Download An Invitation to Formal Reasoning: The Logic of Terms by Frederic Sommers, George Englebretsen PDF

By Frederic Sommers, George Englebretsen

ISBN-10: 0754613666

ISBN-13: 9780754613664

This paintings introduces the topic of formal good judgment when it comes to a approach that's "like syllogistic logic". Its approach, like out of date, conventional syllogistic, is a "term logic". The authors' model of good judgment ("term-function logic", TFL) stocks with Aristotle's syllogistic the perception that the logical sorts of statements which are keen on inferences as premises or conclusions could be construed because the results of connecting pairs of phrases via a logical copula (functor). This perception contrasts markedly with that which informs modern day typical formal good judgment ("modern predicate logic", MPL). The e-book is meant as a device for the creation of TFL to the start scholar of common sense. it is also a bankruptcy introducing commonplace MPL. There are a number of workout sections and a precis of the most principles, legislation and rules of TFL. For the philosophically orientated there are discussions of vital matters on the intersections of semantics, metaphysics, epistemology and good judgment.

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Extra resources for An Invitation to Formal Reasoning: The Logic of Terms

Sample text

A statement that expresses a true proposition is true. Since [some women are farmers] corresponds to , it is a true proposition and the statement expressing it is a true statement. A proposition (and the statement that expresses it) is false if the proposition does not correspond to any characteristic of the world. For example, SOME THING BEING AN ELF is a false characterization that does not correspond to any fact, there being no such fact as {elf}ishness. Among the world's existential characteristics (facts) are the following: the existence of horses; {horse} ishness, being {horse} ish the nonexistence of elves; un {elf} ishness, being un {elf} ish the existence of women farmers; {woman farmer}ishness the existence of elks; {elk} ishness the nonexistence of mermaids; un{mermaid}ishness Using the angle bracket notation for the facts that are characteristics of the world, we represent the fact signified by 'there are elks' by '' and the fact signified by 'there are no elves' by ''.

A true statement such as 'there are elks' signifies a (positive, existential) characteristic of the world ( {elk} ishness) and it too denotes something that has the signified characteristic. Since it is the world that possesses the characteristic of {elk} ishness, the statement 'there are elks' denotes the world. A true negative statement such as 'there are no elves' signifies a (negative existential) characteristic of the world (its un{elf}ishness) and it too denotes what has the signified characteristic.

We noted earlier that 'some X is a Y' is equivalent to its converse 'some Y is an X'. The equivalence of 'Y some X' to 'X some Y' shows that 'some' does indeed behave in a plus-like manner. Using the A-form the equivalence of converses can be stated as 'Y some X = X some Y'. But now, representing 'some' as a plus sign, we can formulate the equivalence as a simple algebraic equation: Y+X=X+Y 3. Affirmation(+) and Denial(-) Recognizing the plus-like character of 'some' is the first step in algebraic notation.

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