering formal
techniques. Overall key issues in the book are lucidly and thoroughly
explained. However, I would recommend that future editions might
benefit from a glossary towards the end of the book for readers to
refer to in between chapters.
>From the outset of the book, Decker frames logic as a human activity
rooted in our capacity for reasoning and inquiry. This is a recurring
theme throughout the book, especially in discussion of natural
language and pragmatics. In fact, Chapter 5 is a strong chapter which
introduces pragmatics into the discussion through Grice’s pragmatic
theory (1957, 1975) to explore insights on logic and the role of
context. Decker addresses the limitations of logic throughout the
book. For example in Chapter 18, he introduces Gödel’s theorems as
philosophical challenges to the foundations of logic. He follows the
same approach with the paradoxes (Sorites and Liar) which are not
presented as merely technical curiosities. I should note that
considering the overall approach is student-friendly, advanced readers
may find its slower pace less challenging.
In a field with abstract concepts and a reputation for being
challenging for novices this book is valuable in that it illuminates
the relevance of logic to other disciplines, and does so in a
systematic approach. I highly recommend this textbook as a core
reference not only in interdisciplinary programmes but also as a
resource for self-directed learners.
REFERENCES
Church, A. (1941) The calculi of lambda-conversion. Princeton:
Princeton University Press.
Decker, J. (2025) Logic for everyone:From proof to paradox. Cambridge:
Cambridge University Press.
Frege, G. (1892) ‘Uber sinn und bedeutung', Zeitschrift für
Philosophie und Phislosophische Kritik, 100 (1), pp. 25-50.
Gödel, K. (1931) On formally undecidable propositions of principia
mathematic and related systems. New York: Basic Books.
Grice, H. P. (1957) ‘Meaning’, The Philosophical Review, 66 (3), pp.
377-388. Grice, H. P. (1975) ‘Logic and conversation’, in P. Cole and
J. Morgan (eds.) Speech acts.
Leiden: Brill, pp. 41-58.
Heim, R. (1982) The semantics of definite and indefinite noun phrases.
PhD Thesis [2011 typeset by Anders J. Schoubye and Ephraim Glick].
University of Massachussets.
Kripke, S. (1980) Naming and necessity. Cambridge, MA: Harvard
University Press.
Meinong, A. (1904) ‘On the theory of objects [translation of ‘U$ber
Gegenstandstheorie’ 1904], in R. Chisholm (ed.) Realism and the
background of phenomenology. New York: Free Press, pp. 76-117.
Montague, R. (1970) ‘Universal grammar’, Theoria, 36(3), pp. 373-398.
Russel, B. (1919) ‘Descriptions’, in A. W. Moore (ed.) Meaning and
reference. Oxford: Oxford University Press
Sperber, D. and Wilson, D. (1995) Relevance: Communication and
cognition (Originally
published 1986). Oxford: Basil Blackwell.
ABOUT THE REVIEWER
Chara Vlachaki is an Early Career Researcher with a PhD in Cognitive
Pragmatics and Aesthetics from the University of Brighton. Her
doctoral thesis was an intersection of relevance-theoretic pragmatics,
cognitive science, neuroaesthetics and philosophy. She examined the
communication and interpretation of vague aspects of meaning as the
ones found in artworks, and the role of emotion in the interpretive
process by proposing a cognitive model of aesthetic experience.
Chara’s research interests include pragmatics and cognitive science,
relevance theory, verbal and non-verbal communication, emotions and
the communication of emotion, aesthetics and aesthetic experience.



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