Abstract
Extensionalism makes it possible to study logic independently of any theory of meaning. Frege’s logic was not fully extensional, however: he developed a theory of meaning in order to have classes uniquely determined. That theory is also flexible enough to allow statements of identity to be at times analytic, at times not. He rejected the traditional empiricist epistemology as an obstacle since it is psychologistic – even though he could not replace it. (A few years after Frege died Popper proposed the first non-psychologistic theory of science.)
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Notes
- 1.
How developed is a field when it ceases to be a part of philosophy? This problem of demarcation differs from the one that Popper studied, though the two obviously overlap. Raising different problems of demarcation should appeal to analytic philosophers and perhaps it will when they will become serious again.
- 2.
Wittgenstein rejected the Cartesian solutions the problem of induction and only hinted at an adequate solution to it. (Will 1974 elaborated on this passage.) Wittgenstein suggested that the framework for research is given and its very use solves the problem. It does not: researchers choose systems tentatively; if they improve them, they have to revise their questions and this they usually do.
- 3.
Modern logic has no sign of affirmation akin to the sign of negation. Wittgenstein suggested that each sentence should have yes/no rubrics – to tick off at most one of them.
- 4.
An example is Kant, Critique of Pure Reason, Preface to the first edition: “In this sphere of thought, opinion is perfectly inadmissible, and … everything which bears the least semblance of a hypothesis must be excluded, as of no value in such discussions. For it is a necessary condition of every cognition that is to be established upon a priori grounds that it shall be held to be absolutely necessary …”
- 5.
Ramsey’s review of Wittgenstein’s Tractatus Logico-Philosophicus declares this obscure. Russell clarified it; the more formal/exact a text is, the more important is the preliminary introduction to it. This is the ladder to throw away. Russell considered this invitation to dogmatism: as preliminaries are pre-critical, Wittgenstein considered them immune to criticism. Oddly, Russell criticized Wittgenstein for his habit of applying forceful criticism in preliminary stages of research. This may be explicable by the ascription (McCutcheon 2001, Ch. 1) to Wittgenstein stress on preliminaries as the fervent pursuit of perspicuity (of achieving clarity through preliminary stages). As the concern of McCutcheon was with religion, she examined Wittgenstein’s early attention to the central role he ascribed to preliminaries both in formal mathematics and in studies of miracles. This is a coincidence at best, to impress only the superstitious.
- 6.
It often is a tautology, observes Bar-Am 2008 , 47 et passim; not if it means mediaeval London is modern London: this is intuitively true but not tautologically so. This is hardly ordinary language, though. “I am the Lord your Lord” (Exodus 20:2) is more like it.
- 7.
Tarski [1936] 1941 , §19 shows that identity sign is synthetic: (x) (y) (x = y) is true of an empty universe and of one that contains only one object but not otherwise. This does not hold for the identity sign in the sentence “Tullius = Cicero ”, of course.
- 8.
In Leibniz idea of his ideal language essences reign supreme, so the name “Caesar ” includes all the characteristics of Caesar, so that understanding it amounts to knowing all about him. The literature on Wittgenstein ignores this, which is strange; so does the literature on Russell, which is not strange.
- 9.
The logical connection is obvious between diverse theses on the limits of natural languages considered formal: The Tarski-Quine no analytic-synthetic dichotomy, the Duhem-Quine limited inter-translatability thesis and the Bar-Hillel-Catford no-full-machine-translatability thesis. Perhaps it is only the Duhem-Quine no-complete-refutability-in-isolation thesis that is slightly less direct and less obvious. All these impossibilities are due to viewing the informal formally; informally, all of these theses are obvious. We obviously agree to tolerate some (hopefully small) imperfections. See Agassi 2014 Ch. 6 .
- 10.
The model standard introductory logic course seems to me to be the deceptively introductory high-powered text of Hilbert and Ackermann, 1928 .
- 11.
See Stanford Encyclopedia of Philosophy, Art. Lakatos .
- 12.
Despite all this, Wittgenstein declared he owed more to Frege than to Russell.
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Agassi, J. (2018). Frege. In: Ludwig Wittgenstein’s Philosophical Investigations. Synthese Library, vol 401. Springer, Cham. https://doi.org/10.1007/978-3-030-00117-9_6
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