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Wittgenstein and Frege on Assertion

  • Christoph C. Pfisterer
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Philosophy of Logic and Mathematics
Ein Kapitel aus dem Buch Philosophy of Logic and Mathematics

Abstract

In the Philosophical Investigations, Wittgenstein famously criticizes Frege’s conception of assertion. “Frege’s opinion that every assertion contains an assumption”, says Wittgenstein, rests on the possibility of parsing every assertoric sentence into two components: one expressing the assumption that is put forward for assertion, the other expressing that it is asserted. But this possibility does not entail that the “assertion consists of two acts, entertaining and asserting” - any more than the possibility of rendering assertions as pairs of questions and affirmative answers entails that they consist of questions. Frege scholars protest that such criticism is inappropriate, not only because Frege doesn’t speak about assumptions, but also - and crucially - because Wittgenstein fails to address the logical nature of assertion as reflected in Frege’s use of the judgment stroke. They seem to read Wittgenstein’s argument in the light of a remark in the Tractatus saying that the judgment stroke is “logically meaningless” because it simply indicates that the author holds the propositions marked with this sign to be true. In this paper, I argue that Wittgenstein’s criticism of Frege is not that the latter’s conception of judgment and assertion contains a corrupting psychological element. Rather, the criticism is that for Frege judgment and assertion are composed of two separate acts, i.e. an act of referring to a truth value and an act of determining which of the two it is. Through a detailed examination of the “black-spot analogy” in the Tractatus, I want to show that Wittgenstein presents a serious objection to Frege’s conception of judgment and assertion.

Abstract

In the Philosophical Investigations, Wittgenstein famously criticizes Frege’s conception of assertion. “Frege’s opinion that every assertion contains an assumption”, says Wittgenstein, rests on the possibility of parsing every assertoric sentence into two components: one expressing the assumption that is put forward for assertion, the other expressing that it is asserted. But this possibility does not entail that the “assertion consists of two acts, entertaining and asserting” - any more than the possibility of rendering assertions as pairs of questions and affirmative answers entails that they consist of questions. Frege scholars protest that such criticism is inappropriate, not only because Frege doesn’t speak about assumptions, but also - and crucially - because Wittgenstein fails to address the logical nature of assertion as reflected in Frege’s use of the judgment stroke. They seem to read Wittgenstein’s argument in the light of a remark in the Tractatus saying that the judgment stroke is “logically meaningless” because it simply indicates that the author holds the propositions marked with this sign to be true. In this paper, I argue that Wittgenstein’s criticism of Frege is not that the latter’s conception of judgment and assertion contains a corrupting psychological element. Rather, the criticism is that for Frege judgment and assertion are composed of two separate acts, i.e. an act of referring to a truth value and an act of determining which of the two it is. Through a detailed examination of the “black-spot analogy” in the Tractatus, I want to show that Wittgenstein presents a serious objection to Frege’s conception of judgment and assertion.

Kapitel in diesem Buch

  1. Frontmatter I
  2. Contents V
  3. Preface IX
  4. Part I: Philosophy of Logic
  5. Link’s Revenge: A Case Study in Natural Language Mereology 3
  6. Universal Translatability: An Optimality- Based Justification of (Classical) Logic 37
  7. Invariance and Necessity 55
  8. Translations Between Logics: A Survey 71
  9. On the Relation of Logic to Metalogic 91
  10. Free Logic and the Quantified Argument Calculus 105
  11. Dependencies Between Quantifiers Vs. Dependencies Between Variables 117
  12. Three Types and Traditions of Logic: Syllogistic, Calculus and Predicate Logic 133
  13. Truth, Paradox, and the Procedural Conception of Fregean Sense 153
  14. Wittgenstein and Frege on Assertion 169
  15. Assertions and Their Justification: Demonstration and Self-Evidence 183
  16. Surprises in Logic: When Dynamic Formality Meets Interactive Compositionality 197
  17. Part II: Philosophy of Mathematics
  18. Neologicist Foundations: Inconsistent Abstraction Principles and Part-Whole 215
  19. What Hilbert and Bernays Meant by “Finitism” 249
  20. Wittgenstein and Turing 263
  21. Remarks on Two Papers of Paul Bernays 297
  22. The Significance of the Curry-Howard Isomorphism 313
  23. Reductions of Mathematics: Foundation or Horizon? 327
  24. What Are the Axioms for Numbers and Who Invented Them? 343
  25. Part III: Wittgenstein
  26. Following a Rule: Waismann’s Variation 359
  27. Propositions in Wittgenstein and Ramsey 375
  28. An Unexpected Feature of Classical Propositional Logic in the Tractatus 385
  29. Ontology in Tractatus Logico-Philosophicus: A Topological Approach 397
  30. Adding 4.0241 to TLP 415
  31. Understanding Wittgenstein’s Wood Sellers 429
  32. On the Infinite, In-Potentia: Discovery of the Hidden Revision of Philosophical Investigations and Its Relation to TS 209 Through the Eyes of Wittgensteinian Mathematics 441
  33. Incomplete Pictures and Specific Forms: Wittgenstein Around 1930 457
  34. „Man kann die Menschen nicht zum Guten führen“ – Zur Logik des moralischen Urteils bei Wittgenstein und Hegel 473
  35. Der Status mathematischer und religiöser Sätze bei Wittgenstein 485
  36. Gutes Sehen 499
  37. Wittgenstein’s Conjecture 515
  38. Index of Names 535
  39. Index of Subjects 539
https://doi.org/10.1515/9783110657883-011

Kapitel in diesem Buch

  1. Frontmatter I
  2. Contents V
  3. Preface IX
  4. Part I: Philosophy of Logic
  5. Link’s Revenge: A Case Study in Natural Language Mereology 3
  6. Universal Translatability: An Optimality- Based Justification of (Classical) Logic 37
  7. Invariance and Necessity 55
  8. Translations Between Logics: A Survey 71
  9. On the Relation of Logic to Metalogic 91
  10. Free Logic and the Quantified Argument Calculus 105
  11. Dependencies Between Quantifiers Vs. Dependencies Between Variables 117
  12. Three Types and Traditions of Logic: Syllogistic, Calculus and Predicate Logic 133
  13. Truth, Paradox, and the Procedural Conception of Fregean Sense 153
  14. Wittgenstein and Frege on Assertion 169
  15. Assertions and Their Justification: Demonstration and Self-Evidence 183
  16. Surprises in Logic: When Dynamic Formality Meets Interactive Compositionality 197
  17. Part II: Philosophy of Mathematics
  18. Neologicist Foundations: Inconsistent Abstraction Principles and Part-Whole 215
  19. What Hilbert and Bernays Meant by “Finitism” 249
  20. Wittgenstein and Turing 263
  21. Remarks on Two Papers of Paul Bernays 297
  22. The Significance of the Curry-Howard Isomorphism 313
  23. Reductions of Mathematics: Foundation or Horizon? 327
  24. What Are the Axioms for Numbers and Who Invented Them? 343
  25. Part III: Wittgenstein
  26. Following a Rule: Waismann’s Variation 359
  27. Propositions in Wittgenstein and Ramsey 375
  28. An Unexpected Feature of Classical Propositional Logic in the Tractatus 385
  29. Ontology in Tractatus Logico-Philosophicus: A Topological Approach 397
  30. Adding 4.0241 to TLP 415
  31. Understanding Wittgenstein’s Wood Sellers 429
  32. On the Infinite, In-Potentia: Discovery of the Hidden Revision of Philosophical Investigations and Its Relation to TS 209 Through the Eyes of Wittgensteinian Mathematics 441
  33. Incomplete Pictures and Specific Forms: Wittgenstein Around 1930 457
  34. „Man kann die Menschen nicht zum Guten führen“ – Zur Logik des moralischen Urteils bei Wittgenstein und Hegel 473
  35. Der Status mathematischer und religiöser Sätze bei Wittgenstein 485
  36. Gutes Sehen 499
  37. Wittgenstein’s Conjecture 515
  38. Index of Names 535
  39. Index of Subjects 539
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Heruntergeladen am 17.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/9783110657883-011/html
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