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He did not write it anywhere. The quote itself only calls Gödel and Skolem "alleged proponents", and later in the article Eklund remarks that "the (supposed) evidence that Skolem adhered to first-order logic is that Skolem held that set theory and arithmetic should be given first-order axiomatizations, whereas... evidence that Gödel adhered to first-order logic is the (alleged) fact that Godel insisted on a first-order metalanguage" (p.151), and proceeds to dispute even this limited evidence. He mentions Gödel-Zermelo correspondence of 1931 as the alleged source, and remarks that "neither Moore nor Shapiro provides us with any quotation from the Gödel-Zermelo correspondence showing it to be the case that Godel there did insist on a first-order metalanguage" (p.158).

The dominance of first order logic is based on technical results of Skolem and Gödel, rather than on philosophical arguments. Skolem proved that first order logic has nice model theory, Gödel proved that it is recursively axiomatizable and hence has a nice proof theory (unlike higher order logics), and compact (unlike infinitary logics). At the same time, first order Zermelo-Fraenkel set theory (made first order by Skolem, who modified Zermelo's comprehension axiom accordingly) proved to be more than sufficient not only for all of classical mathematics, but even for higher set theory and model theory. On the other hand, higher order set theories, like Russell's, proved to be unwieldy. In the end, Russell had to introduce the infamous "axiom of reducibility" which effectively reduces the logic of his set theory to first order.

Since 1950s Quine routinely identified first order logic with the "language of science", Eklund himself mentions him as an influence. As for "true logic" as understood in philosophy Gödel argued quite the contrary. That human reasoning is not only uncaptured by the first order logic, but by any formalized logic, and that his incompleteness results are an indication of that.

He did not. The quote itself only calls Gödel and Skolem "alleged proponents", and later in the article Eklund remarks that "the (supposed) evidence that Skolem adhered to first-order logic is that Skolem held that set theory and arithmetic should be given first-order axiomatizations, whereas... evidence that Gödel adhered to first-order logic is the (alleged) fact that Godel insisted on a first-order metalanguage" (p.151), and proceeds to dispute even this limited evidence. He mentions Gödel-Zermelo correspondence of 1931 as the alleged source, and remarks that "neither Moore nor Shapiro provides us with any quotation from the Gödel-Zermelo correspondence showing it to be the case that Godel there did insist on a first-order metalanguage" (p.158).

The dominance of first order logic is based on technical results of Skolem and Gödel, rather than on philosophical arguments. Skolem proved that first order logic has nice model theory, Gödel proved that it is recursively axiomatizable and hence has a nice proof theory (unlike higher order logics), and compact (unlike infinitary logics). At the same time, first order Zermelo-Fraenkel set theory (made first order by Skolem, who modified Zermelo's comprehension axiom accordingly) proved to be more than sufficient not only for all of classical mathematics, but even for higher set theory and model theory. On the other hand, higher order set theories, like Russell's, proved to be unwieldy. In the end, Russell had to introduce the infamous "axiom of reducibility" which effectively reduces the logic of his set theory to first order.

Since 1950s Quine routinely identified first order logic with the "language of science", Eklund himself mentions him as an influence. As for "true logic" as understood in philosophy Gödel argued quite the contrary. That human reasoning is not only uncaptured by the first order logic, but by any formalized logic, and that his incompleteness results are an indication of that.

He did not write it anywhere. The quote itself only calls Gödel and Skolem "alleged proponents", and later in the article Eklund remarks that "the (supposed) evidence that Skolem adhered to first-order logic is that Skolem held that set theory and arithmetic should be given first-order axiomatizations, whereas... evidence that Gödel adhered to first-order logic is the (alleged) fact that Godel insisted on a first-order metalanguage" (p.151), and proceeds to dispute even this limited evidence. He mentions Gödel-Zermelo correspondence of 1931 as the alleged source, and remarks that "neither Moore nor Shapiro provides us with any quotation from the Gödel-Zermelo correspondence showing it to be the case that Godel there did insist on a first-order metalanguage" (p.158).

The dominance of first order logic is based on technical results of Skolem and Gödel, rather than on philosophical arguments. Skolem proved that first order logic has nice model theory, Gödel proved that it is recursively axiomatizable and hence has a nice proof theory (unlike higher order logics), and compact (unlike infinitary logics). At the same time, first order Zermelo-Fraenkel set theory (made first order by Skolem, who modified Zermelo's comprehension axiom accordingly) proved to be more than sufficient not only for all of classical mathematics, but even for higher set theory and model theory. On the other hand, higher order set theories, like Russell's, proved to be unwieldy. In the end, Russell had to introduce the infamous "axiom of reducibility" which effectively reduces the logic of his set theory to first order.

Since 1950s Quine routinely identified first order logic with the "language of science", Eklund himself mentions him as an influence. As for "true logic" as understood in philosophy Gödel argued quite the contrary. That human reasoning is not only uncaptured by the first order logic, but by any formalized logic, and that his incompleteness results are an indication of that.

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He did not. The quote itself only calls Gödel and Skolem "alleged proponents". Later, and later in the article Eklund explainsremarks that "the (supposed) evidence that Skolem adhered to first-order logic is that Skolem held that set theory and arithmetic should be given first-order axiomatizations, whereas... evidence that Gödel adhered to first-order logic is the (alleged) fact that Godel insisted on a first-order metalanguage" (p.151), and proceeds to dispute even this limited evidence. He mentions Gödel-Zermelo correspondence of 1931 as the alleged source, and remarks that "neither Moore nor Shapiro provides us with any quotation from the Gödel-Zermelo correspondence showing it to be the case that Godel there did insist on a first-order metalanguage" (p.158).

The dominance of first order logic is based on technical results of Skolem and Gödel, rather than on philosophical arguments. Skolem proved that first order logic has nice model theory, Gödel proved that it is recursively axiomatizable and hence has a nice proof theory (unlike higher order logics), and compact (unlike infinitary logics). At the same time, first order Zermelo-Fraenkel set theory (made first order by Skolem, who modified Zermelo's comprehension axiom accordingly) proved to be more than sufficient not only for all of classical mathematics, but even for higher set theory and model theory. On the other hand, higher order set theories, like Russell's, proved to be unwieldy. In the end, Russell had to introduce the infamous "axiom of reducibility" which effectively reduces the logic of his set theory to first order.

Since 1950s Quine routinely identified first order logic with the "language of science", and Eklund himself mentions him as an influence. As for "true logic" as understood in philosophy Gödel argued quite the contrary. That human reasoning is not only uncaptured by the first order logic, but by any formalized logic, and that his incompleteness results are an indication of that.

The quote itself only calls Gödel and Skolem "alleged proponents". Later in the article Eklund explains that "the (supposed) evidence that Skolem adhered to first-order logic is that Skolem held that set theory and arithmetic should be given first-order axiomatizations, whereas... evidence that Gödel adhered to first-order logic is the (alleged) fact that Godel insisted on a first-order metalanguage" (p.151), and proceeds to dispute even this limited evidence. He mentions Gödel-Zermelo correspondence of 1931 as the alleged source, and remarks that "neither Moore nor Shapiro provides us with any quotation from the Gödel-Zermelo correspondence showing it to be the case that Godel there did insist on a first-order metalanguage" (p.158).

The dominance of first order logic is based on technical results of Skolem and Gödel, rather than on philosophical arguments. Skolem proved that first order logic has nice model theory, Gödel proved that it is recursively axiomatizable and hence has a nice proof theory (unlike higher order logics), and compact (unlike infinitary logics). At the same time, first order Zermelo-Fraenkel set theory (made first order by Skolem, who modified Zermelo's comprehension axiom accordingly) proved to be more than sufficient not only for all of classical mathematics, but even for higher set theory and model theory. On the other hand, higher order set theories, like Russell's, proved to be unwieldy. In the end, Russell had to introduce the infamous "axiom of reducibility" which effectively reduces the logic of his set theory to first order.

Since 1950s Quine routinely identified first order logic with the "language of science", and Eklund mentions him as an influence. As for "true logic" as understood in philosophy Gödel argued quite the contrary. That human reasoning is not only uncaptured by the first order logic, but by any formalized logic, and that his incompleteness results are an indication of that.

He did not. The quote itself only calls Gödel and Skolem "alleged proponents", and later in the article Eklund remarks that "the (supposed) evidence that Skolem adhered to first-order logic is that Skolem held that set theory and arithmetic should be given first-order axiomatizations, whereas... evidence that Gödel adhered to first-order logic is the (alleged) fact that Godel insisted on a first-order metalanguage" (p.151), and proceeds to dispute even this limited evidence. He mentions Gödel-Zermelo correspondence of 1931 as the alleged source, and remarks that "neither Moore nor Shapiro provides us with any quotation from the Gödel-Zermelo correspondence showing it to be the case that Godel there did insist on a first-order metalanguage" (p.158).

The dominance of first order logic is based on technical results of Skolem and Gödel, rather than on philosophical arguments. Skolem proved that first order logic has nice model theory, Gödel proved that it is recursively axiomatizable and hence has a nice proof theory (unlike higher order logics), and compact (unlike infinitary logics). At the same time, first order Zermelo-Fraenkel set theory (made first order by Skolem, who modified Zermelo's comprehension axiom accordingly) proved to be more than sufficient not only for all of classical mathematics, but even for higher set theory and model theory. On the other hand, higher order set theories, like Russell's, proved to be unwieldy. In the end, Russell had to introduce the infamous "axiom of reducibility" which effectively reduces the logic of his set theory to first order.

Since 1950s Quine routinely identified first order logic with the "language of science", Eklund himself mentions him as an influence. As for "true logic" as understood in philosophy Gödel argued quite the contrary. That human reasoning is not only uncaptured by the first order logic, but by any formalized logic, and that his incompleteness results are an indication of that.

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The quote itself only calls Gödel and Skolem "alleged proponents". Later in the article Eklund explains that "the (supposed) evidence that Skolem adhered to first-order logic is that Skolem held that set theory and arithmetic should be given first-order axiomatizations, whereas... evidence that Gödel adhered to first-order logic is the (alleged) fact that Godel insisted on a first-order metalanguage" (p.151), and proceeds to dispute even this limited evidence. He mentions Gödel-Zermelo correspondence of 1931 as the alleged source, and remarks that "neither Moore nor Shapiro provides us with any quotation from the Gödel-Zermelo correspondence showing it to be the case that Godel there did insist on a first-order metalanguage" (p.158).

The dominance of first order logic is based on technical results of Skolem and GodelGödel, rather than on philosophical arguments. Skolem proved that first order logic has nice model theory, GodelGödel proved that it is recursively axiomatizable and hence has a nice proof theory (unlike higher order logics), and compact (unlike infinitary logics). At the same time, first order Zermelo-Fraenkel set theory (made first order by Skolem, who modified Zermelo's comprehension axiom accordingly) proved to be more than sufficient not only for all of classical mathematics, but even for higher set theory and model theory. On the other hand, higher order set theories, like Russell's, proved to be unwieldy. In the end, Russell had to introduce the infamous "axiom of reducibility" which effectively reduces the logic of his set theory to first order.

Since 1950s Quine routinely identified first order logic with the "language of science", and Eklund mentions him as an influence. As for "true logic" as understood in philosophy Gödel argued quite the contrary. That human reasoning is not only uncaptured by the first order logic, but by any formalized logic, and that his incompleteness results are an indication of that.

The quote itself only calls Gödel and Skolem "alleged proponents". Later in the article Eklund explains that "the (supposed) evidence that Skolem adhered to first-order logic is that Skolem held that set theory and arithmetic should be given first-order axiomatizations, whereas... evidence that Gödel adhered to first-order logic is the (alleged) fact that Godel insisted on a first-order metalanguage" (p.151), and proceeds to dispute even this limited evidence. He mentions Gödel-Zermelo correspondence of 1931 as the alleged source, and remarks that "neither Moore nor Shapiro provides us with any quotation from the Gödel-Zermelo correspondence showing it to be the case that Godel there did insist on a first-order metalanguage" (p.158).

The dominance of first order logic is based on technical results of Skolem and Godel, rather than on philosophical arguments. Skolem proved that first order logic has nice model theory, Godel proved that it is recursively axiomatizable and hence has a nice proof theory (unlike higher order logics), and compact (unlike infinitary logics). At the same time, first order Zermelo-Fraenkel set theory (made first order by Skolem, who modified Zermelo's comprehension axiom accordingly) proved to be more than sufficient not only for all of classical mathematics, but even for higher set theory and model theory. On the other hand, higher order set theories, like Russell's, proved to be unwieldy. In the end, Russell had to introduce the infamous "axiom of reducibility" which effectively reduces the logic of his set theory to first order.

Since 1950s Quine routinely identified first order logic with the "language of science", and Eklund mentions him as an influence. As for "true logic" as understood in philosophy Gödel argued quite the contrary. That human reasoning is not only uncaptured by the first order logic, but by any formalized logic, and that his incompleteness results are an indication of that.

The quote itself only calls Gödel and Skolem "alleged proponents". Later in the article Eklund explains that "the (supposed) evidence that Skolem adhered to first-order logic is that Skolem held that set theory and arithmetic should be given first-order axiomatizations, whereas... evidence that Gödel adhered to first-order logic is the (alleged) fact that Godel insisted on a first-order metalanguage" (p.151), and proceeds to dispute even this limited evidence. He mentions Gödel-Zermelo correspondence of 1931 as the alleged source, and remarks that "neither Moore nor Shapiro provides us with any quotation from the Gödel-Zermelo correspondence showing it to be the case that Godel there did insist on a first-order metalanguage" (p.158).

The dominance of first order logic is based on technical results of Skolem and Gödel, rather than on philosophical arguments. Skolem proved that first order logic has nice model theory, Gödel proved that it is recursively axiomatizable and hence has a nice proof theory (unlike higher order logics), and compact (unlike infinitary logics). At the same time, first order Zermelo-Fraenkel set theory (made first order by Skolem, who modified Zermelo's comprehension axiom accordingly) proved to be more than sufficient not only for all of classical mathematics, but even for higher set theory and model theory. On the other hand, higher order set theories, like Russell's, proved to be unwieldy. In the end, Russell had to introduce the infamous "axiom of reducibility" which effectively reduces the logic of his set theory to first order.

Since 1950s Quine routinely identified first order logic with the "language of science", and Eklund mentions him as an influence. As for "true logic" as understood in philosophy Gödel argued quite the contrary. That human reasoning is not only uncaptured by the first order logic, but by any formalized logic, and that his incompleteness results are an indication of that.

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