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Arnauld’s Logic and Cartesianism

It can be tempting to view Antoine Arnauld only in relation to Descartes because when looking at any scholarship written about Arnauld, authors do not hesitate to make this link clear. While Arnauld advocates much Cartesian rhetoric in all his works, there are stark distinctions that show the reductivity of such a statement. It is not absurd to point out that Arnauld writes about many of the things Descartes does. However, it is important not to discount the Cartesian influences on Arnauld’s writings; I argue that Arnauld’s works appear to be representations of Cartesian theory in practice.

For example, Arnauld’s Logic and Grammar can be viewed as a direct application of Descartes’ description of spatial relations between objects and a way to describe these translations to our own lives.  Though Arnauld does not focus on a hypothetical object in a realm we cannot see, he applies this metaphysical thinking to our speech about such ideas and our speech in general.

Arnauld describes the realm of logic as Descartes describes space. Logic is a space that we cannot see and cannot fully grasp, but we know it is there. Just as there are no cartesian axes within which we live and are bounded by, logic is the same regardless of who reaches it, but our description or interpretation of this logic to others becomes jumbled as we need some method to move it between one another.

In an almost Platonic sense, our description of a true idea is merely a projection of the real idea into terms we accept. Arnauld does not deny that there are fundamental tenets of logic and truth that we all experience. He does say that we cannot always convert experiential beliefs into intellectual understandings. Without having their experience, we will never fully be able to understand how our colleagues came to the conclusions they wish to share. This does not mean that their conclusions are true – only that the events which led them to draw these conclusions are infallible. Although we cannot translate and share the wisdom of experience and understanding, there are things that do happen and there are reasons for them even if we cannot grasp these.

In a relativistic sense, just as two observers facing each other see a ball thrown in opposite directions, two people may experience the same things differently. We may struggle to describe the ball’s motion (right or left), but that does not affect the ball’s motion. Nothing about the ball’s path changed, but we are able to draw different conclusions about the ball. This is not to say that there is not a right answer. Even if we do not reach it, the answer is there.

The logic of our world is universal and we all experience it as such, but our ascriptions of meaning and causation to such logic is a never-ending task. We will never fully understand our world, but this does not mean that we should not try. In fact, Arnauld’s work describes common problems in sharing these experiences and what we need to overcome them. 

Arnauld’s description of logic and language and the faults of translation is predicated on the Cartesian plane and the Platonic ideals, but Arnauld’s clarity and application of metaphysics to our everyday interactions is his accomplishment. While we disagree feverishly, there is some objective standard that would allow us to combine contradictory understandings — we just cannot access it.

 Giving all of our respect to Descartes for Arnauld’s applications of his theory is ignorant of the importance of arduousness of practicality. Descartes’ meditations would not wrongly be critiqued as an intellectual exercise. Arnauld’s decision to apply these abstract musings to interactions we all undergo takes as much insight and creativity as the musing in the first place.

Being able to diagram the flow of ideas is similar to showing the translation of an object in space. While Descartes can be credited for the assertion that there is a plane which houses both points of travel, Arnauld describes the travel of ideas and the warping of the truth when we share them. If we did not know about the plane that an object traveled on, knowing where it started and ended would give us insight into what areas the plane encompassed. It will never be perfect, but it is more accurate than our understanding of the plane before we traced the path of our object.

Descartes can and should be given credit for allowing Arnauld to use the idea of a space in which truth resides and which we can somewhat grasp, but Arnauld’s determination to trace an idea from beginning to end was his own work and no easy feat. As with our ball in motion, Arnauld’s work required that he be able to separate his view of the motion from that of the true motion of logic and generalize this for people whose experiences he could not partake in. While many philosophers assert that their experiences and intuitions are the only ones needed to describe the universe (because any universal experience would be given to them as well), Arnauld’s narrower focus on the physics of ideas among people required more care to distinguish between his exchanges with others and their exchanges with themselves.

Describing the flow of real ideas is more arduous than just accepting that there are objective measurements of truth. Arnauld’s work sought to find out how ideas morphed without knowing what the ideas looked like to begin with. Even tracing an object while presupposing a coordinate system that an object must travel on is easier than tracing the path of an object if you do not know what the coordinate system looks like. Arnauld’s task was smaller in scale than Descartes’, but his methodology and intellectual labor was no less than Descartes’. 

Humans are confusing, contradictory entities that defy any attempt at categorization, so it is unfortunate that a social, philosophical inquiry would be given less recognition than a metaphysical meditation. This is not to say that Descartes’ work is minimal or unimportant. It is only to say that viewing Antoine Arnauld in terms of Descartes’ exclusively reduces Arnauld’s contributions to a footnote and does not allow us to engage with his work.