A mines are one of the most important structural motifs in pharmaceuticals, agrochemicals and organic materials 1,2 . Alkylation and reductive amination reactions are still commonly used to prepare and modify amines, and new methods derived from reductive amination, such as the borrowing hydrogen 3 strategy, have been reported [4][5][6][7] . Nevertheless, the most significant development in amine synthesis has been transition-metal-catalysed C-N coupling of aryl electrophiles (halides and pseudo halides) with amine nucleophiles [8][9][10][11] (Fig. 1a). The C-N coupling of alkyl electrophiles, however, is largely under-developed (Fig. 1a). A perceived difficulty is β -hydrogen elimination from a metal alkyl intermediate originated from oxidative addition of the alkyl electrophile, which has posed considerable challenges in analogous C-C crosscoupling of alkyl electrophiles [12][13][14] . Moreover, the product-yielding C(sp 3 )-N reductive elimination step is rarely demonstrated 15 . A notable exception is the light-induced, copper-catalysed C-N coupling of alkyl halides recently developed [16][17][18] . Nevertheless, the scope of amine nucleophiles is limited to carbazoles 16,18 and amides 17,19 . Alternative, formal C-N coupling of alkyl electrophiles via the addition of alkyl radicals to nitroarenes has been reported 20,21 .The group of Baran has recently trailblazed the use of redox-active esters derived from alkyl carboxylic acids as superior surrogates of alkyl halides in decarboxylative C-C cross-coupling reactions [22][23][24] . Extension to a decarboxylative carbon-heteroatom, particularly C-B bond formation has also been reported 19,[25][26][27][28][29] . The key attributes of alkyl carboxylic acids 30,31 are their unparalleled availability, stability and non-toxic nature, which are in stark contrast with alkyl halides, ketones and aldehydes. While several precedents of decarboxylative imidation 32 and amination 19,33 are known, they are limited to a narrow scope of very special substrates or intramolecular reactions. A general metal-catalysed decarboxylative C-N coupling of redox-active esters with anilines will provide valuable methodology for the synthesis of alkylated anilines (Fig. 1b), which requires alkyl halides and carbonyl compounds 6 as starting reagents using the currently standard methods of alkylation and reductive amination, respectively. Further foreseen advantages of such a decarboxylative amination include applicability to bulky primary and secondary alkyl groups and immunity to over-alkylation, both of which are major limitations of direct alkylation (Fig. 1b). Despite its conceptual simplicity and resemblance to decarboxylative C-C coupling, the intermolecular decarboxylative C-N coupling of redoxactive esters poses significant hurdles. The activation principle of redox-active esters originates from amide-bond synthesis; thus, amide formation can compete when amine nucleophiles are used. Moreover, decarboxylative C-C coupling reactions of redox-active esters were, until now, all init...
According to Carnap an account of the nature of mathematics, both pure and applied, must include the thesis that mathematical truths are devoid of factual content. He first formulated this thesis around 1930 and in its defence attempted to combine the reduction of mathematics to logic undertaken in the Principia with Wittgenstein’s insights into the nature of logic. In this paper I will show that this synthesis faces serious difficulties. Thus, it plays, with good reason, no longer a role in Carnap’s mature philosophy of mathematics.
SummaryKitcher’s philosophy of mathematics rests on the idea that a philosopher who tries to understand mathematical knowledge ought to take its historical development into consideration. In this paper, I take a closer look at Kitcher’s reasons for proposing such a historical turn. I argue that, whereas a historical account is indeed an essential part of the standpoint advanced in The Nature of Mathematical Knowledge, this is no longer the case for the position defended in the manuscript Mathematical Truth? The Wittgensteinian account of mathematics advocated in that manuscript does not force us to take a historical turn.
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