Overview
The Problem Situation
The Tentative Solution
Critical Discussion
Correspondence
Content Logic
Class Logic
Logic of Arithmetic
Logic of Physics
Conclusion
Footnotes
Bibliography
1. This methodology is formulated in Popper, “Status of Science and Metaphysics,” 199.
2. Tarski, “The Semantic Conception of Truth,” 674.
3. Frege, “On Sense and Meaning,” 62‒65.
4. Frege, Logical Investigations, 4, 6.
5. The position that true sentences name existing states of affairs is formulated in Tarski, “The Semantic Conception of Truth,” 667, but see footnote 6 there. Alfred Tarski does not identify facts and existing states of affairs, as is purported here.
6. This methodological principle is formulated for empirically testable theories in Popper, “Conjectural Knowledge,” 15, number (8).
7. Popper, Realism and the Aim of Science, section *53, and Popper, “A World of Propensities,” 9–21.
8. For these consequences, see Popper, Quantum Theory and the Schism in Physics, 125–130, “Particles, Waves and the Propensity Interpretation.”
9. Popper, Realism and the Aim of Science, 356.
10. Popper, “A World of Propensities,” 12.
11. The idea of classes of similar sentences or expressions is taken from Tarski, “The Semantic Conception of Truth,” 666, footnote 5.
12. For an account of differences between rules and theorems, see Popper, “Calculi of Logic and Arithmetic,” 203, and Tarski, Introduction to Logic, 47.
13. Tarski, “The Semantic Conception of Truth,” sections 5, 8–10.
14. Ibid., 668.
15. For sentential functions see Tarski, Introduction to Logic, 4.
16. Naturally, the next step is to construct Tarski’s semantic definition of truth for contents instead of sentences. This is beyond the scope of this essay.
17. The method to mark levels by different notations is taken from Tarski, “The Concept of Truth,” 168–73. There, Tarski uses two different notations to mark the object level and the metalevel of sentences.
18. The conjunction could be formalized with this rule: The sequence of “p,” “and,” and “q” creates object-level content in the conjunctive logical form.
19. An example proof is provided at the end of this section.
20. Popper, “Calculi of Logic and Arithmetic,” 203.
21. Tarski, Introduction to Logic, 147–8.
22. Tarski, Introduction to Logic, 141.
23. This is an extension of Karl Popper’s description of the situation. See Popper, Logic of Scientific Discovery, 38. The additional component is the mathematical content.
24. Tarski, Introduction to Logic, 157.
25. See Tarski, Introduction to Logic, 158, for a proof in syntactical terms.
26. For the following summary, see Popper, Logic of Scientific Discovery, sections 12, 13, 15 and 28.
27. Ibid., 49.
28. See Popper, Logic of Scientific Discovery, 82, especially note *1.
Overview
The Problem Situation
The Tentative Solution
Critical Discussion
Correspondence
Content Logic
Class Logic
Logic of Arithmetic
Logic of Physics
Conclusion
Footnotes
Bibliography
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