Symbolic Logic Informative Summary

Overview:

This ebook presents a unique and engaging approach to understanding Symbolic Logic, written by the renowned author, Lewis Carroll. The book is divided into eight chapters, each focusing on different aspects of logic, starting with a definition of ‘things’ and ‘attributes’ and moving on to propositions, syllogisms, and soriteses. The primary goal of the book is to popularize the subject, making it accessible and enjoyable for a wide audience, including intelligent children.

Carroll employs a novel method of diagrams and counters to represent and analyze logical propositions and arguments. The Biliteral Diagram, a simple grid divided into four cells, is used to represent basic propositions of existence and relation. The Triliteral Diagram, an extension of the Biliteral, is introduced to represent propositions involving three attributes, and the concept of ‘underscoring’ is introduced as an alternative method for solving soriteses. This approach provides a visual and interactive way to understand the complexities of logic.

Key Findings:

  • Symbolic Logic can be an engaging and enjoyable mental recreation.
  • The book provides a method of representing propositions visually, making the concepts easier to grasp.
  • The text offers a unique approach to solving syllogisms and soriteses, utilizing three distinct figures and rules for each.
  • The book refutes common misconceptions about logic, such as the belief that two negative premises prove nothing.

Facts:

  • Every Name is either a Substantive only, or else a phrase consisting of a Substantive and one or more Adjectives. This is a core principle of the book, establishing that a Name is defined by the inclusion of an Attribute.
  • A Proposition of Relation, beginning with “All”, is a Double Proposition, and is equivalent to (i.e. gives the same information as) the two Propositions (1) “Some Members of the Subject are Members of the Predicate”; (2) “No Members of the Subject are Members of the Class whose Differentia is contradictory to that of the Predicate”. This highlights the inherent duality of universal propositions.
  • The Proposition “Some xy exist” is equivalent to “Some x are y” and “Some y are x”. This explains the concept of conversion in propositions of relation.
  • Propositions are of two kinds, ‘Propositions of Existence’ and ‘Propositions of Relation’. This fundamental distinction is key to understanding the book’s structure and methods.
  • A ‘Proposition of Existence’, when in normal form, has, for its Subject, the Class “existing Things”. This establishes the framework for analyzing propositions about the existence of entities.
  • A ‘Proposition of Relation’, of the kind to be here discussed, has, for its Terms, two Specieses of the same Genus, such that each of the two Names conveys the idea of some Attribute not conveyed by the other. This sets the stage for analyzing propositions that relate different classes within a specific universe.
  • A Class, containing only one Member is called an ‘Individual’. This definition clarifies the concept of an individual as a single member of a class.
  • A Class, containing two or more Members, is sometimes regarded as one single Thing. This explains the concept of a class acting as a singular entity.
  • A Proposition, that begins with “Some”, is said to be ‘Particular’. It is also called ‘a Proposition in I’. This definition clarifies the distinction between particular and universal propositions.
  • A Proposition, that begins with “No”, is said to be ‘Universal Negative’. It is also called ‘a Proposition in E’. This definition clarifies the distinction between particular and universal propositions.
  • A Proposition, that begins with “All”, is said to be ‘Universal Affirmative’. It is also called ‘a Proposition in A’. This definition clarifies the distinction between particular and universal propositions.
  • A Proposition, whose Subject is an Individual, is to be regarded as Universal. This principle applies to propositions about individual entities.
  • ‘Division’ is a Mental Process, in which we think of a certain Class of Things, and imagine that we have divided it into two or more smaller Classes. This explains the concept of division as a mental process.
  • A Class, that has been obtained by a certain Division, is said to be ‘codivisional’ with every Class obtained by that Division. This defines the concept of codivisionality between classes.
  • If we think of a certain Class, and imagine that we have picked out from it a certain smaller Class, it is evident that the Remainder of the large Class does not possess the Differentia of that smaller Class. This highlights the inherent duality in classifying things through dichotomy.
  • Every Name is either a Substantive only, or else a phrase consisting of a Substantive and one or more Adjectives (or phrases used as Adjectives). This establishes the foundation for defining names in terms of substantives and adjectives.
  • A Name, whose Substantive is in the plural number, may be used to represent either (1) Members of a Class, regarded as separate Things; or (2) a whole Class, regarded as one single Thing. This explains the dual meaning of plural names.
  • Every Member of a Species is also a Member of the Genus out of which that Species has been picked, and that it possesses the Differentia of that Species. This establishes the relationship between species and genus in classification.

Statistics:

  • Nineteen different forms of Syllogisms are discussed in traditional logic texts. This highlights the complexity of the traditional approach to Syllogisms.
  • The book presents 101 examples of Syllogisms for the reader to work through. This demonstrates the extensive coverage of the book.
  • The book presents 17 Examination Papers for the reader to complete. This gives the reader an opportunity to assess their understanding.
  • The book presents 32 different types of propositions of existence and relation. This highlights the scope of the book’s coverage.
  • The book presents 129 different examples of Soriteses for the reader to work through. This demonstrates the extensive coverage of the book.
  • The book presents 273 different examples of concrete Soriteses for the reader to work through. This demonstrates the extensive coverage of the book.

Terms:

  • Dichotomy: A division of a class into two mutually exclusive subclasses.
  • Differentia: The attribute that distinguishes a species from other species of the same genus.
  • Genus: A larger class that contains several species.
  • Species: A smaller class that is a subset of a genus.
  • Syllogism: A logical argument that consists of three propositions: two premises and a conclusion.
  • Sorites: A logical argument that consists of a series of propositions, where the predicate of each premise is the subject of the next, leading to a final conclusion.
  • Proposition: A statement that asserts or denies something about a subject.
  • Counter: A physical object used in the book’s diagrams to represent logical values.
  • Entity: A proposition that asserts the existence of something.
  • Nullity: A proposition that asserts the non-existence of something.

Examples:

  • The Proposition “Some apples are not ripe” may be interpreted as “Some existing Things are not-ripe apples”. This demonstrates the translation of a proposition of relation into a proposition of existence.
  • The Proposition “Some farmers always grumble at the weather, whatever it may be” may be interpreted as “Some existing Things are farmers who always grumble at the weather, whatever it may be”. This demonstrates the translation of a complex proposition into a simpler form.
  • The Proposition “No lambs are accustomed to smoke cigars” may be interpreted as “No existing Things are lambs accustomed to smoke cigars”. This demonstrates the translation of a negative proposition into a simpler form.
  • The Proposition “None of my speculations have brought me as much as 5 per cent.” may be interpreted as “No existing Things are speculations of mine, which have brought me as much as 5 per cent.” This demonstrates the translation of a complex proposition into a simpler form.
  • The Proposition “None but the brave deserve the fair” may be interpreted as “No existing Things are not-brave men deserving of the fair.” This demonstrates the translation of a complex proposition into a simpler form.
  • The Proposition “All bankers are rich men” may be interpreted as the two Propositions (1) “Some bankers are rich men”; (2) “No bankers are poor men”. This demonstrates the duality of universal propositions.
  • The Proposition “All diligent students are successful” may be interpreted as the two Propositions (1) “Some diligent students are successful”; (2) “No diligent students are unsuccessful”. This demonstrates the duality of universal propositions.
  • The Proposition “All ignorant students are unsuccessful” may be interpreted as the two Propositions (1) “Some ignorant students are unsuccessful”; (2) “No ignorant students are successful”. This demonstrates the duality of universal propositions.
  • The Proposition “I admire these pictures” may be interpreted as “All these pictures are things admired by me”. This demonstrates the translation of a concrete proposition into abstract form.
  • The Proposition “When I admire anything I wish to examine it thoroughly” may be interpreted as “All things admired by me are things which I wish to examine thoroughly”. This demonstrates the translation of a complex proposition into a simpler form.

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