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Arnauld — Port-Royal Logic

Among Antoine Arnauld’s intellectually diverse scholarship, his time and writings at the port-royal were prolific in meta-cognition and expanded on the already immensely impactful Cartesian theories of the mind and body.

Arnauld’s Logic, or the Art of Thinking was among his most renowned works for examining the metaphysical relationship between our intuitions and senses.

Logic was written in French rather than Latin which was unusual for mathematical and philosophical scholarship at the time. The Cartesian and Platonic influences are obvious in Arnauld’s work when he examines the relationship between physical objects in our world and our perceptions of them. Drawing from Descartes, Arnauld describes the phenomenon of characterization. We see something in the world and we have already placed it in a broader framework of the group with which it resides.

In a platonic manner, Arnauld describes these fundamental concepts that our minds understand. We can only see physical things in relation to the objects that our minds see. However, these may not be the true (highest) form and category of these objects. The divine idea of the things we interact with are not what our mind sees, but we still cannot see an individual instance of an object. We will always group these objects with properties we understand, so discussions of an instance are no different than a discussion of the basis.

Arnauld further speaks about the connections between physical things, our ideas, and divine ideas in relation to the way in which we communicate them. Arnauld believes that we all have the same understanding (in terms of ideas) of the objects we see (separate from the divine idea), but where we disagree is in our dissemination of our thinking. A divine (naturally true) idea’s clarity would not suffer in any respect because that is the true form of this thing. However, our understandings will all be wrong in the same way. We cannot appreciate the divine truth, but from human to human, there should not be such a large gap in beliefs. We all see the same objects, and should associate them in the same way. However, because our ideas are not perfect, describing a fuzzy theory to another can result in a loss of an already decreased understanding.

Thus, it becomes crucial to minimize the confusion in our speech by articulating the nature of what we talk about. This too, is subject to the same constraints of misunderstanding, but this is a fundamental step to be able to appreciate the experiences of others instead of dismissing them due to our inability to comprehend a clearly inept theory built from the senses we all share. For example, we may disagree with the details of a theory because it is impossible to articulate the nuances to another, but the substance of the theory should be unchanged from person to person. The boundaries of these ideas spatially and temporally is frequently disputed (such as the question of Thesius’ ship).

Arnauld argues that the fundamentals of language are due to the rectifying these inconsistencies (the ones not in theories of understanding, but in communication of these ideas and the search for the greater truth. Just as our ideas have boundaries over which objects they apply to, language can refer to objects through these categories. We can speak about the categories (what strings tie their components together) rather than specific instances. This would be impossible, though, if we weren’t able to reference what was enclosed by a category.

We can also specify which objects within these groups we refer to by specifying attributes of the objects which we want to discuss. For example, we sense that a house has a color, or that it’s foundation is sturdy, or that it is made of wood.

Strangely, describing the house relies on understanding the concepts of color, strength, and composition each of which has the same problem in definition. Describing a house in terms of its attributes makes sense when it’s attributes are defined mentally and linguistically, but they all suffer from the incoherence in understanding and articulation. Likewise, describing an idea of something can typically be done in terms of its parts, but when we cannot clearly place a part in this category, or it can be placed in multiple categories, our definitions become circular and, at best, uncertain.

Arnauld does acknowledge that our conceptions of the whole are informed by (if not comprised of) our understanding of its parts, but that by aggregating its parts, we do get a picture of the whole and how to describe it. Unfortunately, in reality, we define parts or attributes of these parts from its categories. We can define a specific triangle with specific properties, but in understanding it, we assign properties of all triangles to this triangle. However the concept of triangles is supposed to be understood as a sum of all the triangles such as the ones we look at. It cannot then be defined by its category if its category is defined from it.

Arnauld would likely respond that an instance being defined in terms of a group or vice versa is not a tautology because, although we do not fully understand the platonic ideal of the group, this ideal exists, and it is not absurd to grant that the instances of a triangle will draw from this fundamental ideal.

Still, allowing this tautology to exist in his argument seems to be a flaw when we cannot conceptualize or communicate this God-given truth. Even if there is a certain truth that God has bestowed, if we cannot reach it, we cannot make assumptions about what comprises it without acknowledging the imprecision in our minds.

Although it would make sense that, given the same set of stimuli, we all experience the same things, assuming that all the confusions and differences in opinion come only from our ability to speak about our universal experiences rather than just having different experiences seems like an arbitrary place to draw this line. If we know that we do disagree on things, why would Arnauld decide that we only disagree because we cannot describe what we experience. Could there not also be a difference in experience that describes this? Although it is an interesting question, and Arnauld answers it well, it seems that even when his logic is consistent his application of this logic seems arbitrary in what it is applied to.