According to conventional wisdom, mathematicians tend to accept platonism but find logicism wildly implausible if not ridiculous, whereas philosophers tend to find platonism wildly implausible if not ridiculous while being attracted to logicism.
Q1. Where can one find versions or variants of this conventional wisdom in print? Of course, the writings of respected authors are preferred.
Q2. Where can one find philosophers’ statements deploring or ridiculing platonism?
Q3. Where can one find mathematicians’ statements deploring or ridiculing logicism?
Q4. Where can one find mathematicians’ statements deploring or ridiculing people who reject platonism?
Q5. Where can one find philosophers’ statements deploring or ridiculing people who reject logicism?
Platonism in the narrow sense (that getting ideas is merely recollecting them) is, I believe, quite uncommon among mathematicians, but Platonism in a broader sense (that mathematical ideas exist in some way independent of human mind and are discovered rather than invented) is indeed shared by quite a number of prominent mathematicians. These include inter alia Yuri Manin (see e.g. this interview: http://www.ams.org/notices/200910/rtx091001268p.pdf ) and Vladimir Arnold (see e.g. here: http://www.ams.org/notices/201203/rtx120300378p.pdf )
In the sense intended in my question, there are many varieties of platonism in philosophy of mathematics but they all share the view that some or all mathematical sciences study mathematical objects. This separates platonisms from formalisms which holds that all mathematical sciences are devoid of reference and are based on arbitrary rules for manipulating strings meaningless characters.
Platonisms also hold that mathematical objects, those entities over which range individual variables of mathematical sciences, are existent, abstract, non-mental, non-created, non-material, non-temporal. This separates platonisms from fictionalisms that hold mathematical objects to be fictional like mythical creatures and literary characters. It also separates platonisms from nominalisms such as pansomatism that hold mathematical objects are constructed from material bodies.It also separates platonisms from conceptualisms like intuitionism that hold mathematical objects are mental constructions.
Platonism is implicitly presupposed in all of my dozens of articles and reviews. It is an explicit underlying assumption of my "Gaps between logical theory and mathematical practice", available on RG.
NB: my question has nothing to do with "recollectionism". And I do not see how the sense of platonism used here could be considered "broader" than the recollectionism sense. BTW, I have never seen 'platonism' used in the recollectionism sense before reading Artur Sergyeyev's otherwise interesting and useful answer .
Yr initial query contrasted platonism w logicism. Yr subsequent note contrasts platonism w formalism. As logicians &philosophers of mathematics use the terms, logicism is compatible w platonism and opposed to what you are calling formalism. Cf on line Stanford Encylopedia of Philosophy
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