Analytic metaphilosophy

By analytic metaphilosophy we mean a methodology which aims to apply mathematical and formal logical rigor and the full force of linguistic analysis to philosophical texts in order to assess their argumentative and epistemic value. Analytic metaphilosophy has a strong affinity and connection to early classical analytic philosophy (though it has many brilliant precursors before that time) but no connection to subsequent post-classical analytic philosophy - indeed it can be conceived as the ultimate tool to thoroughly refute and show the nonsense and vacuity of its various currents as well as some of those that claim to break with it.  A novel aspect is that it attaches an enormous importance to the style of philosophical texts and aims to be far more wary and careful about the pitfalls, delusions and psychological foibles of the whole process of literary creation. It never forgets that the philosophical writer is never far from the precipice of literary fantasy often exhibiting egocentric and sycophantic qualities geared to socio-economic advantages rather than epistemic and ethical goals.  Analytic metaphilosophy studies in particular the sociology and psychology of sophistry and literary delusion. More Platonico we shamelessly proclaim that it is impossible to engage in analytic metaphilosophy without either a solid undergraduate background in mathematics and mathematical logic or at least a couple of years of experience working on a formal mathematics project employing a proof assistant.  In a nutshell: analytic metaphilosophy applies mathematical standards of logic and rigour to philosophical texts and refuses to be impressed by the mirages and artifices of language (though an ideal philosophical text can have also beauty, elegance and clarity of style as in the writings of Frege and Claire Ortiz Hill). Jargon-laden and convoluted texts rarely betray deep, complex, rigorous or valid thoughts. Such pseudo-difficulty is of an entirely different nature from the 'difficulty' of mathematical texts. Analytic metaphilosophy can also be seen as a kind of prolegomena and justification for the formal philosophy project we described in previous posts.

In that most rigorous, clear and certain of the sciences, mathematics,  mistakes and confusions still arise, there are gaps in proofs, there are unjustified assumptions, careless generalizations, confusions in terminology, silly oversights, circular reasoning, etc. As the length of the proof increases so does the probability of error, even for the best mathematicians and Fields Medalists like Vladimir Voevodsky. Careful checking by several experts is absolutely necessary. In some areas the length of the proofs become almost too long for this to be feasible, so proofs are formalized and run through specialized proof checking software.

Now consider philosophy, the least rigorous, clear and certain of human epistemic enterprises. Once a philosophical 'argument' becomes long, convoluted and (on the surface level) complex one can be almost certain that it is wrong or inconclusive. The same goes for texts with an elevated number of technical terms or  'jargon density', so to speak. 

Mathematicians have an artist's liberty to use and invent symbols for their primitive and defined notions and variables.  The philosopher, shackled by natural language and lack of mathematical training, is in a very dire situation, terms are pathologically and enormously semantically overloaded and the resulting terminology is opaque, ambiguous and stylistically repugnant. Perhaps this can be partially overcome by the construction of an artificial language for philosophical terms.

The majority of philosophical texts have nothing to do with the logical standards and rigour of mathematics or even the exact sciences. What reason is there to attribute to them any meaning or epistemic value at all ? Or even social value ?  And many of their authors are aware of this, don't care, or consider it a virtue.  They have their communities with their founding narratives and (non-reflectively) received doctrines and they happily engage in their 'language-games'  and strictly controlled boxed (bottled ?) 'innovations'. They have their own 'logic' and 'rules' and 'criteria' for parsing and deciding the value or legitimacy of textual-output - and this output is a torrent, an endless deluge and logorrhoea that seemingly might be generated by large language models. Ex falso quodlibet. 

Analytic metaphilosophy (which favours Martin-Löf type theory as an adequate intensional and modal logic) is entirely immune from objections culled from mathematical logic itself such as all-too-common misunderstandings and misappropriations of Gödel's incompleteness theorems.  Although mathematics can be conceived as a subset  of logic (by assuming special axioms such as univalence), logic can also be conceived as an application of mathematics. There is no concept of computability without involving arithmetic and no concept of arithmetic which does not involve some notion of computability.

Recall that we hold that logic is embodied in a closely unified (organic) family of formal systems which are related to each other by gradation or (mutual) embeddability and reflection. There is no trace of convention or arbitrariness.

And in nowise does our metaphilosophy claim to be philosophy itself or a substitute for it. However knowledge of applied mathematics at an advanced theoretical level has huge conceptual advantages for thinking about possible worlds, possibility, causality, identity and states of being which far surpass the crude models used in analytic philosophy.

Analytic metaphilosophy can be integrated seamlessly into the Gödelian and Husserlian frameworks as complementing and helping the metaphilosophy and methodology of ultimate evidences and intuitions as well as ethical metaphilosophy*. It works alongside it and provides powerful aid by refuting anti-idealist arguments.

Schopenhauer's detailed criticism of Kant in the WWR and T. H. Green's long introduction to Hume's Treatise are  good examples of pre-Fregean analytic metaphilosophy. The investigation of the expression of multiple generality and its associated reasoning in ancient philosophy is clearly a cornerstone to analytic metaphilosophy's  approach to ancient and early modern philosophy.

*ethical metaphilosophy focuses on the explicit and implicit content relating to human and animal rights, in particular the status, dignity and consciousness of animals,  in historical philosophy - and thereby comes to general conclusion about the value and merit of different philosophical systems.  Leaving aside ancient eastern philosophy, the cases of Porphyry, Schopenhauer and Husserl are enough to de-fang ethics-based anti-idealist arguments whilst arch-anti-idealist Nietzsche's raving praise of Descartes' view of animals delivers a fatal counter-blow.

Medieval philosophy has been criticized for being the handmaiden of theology and merely a tool for the apologetics of the dogma of organized religion.  If this is justified then philosophy also cannot be allowed to be the handmaiden for para-scientific ideology and dogma either, which is what we find predominantly in the so-called 'philosophy of mind'. Is there anything more silly than  a priori arguments for speculations  based on incomplete or faulty experimental science ? Image the money it saves on equipment and resources for the materialist neuroscientist.

Nevertheless Kant's language is often indistinct, indefinite, inadequate, and sometimes obscure. Its obscurity, certainly, is partly excusable on account of the difficulty of the subject and the depth of the thought; but he who is himself clear to the bottom, and knows with perfect distinctness what he thinks and wishes, will never write indistinctly, will never set up wavering and indefinite conceptions, compose most difficult and complicated expressions from foreign languages to denote them, and use these expressions constantly afterwards, as Kant took words and formulas from earlier philosophy, especially Scholasticism, which he combined with each other to suit his purposes; as, for example, "transcendental synthetic unity of apperception," and in general "unity of synthesis" (_Einheit der Synthesis_), always used where "union" (_Vereinigung_) would be quite sufficient by itself. Moreover, a man who is himself quite clear will not be always explaining anew what has once been explained, as Kant does, for example, in the case of the understanding, the categories, experience, and other leading conceptions. In general, such a man will not incessantly repeat himself, and yet in every new exposition of the thought already expressed a hundred times leave it in just the same obscure condition, but he will express his meaning once distinctly, thoroughly, and exhaustively, and then let it alone. "_Quo enim melius rem aliquam concipimus eo magis determinati sumus ad eam unico modo exprimendam_," says Descartes in his fifth letter. But the most injurious result of Kant's occasionally obscure language is, that it acted as _exemplar vitiis imitabile_; indeed, it was misconstrued as a pernicious authorisation. The public was compelled to see that what is obscure is not always without significance; consequently, what was without significance took refuge behind obscure language. - Schopenhauer, WWR (II).