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  • Print publication year: 2001
  • Online publication date: December 2009

2 - First Order Logic

Summary

Introduction

Traditionally, logic has been regarded as the science of correct thinking or of making valid inferences. The former characterization of logic has strong psychological overtones—thinking is a psychological phenomenon—and few writers today think that logic can be a discipline that can successfully teach its students how to think, let alone how to think correctly. Furthermore, it is not obvious what “correct” thinking is. One can think “politically correct” thoughts without engaging in logic at all. We shall, at least for the moment, be well advised to leave psychology to one side, and focus on the latter characterization of logic: the science of making valid inferences.

To make an inference is to perform an act: It is to do something. But logic is not a compendium of exhortations: From “All men are mortal” and “Socrates is a man” do thou infer that Socrates is mortal! To see that this cannot be the case, note that “All men are mortal” has the implication that if Charles is a man, he is mortal, if John is a man, he is mortal, and so on, through the whole list of men, past and present, if not future. Furthermore, it is an implication of “All men are mortal” that if Fido (my dog) is a man, Fido is mortal; if Tabby is a man, Tabby is mortal, etc. And how about inferring “If Jane is a man, Jane is mortal”? As we ordinarily construe the premise, this, too is a valid inference. We cannot follow the exhortation to perform all valid inferences: There are too many, they are too boring, and that, surely, is not what logic is about.

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Uncertain Inference
  • Online ISBN: 9780511612947
  • Book DOI: https://doi.org/10.1017/CBO9780511612947
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