Course: Descartes & What Holds Everything Together: Infinite Reality and Causality (Spring 2016)

Course: Topics in Early Modern Philosophy

Teachers: Joseph Almog & Jani Sinokki

On Thursdays 12–14 (Begins 4.2.) in In Seminar room Sh150 (Philosophy Corridor)

Substitution for courses: A1, T1, K1 (3 credits)


The course focuses on some of the most fundamental metaphysical questions – the nature of reality, existence, and causality – and addresses them through Descartes’ unique views on them. The course addresses these fundamental issues through three big “dualisms” that can be found in Descartes’ Meditations on First Philosophy: Thinker vs. World; Mind vs. Body; Cause vs. Effect.

We begin by discussing the Third Meditation, in which Descartes makes the following claim about causality:

There must be at least as much <reality> in the efficient and total cause as in the effect of that cause. For where, I ask, could the effect get its reality from, if not from the cause? And how could the cause give it to the effect unless it possessed it? It follows from this both that something cannot arise from nothing, and also that what is more perfect — that is, contains in itself more reality — cannot arise from what is less perfect. (CSM2: 28; AT7: 40–41).

From this emerges a seldom examined picture of causality. For Descartes, causality is not merely a relation between cause and effect, but the two are only two parts of one single process which is to be understood as a kind of reality transmission or conservation.

Reality, in this singular sense, for Descartes, is tied to the existence of a thing, be that thing an object or a property of an object. Consequently, the process of transmission is not tied to any particular type of things or properties (physical or mental, concrete or abstract). As everything that exists operates in accordance to this principle, this view essentially claims that the World – everything that exists – is a one single interdependent system of reality transmissions. When we understand this highly general account of causality properly, we can proceed to examine the other “dualisms” with the help of it.

In case of mind vs. body, we can see that the so-called real distinction Descartes draws between them is in fact subordinate to the account of causality. This means that both mind and body operate under the same causal laws, and for this, we need to reconsider the traditional mind-body problematic attributed to Descartes.

Thinker vs. world dualism is a widespread view in modern philosophy. It is the implicit assumption that thinking beings are somehow distinct from the rest of the reality; that thinking – as cases of dreams, illusions, and hallucinations are supposed to witness – floats freely and independently of all the rest there is. In light of the Meditations read through the Third Meditation causal principle, the case is according to Descartes just the opposite. Thinking is part of the one and single causal network, the World, and seeing that even the problematic cases like dreams or cunning demons have to operate in accordance to the causal principle, we can see that the skeptical challenges “should be dismissed as laughable” (CSM2: 61; AT7: 89)

Finally, we can ask a question about the nature of infinite God. In light of the principle, God is the ultimate source and transmitter of reality to the World. Is this picture postulating a source of World’s existence really as outmoded as some have suggested, or should we reconsider our attitude towards it in accordance to Descartes’ causal principle?

Philosophy & Mathematics Seminar on Thinking and Computation (Spring 2016)

Thinking and Computing — Machines and Humans

Responsible Teachers: Joseph Almog, Vesa Halava, and Tero Harju

Substitution possible for courses: A6,A9, V11,T1, K1 (4 credits)

From 2.2. to 19.4. on Tuesdays 10–12 at Seminar room SH 150 (Philosophy Corridor)


We will discuss the very idea of “thinking” and “computing” as it occurs in mathematical work of human beings and machines. This involves simple thinking, as in adding 5 and 7 to make 12 or show—within a given geometry—that triangles have a certain angle-sum and all the way to considering very abstract problems—how many points are there on the real line? Is there a general systematic method (“algorithm”) for solving arithmetical problems in the form of polynomials (simple ones encountered at school)? Is Arithmetic consistent? Is there a general method for deciding whether when it “runs”, any such general method terminates?
The course aims to discuss very different approaches to the question of human (mathematical) thinking. We will contrast the “reductive” finitistic view, the one dominating contemporary thinking, according to which we are “finite minds” and according to which this itself is represented by the processing effected by certain kinds of “machines”, called Turing Machines. This we will contrast without our own view—a marginal one but with some interesting notable sponsors(see below the quote from Cantor) that we are not “finite minds’ (even if our brain is just 1200 cubic cm and 1.5 kg) because of our grasp of infinity, in a way that (1) is not reducible to finitistic formal operations and (2) in a way which is necessary as background to operation with “finite structures”.

We would like to read great classics on the matter that have not been really dissected enough and have been reported-on incorrectly. This includes on the “reductive” side the reading of: Hilbert, Turing and Saul Kripke’s latest (e.g. the “Turing Thesis” being for him a corollary of the completeness theorem!).

On the other side we will focus on Emil Post, the jewel in the crown, as well as Cantor and Woodin. Interesting non classifiable cases are Godel and Wittgenstein (themselves in dispute with one another). In the background, are the great figures of Leibniz and his project of Ars Combinatoria and in contrast, Descartes’ and his notion of mathematical understanding. We plan on having visitors speak of Frege’s Bwegriffschrift and Husserll/Godel phenomenology of mathematical thinking, as well as deeply involved key figure (surprise!) on Hilbert’s tenth problem.

The course is not accessible merely to people with “advanced” knowledge. If you are interested in computers, philosophy of mind, strategies in games and strategic thinking in general, you are most welcome. The discussion is going to be dialogical and informal.

We attach an inspiring motif from Cantor’s Grundlagen 1883.

Quite often the finitude of the human understanding is adduced as a reason why only finite numbers are thinkable…for by ‘finitude of the understanding’ is tacitly meant that the capacity of the understanding in respect to the formation of numbers is limited to finite numbers. If it should turn out, however, that the understanding in a certain sense is also able to define infinite i.e. transfinite (uber-endliche) numbers and distinguish them from one another, then either the words ‘ finite understanding’ must be given an extended meaning … or else the human understanding must also be granted the predicate ‘infinite’ in certain respects, which, in my considered opinion, is the only correct thing to do. The words ‘finite understanding’ which one hears on so many occasions are, as I believe, in no way on the mark as limited as human nature may in fact be, much of the infinite nonetheless adheres to it and I even think that if it were not in many respects infinite itself, the strong confidence and certainty regarding the existence (‘desseins’) of the absolute, about which we are all in agreement, could not be explained.