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| Propositions and Propositional Logic | |
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| Logic | |
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| Propositions | |
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| Propositions and agreements | |
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| Other views of propositions | |
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| Words and Propositions as Types | |
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| Propositions in English | |
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| Exercises for Sections A-D | |
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| The Basic Connectives of Propositional Logic | |
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| A Formal Language for Propositional Logic | |
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| Defining the formal language | |
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| Realizations: semi-formal English | |
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| Exercises for Sections E and F | |
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| Classical Propositional Logic | |
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| The Classical Abstraction and truth-functions | |
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| Models | |
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| Validity and semantic consequence | |
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| Determining whether a wff is a tautology | |
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| Examples of Formalization | |
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| Exercises for Sections G and H | |
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| Relatedness Logic | |
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| The subject matter of a proposition | |
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| Relatedness relations | |
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| Subject matter as the content of a proposition | |
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| Models | |
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| An Overview of Semantics for Propositional Logics | |
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| Exercises for Sections J and K | |
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| The Internal Structure of Propositions | |
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| Things, the World, and Propositions | |
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| Names and Predicates | |
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| Propositional Connectives | |
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| Variables and Quantifiers | |
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| Compound Predicates and Quantifiers | |
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| The Grammar of Predicate Logic | |
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| Exercises | |
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| A Formal Language for Predicate Logic | |
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| A Formal Language | |
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| The Unique Readability of Wffs | |
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| The Complexity of Wffs | |
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| Free and Bound Variables | |
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| The Formal Language and Propositions | |
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| Exercises | |
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| Semantics | |
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| Syntax vs. Semantics as a Basis for Logic | |
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| Atomic Propositions | |
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| Names | |
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| A name picks out at most one thing | |
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| A name picks out at least one thing | |
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| Predicates | |
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| A predicate applies to an object | |
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| Predications involving relations | |
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| Other conceptions of predicates and predications | |
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| How many predicates are there? | |
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| Naming, Pointing, and What There Is | |
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| Agreements | |
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| Naming, pointing, and descriptions | |
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| Avoiding names completely? | |
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| Forms of pointing: what there is | |
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| Exercises for Sections A-E | |
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| The Universe of a Realization | |
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| The Self-Reference Exclusion Principle | |
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| Models | |
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| The assumptions of the realization: Form and Meaningfulness | |
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| Interpretations: assignments of references and valuations | |
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| The Fregean Assumption and The Division of Form and Content | |
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| The truth-value of a complex proposition | |
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| Truth in a model | |
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| Logics, Validity, Semantic Consequence | |
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| Exercises for Sections F-J | |
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| Summary Chapters II-IV.J | |
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| Tarski's Definition of Truth | |
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| Eliminating semantic terms: Convention T | |
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| Other logics, other views of truth | |
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| Extensionality | |
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| Intensional predicates | |
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| The Extensionality Restriction | |
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| Quantification and intensional predicates | |
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| Languages without names | |
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| Models in which every object is named | |
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| Inconsistent predications and quantification | |
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| Other Interpretations of the Quantifiers and the Use of Variables | |
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| A current variation on Tarski's definition | |
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| The substitutional interpretation | |
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| Naming all elements of the universe at once | |
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| Surveying all interpretations of the name symbols | |
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| Exercises for Sections K-M | |
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| The Logical Form of a Proposition | |
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| Rewriting English Sentences | |
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| Common Nouns as Subject and Object | |
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| Relative quantification: [for all] | |
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| Relative quantification: [exist] | |
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| Nouns into Predicates | |
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| Adjectives | |
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| Indexicals | |
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| Adverbs | |
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| Tenses | |
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| Collections and Qualities | |
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| Mass Terms | |
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| Aristotelian Logic | |
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| Formalizations Relative to Formal Assumptions | |
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| Analysis vs. formalization | |
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| Extending the scope of predicate logic | |
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| Formalizing a notion | |
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| Criteria of Formalization | |
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| Examples of Formalization | |
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| Exercises | |
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| Identity | |
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| Identity | |
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| The Equality Predicate | |
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| The Interpretation of '=' in a Model | |
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| The Identity of Indiscernibles | |
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| The Predicate Logic Criterion of Identity (p.l.c.i.) | |
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| The p.l.c.i. vs. the implicit identity of the universe | |
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| The p.l.c.i. and names | |
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| Validity | |
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| Is the Equality Predicate Syncategorematic? | |
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| Exercises | |
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| Quantifiers | |
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| The Order of Quantifiers | |
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| [for all]x[exist]y and [exist]y[for all]x | |
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| [for all]x[exist]y and [exist]x[exist]y | |
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| Superfluous quantifiers | |
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| The Scope of Quantifiers: Substituting One Variable for Another | |
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| Names, Quantifiers, and Existence | |
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| Is '--exists' a Predicate? | |
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| Quantifying Over a Finite Universe: [for all] as Conjunction, [exist] as Disjunction | |
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| Modeling Other Quantifiers | |
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| Positive quantifiers: 'there are at least n' | |
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| Negative quantifiers: 'there are at most n', 'no', 'nothing' | |
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| Exact quantifiers: 'there are exactly n' | |
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| Quantifications we can't model | |
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| Relative Quantification | |
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| Nouns into Predicates revisited | |
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| Formalizations involving the same quantifier | |
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| Formalizations involving mixtures of quantifiers | |
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| Examples of Formalization | |
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| Exercises | |
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| Descriptive Names | |
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| Descriptive Names: A Problem in Formalization | |
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| Descriptive Names Relative to Formal Assumptions | |
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| Russell's Method of Eliminating Descriptive Names from Atomic Propositions | |
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| Eliminating All Names? | |
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| Examples of Formalization | |
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| Exercises | |
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| Functions | |
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| Name-Makers | |
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| Functions | |
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| A definition | |
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| Terms | |
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| The value of a function | |
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| Functions compared to predicates | |
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| A Formal Language with Function Symbols and Equality | |
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| Realizations and Truth in a Model | |
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| Partial Name-Makers | |
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| Russell's abstraction operator | |
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| The [varepsilon]-operator | |
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| Examples of Formalization | |
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| Exercises | |
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| Quantifying Over Predicates: Second-Order Logic | |
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| Quantifying over Predicates? | |
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| Predicates and Things | |
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| Predicate Variables and their Interpretation: Avoiding Self-Reference | |
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| Predicate variables | |
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| The interpretation of predicate variables | |
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| Note: Higher-order logics | |
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| A Formal Language for Second-Order Logic: L[subscript 2] | |
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| Realizations | |
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| Identifying Predicates with Collections of n-tuples of the Universe | |
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| Exercises for Sections A-F | |
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| Models | |
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| Examples of Formalization | |
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| Exercises for Sections G and H | |
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| Predicates as Things: Reducing General Second-Order Logic to First-Order Logic | |
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| One universe for predicates and individuals | |
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| The translation | |
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| Proof that the mapping preserves consequences | |
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| Does the reduction preserve meaning? | |
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| Quantifying over Functions | |
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| Why quantify over functions? | |
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| A formal language: L[subscript 2F] | |
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| Realizations and models | |
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| The difficulty of reducing quantification over functions to first-order logic | |
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| Many-Sorted Languages | |
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| Exercises for Sections J-L | |
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| Language, the World, and Predicate Logic | |
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| The World | |
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| The Template Analogy | |
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| Eliminating Natural Languages? | |
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| Predicate Logic as a Model of or Guide to Reasoning | |
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| Appendices | |
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| The Notion of Thing in Predicate Logic | |
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| What There Is: Restrictions on the Universe of a Realization | |
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| Primitives and Assumptions of Predicate Logic | |
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| Formalization: Criteria and Agreements | |
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| Bibliography | |
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| Index of Examples | |
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| Index of Notation | |
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| Index | |