[E]veryone who works as a mathematical philosopher [a] knows some papers in which the respective authors hide behind the symbols—where mathematical clothing is meant to conceal lack of philosophical content. Or [b] where mathematics does not do much other than complicate some states of affairs that could, and should, have been described in more elementary terms. Or [c] where a mathematical method is applied blindly without any awareness of its potential limitations. In other words: just like all other tools, mathematical methods can be abused. But clearly that should not stop us from putting them to good use in philosophy. (Leitgeb, "SCIENTIFIC PHILOSOPHY, MATHEMATICAL PHILOSOPHY, AND ALL THAT" 274-5) [a-c, added to facilitate discussion.--ES]
The forthright paragraph above is the main one devoted to substantiating one of the aims announced in the abstract of Leitgeb's (2013) nine-page manifesto, that is: "it aims to undermine some worries about mathematical philosophy."* Clearly, Leitgeb's "clearly" skips over an argument and a lot of potential concerns. For, the potential abuses of mathematical methods developed, explored, and taught in philosophical circles are not exhausted by [a-c]. (To be clear: elsewhere in his piece, Leitgeb addresses other concerns about the use of mathematical methods in philosophy -- including a very interesting engagement with Kantian concerns -- , but these do not concern me here.) Moreover, without evaluating the significance or costs/benefits of the unmentioned potential abuses, it is unclear how clear Leitgeb's "clearly" really is. (Note, too, that even if one were to grant that mathematical methods primarily have good uses inside philosophy (and we ignore concerns over non-philosophical abuses/applications), it still might be the case that they displace better methods within philosophy, or are oversold. I leave this aside.) First a brief historical detour.
Formal philosophy has a long-standing relationship with the war-making machinery of the modern state. During the cold-war the main conduit for this activity was the Rand Corporation, when it was primarily funded by, first, the Douglas aircraft corporation and then the U.S. department of defense (I think it still is); many of the most celebrated formal philosophers (and economists, artificial intelligence, operations researchers, cybernetics etc.) passed through Rand at point or another. (This started, I think, with Olaf Helmer -- a student of Reichenbach [later also prominently involved at Rand] and a member of the original die Berliner Gruppe.) Even today, if you scan the CVs of senior figures in the field you will find stints as visiting reseacher, fellow, (etc) at Rand. Undoubtedly, in addition to a nice pay-check and a wonderful research environment, for many it must have seem a noble calling in the fight against Totalitarianism. For some it meant working on topics related to improving education, linguistics, data-storage and other potentially beneficial civilian enterprises. To the best of my knowledge, Daniel Ellsberg (the great decision-theorist and leaker of the Pentagon papers) was the first of the Rand-funded insiders to question publicly this cozy nexus during the Vietnam war.
Some of this history has been told (by Amadae, Mirowksi, and more focused on philosophy, George Reisch, who is also philosophically sophisticated), but the full story of scientific philosophy's entanglement with the military-industrial complex has not been explored either from within formal philosophy or without. (I would love to learn otherwise.) This is not to deny -- on the contrary -- that there have not been conscientious and heroic formal philosophers who have individually distanced themselves from such funding. I was raised philosophically on inspiring, even heroic accounts about Carnap's pacificism and resistance to loyalty oaths, and about Malament's stance during the Vietnam War. (I would love to learn more!) Clearly, there is nothing within formal approaches that prevents a politically self-aware stance; in fact, I am very impressed by the ongoing, political role of some formal philosophers in their attempts to warn about and limit the reach of the surveillance state.