One does not have to do more than a cursory review of intellectual history to find intellectual bifurcations everywhere. There’s nominalism vs. realism, rationalism vs. empiricism, analytic vs. continental, and so on. 
Earlier this month at the Claremont Conference Steven Shaviro nicely articulated the bifurcation between his position and Graham Harman’s. Whereas the problem for Harman is how objects can enter into contact and communication with one another, a problem he solves with his notions of vicarious causation and allure, the problem for Shaviro is one of how to break free from the incessant web of contacts and relations, how to get some elbow room as Shaviro put it (citing Whitehead). In Priest’s book in contradiction, which I discussed here in yesterday’s post, he highlights the early modern bifurcation between the continuous and the discrete (a bifurcation that of course predates early modern thought and is not exclusive to the western tradition). Priest signals Leibniz and Hume as emblematic of this bifurcation. In a response Leibniz wrote to a letter of Malebranche, Malebranche arguing for his occasionalist position (that is, coming down in favor of the discrete), Leibniz puts forth what Priest calls the “Leibniz Continuity Condition.” Citing Leibniz:
When the difference between two instances in a given series or that which is presupposed can be diminished until it becomes smaller than any given quantity whatever, the corresponding difference in what is sought or in their results must of necessity also be diminished or become less than any given quantity whatever. Or to put it more commonly, when two instances or data approach each other continuously, so that one at last passes over into the other, it is necessary for their consequences or results (or the unknown) to do so also).
Priest sums this up by saying that for Leibniz if ‘anything is going on arbitrarily close to a certain time [then] it is going on at that time too.’ Hume, by contrast, has no place in his thought for the continuous – it is continuity that is the problem, a problem solved by the principles of human nature working on the association of discrete impressions and ideas. As Priest puts it, for Leibniz ‘succeeding states of affairs in nature are not atomistic: there are connections. This would be denied by a Humean. For her, if the principle held it could only be by a global accident.’ There is thus no place in Hume’s thought for the principle of sufficient reason, as there was for Leibniz, since there is nothing in the nature of the discrete themselves to provide connections with one another – the relations between things are external to the things themselves and could very well be other than they are. It is this aspect of Hume’s thought that Meillassoux highlights (as I discuss here). Priest’s views of the bifurcation between Leibniz and Hume is by far the consensus view. Robert Brandom and many others, for instance, will point to Hume as the atomistic empiricist and look to Spinoza, Leibniz, and Hegel as holistic rationalists. So intellectual bifurcations abound.
I once thought such intellectual bifurcations were a problem, a sign of intellectual partisanship that does neither side any good. I’m now beginning to understand it as part of the process of intellectual creativity itself, a form of intellectual mitosis such that the emergence of the new comes to be actualized only in a bifurcated form. The Shaviro/Harman bifurcation is thus symptomatic of the emergence of a new intellectual problematic, a new conceptual plane, and as discursive representations actualize various solutions to this problematic they necessarily entail an intellectual mitosis, a bifurcation of positions.
In my Deleuze’s Hume book I draw attention to a similar bifurcation among Deleuze scholars. On the one hand there is the materialist or realist Deleuze. From this perspective Deleuzian concepts are understood to be capable of explicating and clarify the processes of the real. Much of this work, as found in DeLanda as well as my own work (and in Protevi, Levi, and others) emphasizes the conceptual role dynamic systems plays in Deleuze’s thought. This position is classically realist in the sense that these concepts are generally taken to be helpful in clarifying the processes of a reality that is independent of, and indifferent to, the conceptual formations developed to clarify them. At the same time there is the nominalist or idealist Deleuze. This approach focuses on Deleuze’s discussions of the Idea as problem, as problematic that is only identifiable as such as actualized. The problematic is thus not a reality independent of its actualization, an ideal possible merely waiting its actualization; rather, it is a reality identifiable as such only as actualized. This bifurcation of interpretation is itself another example of intellectual mitosis, a consequence of the emergence of a new conceptual plane. Moreover, in his early essay on Bergson Deleuze already recognized the necessity of actualization occurring always as bifurcated actualities. In reference to Bergson’s philosophy of difference, Deleuze argues that ‘virtuality exists in such a way that it actualizes itself as it dissociates itself; it must dissociate itself to actualize itself’; and he adds, a few pages later in the same essay that ‘what is differentiating itself in two divergent tendencies is a virtuality.’ The realist and nominalist Deleuze are thus these two divergent tendencies as the actualization of discursive thought emerges in the process of addressing and actualizing the conceptual problematics of Deleuze’s thought.
What is important for philosophy, therefore, at least from the Deleuzo-Humean perspective I have been charting, is not to avoid the bifurcations of thought. Such bifurcations are evidence of the intellectual mitosis that accompanies thought when it is creative. What philosophy ought to do is to return to the problematic which is inseparable from the mitosis and bifurcation, from the splits that actualize divergent discursive positions. A proper philosophical concept does just this. Hume’s concept of ‘belief’, for example, has given rise to a number of bifurcations among Hume scholars. In what has come to be called the New Hume debate there are the realists who claim that Hume never was truly a skeptic, that he believed in the reality of an independent, lawful nature which accounts for the regularities of experience; and then there is the Hume who is seen as a skeptic, for whom there is no principle of sufficient reason and where everything could be other than it is. The lesson to be drawn from this is not that Hume was inconsistent but rather that he created a philosophical concept, a problematic plane that has prompted creative intellectual thought, and as this thought proceeds it naturally gives way to its own unique form of intellectual mitosis.