This chapter presents an early and key argument in Thoughts (the first book in Logical Investigations) so-called ‘The Treadmill’. Frege deploys this argument to show that truth is indefinable. But this argument has become infamous for its lack of rigour. As a result, various interpretations and fixes have been proposed. After examining the predominant interpretive camps and finding them wanting, I revisit the argument within the context in which it appears. That context, I argue, consists of both the conception of logic Frege establishes in the early paragraphs, and the motivations he has for demonstrating its conclusion at this early stage. I argue that The Treadmill is intended, not only to demonstrate that ‘is true’ has a sui generis and indefinable sense, but also that thoughts are the objects of investigation for logicians. I then mention two other highly relevant consequences he draws from The Treadmill. The first is that sentences of the form ‘A’ express the same thought as those of the form ‘it is true that A’ (the equipollence thesis). The second is that truth is not a property in the ordinary sense. Each of these ideas will be revisited in later chapters.

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The Treadmill

  • Nathan Hawkins

摘要

This chapter presents an early and key argument in Thoughts (the first book in Logical Investigations) so-called ‘The Treadmill’. Frege deploys this argument to show that truth is indefinable. But this argument has become infamous for its lack of rigour. As a result, various interpretations and fixes have been proposed. After examining the predominant interpretive camps and finding them wanting, I revisit the argument within the context in which it appears. That context, I argue, consists of both the conception of logic Frege establishes in the early paragraphs, and the motivations he has for demonstrating its conclusion at this early stage. I argue that The Treadmill is intended, not only to demonstrate that ‘is true’ has a sui generis and indefinable sense, but also that thoughts are the objects of investigation for logicians. I then mention two other highly relevant consequences he draws from The Treadmill. The first is that sentences of the form ‘A’ express the same thought as those of the form ‘it is true that A’ (the equipollence thesis). The second is that truth is not a property in the ordinary sense. Each of these ideas will be revisited in later chapters.