An attempt to diagram the tension between determinism and belief in causa sui

My understanding of the story so far, following lengthy and ongoing discussions with I, L, P and others (see also the free will tag on this site, stretching back to 2007):

  1. Nothing can be a cause of itself, causa sui.
  2. To be truly, really, wholly responsible for your actions, you would have to be causa sui (the self-determination thesis).
  3. Your choices depend on who you are (e.g., your personality, values, beliefs, desires, powers) and where and when you are (linked to your opportunities). Who, where, and when in turn depend on billions of complex causal chains that precede your existence and stretch back to the beginning of time.
  4. Therefore, you are not truly, really, wholly responsible for your actions.
  5. However, you can still change: your personality, values, beliefs, powers, etc. – your nature is not fixed. You clearly don’t stay still in time or space either.
  6. You can also carry out actions and have an effect on the world as an active participant in cause-effect chains.
  7. Moreover, praise and blame and other common attributions people bestow upon one another, though difficult to comprehend in light of conclusion 4 above, are example causes of actions since they have an effect on people.

Here is an attempt to diagram the above, assuming that determinism holds (though that need not be the case for the self-determinism thesis to fail). Instead of a complex web of billions of cause-effect chains stretching back to the beginning of time, I have embodied that long history all in a cat that has a grand unplan (I’m not sure how the conversation arrived there), borrowed from the interweb.

The arrows above are intended to be wholly determining and not the statistical associations common in social science that explain 5% of the variance in outcomes. All the variance is explained here: 100%.

Below is the cat, viewing the outcomes. Determinism does not imply that it is possible to predict outcomes from starting states. Prediction is tricky even for simple cellular automata let alone something as messy as a universe. You have to “wait” (actively, moving) and see what happens and enjoy the phenomenology that goes along for the ride, including the intense illusion of causa sui. (“You should go on living – if only to satisfy your curiosity” – from a Yiddish proverb, which can also have a causal effect on its readers under determinism.) Unpredictability does not challenge the impossibility of causa sui, though.

Nietzsche on causa sui

‘The causa sui is the best self-contradiction that has yet been conceived, it is a sort of logical violation and unnaturalness; but the extravagant pride of man has managed to entangle itself profoundly and frightfully with this very folly. The desire for “freedom of will” in the superlative, metaphysical sense, such as still holds sway, unfortunately, in the minds of the half-educated, the desire to bear the entire and ultimate responsibility for one’s actions oneself, and to absolve God, the world, ancestors, chance, and society therefrom, involves nothing less than to be precisely this causa sui, and, with more than Munchausen daring, to pull oneself up into existence by the hair, out of the slough of nothingness.’
– Friedrich Nietzsche (written 1886), Beyond Good and Evil, translated from German by Helen Zimmern, upper case lowered again and italicised

Doings and deliberations can change things

“Naive fatalism holds that there is no point in doing anything because everything is predetermined (or is the will of God, for example), hence nothing you can do can change how things will be. It is false, because one’s doings and deliberations can change things, being themselves real parts of the (possibly deterministic) causal process.”
– Strawson (2010, p. 247, footnote 22) [Freedom and Belief, Revised Edition.]

Freedom under determinism

“Behind the whole compatibilist enterprise lies the valid and important insight that, from one centrally important point of view, freedom is nothing more than a matter of being able to do what one wants or chooses or decides or thinks right or best to do, given one’s character, desires, values, beliefs (moral or otherwise), circumstances, and so on. Generally speaking, we have this freedom. Determinism does not affect it at all, and it has nothing whatever to do with any supposed sort of ultimate self-determination, or any particular power to determine what one’s character, desires, and so on will be.”
– Strawson (2010, p. 94) [Freedom and Belief, Revised Edition.]

What physics thinks about now


Image generated using Stable Diffusion 2.1

Einstein was worried that physics didn’t have any way to identify in spacetime where Now is: that special feeling we take for granted now… and now… and again now. When solid-state physicist David Mermin told colleagues he was going to write about Now, they assumed he was either going to show that it’s an illusion or write about “chauvinism of the present moment” (Mermin 2014, p. 422).

Nows are personal things. I experience my fingers dancing around a keyboard now in way that, by the time you have found this text, you can’t. Mermin’s more general insight is that theories are used by people with particular experiences and beliefs and in a particular context. The user of a theory is implicitly an ingredient in its predictions and could well reach different conclusions if they were in a different context. This is simultaneously deep and obvious. If I’m calculating the probability that the outcome of a throw of two fair dice will be double-six, my sums will be different to those of someone who knows that one of the dice is actually loaded.

Even though it’s possible to draw out a 4D spacetime diagram of a sequence of Nows – potentially all the Nows of someone’s life – and no Now seems special therein, the user of the diagram knows (at least approximately) where Now is for them and is likely interested in some Nows more than others. The ability to theorise spacetime in such a way that no Now is special does not imply that no Now is special for users of the theory.

One interesting puzzle is, if I’m having a cup of tea with you, is my Now in the same location of spacetime as yours, or can I be, to all intents and purposes, conversing with a zombie whose experience of Now is spatially and temporally elsewhere, maybe an hour later down the road, doing the shopping.

Mermin (2014, p. 423) tackles a relevant puzzle. Consider two twins, Alice and Bob, who begin with their experiences of Now in sync. What happens to their Nows when one zooms off near lightspeed and returns a few years later? Mermin argues that all that is needed is the principle from relativity that someone’s personal time keeps pace with their reading of a watch, wherever they are in spacetime. Here is the principle applied to Alice and Bob:

“When they are together at home, their Nows coincide. Then Alice flies off to a nearby star at 80% of the speed of light, turns around and flies back home to Bob at the same speed. Relativity requires that if Bob’s watch has advanced ten years in the meantime, Alice’s has advanced only six. But because each of their present moments has advanced in step with the watch each is carrying, the moment of their reunion continues to be Now for them both.”

So, Mermin concludes, physics – and in particular relativity – does actually have something to say about Now. And reassuringly, if a loved one dashes off near lightspeed, when they return their Now returns to sync with yours too (assuming you were synced at the outset).

There is rather a fragile premise supporting Mermin’s argument, though: “That there is a place for the present moment in physics becomes obvious when I take my experience of it as the reality it clearly is to me” (Mermin, 2014, p. 422). Any compelling challenge to this and the whole lot falls asunder.


Mermin, N. D. (2014). Physics: QBism puts the scientist back into science. Nature, 507(7493), 421–423.

The object-subject relation in science

“One can only help oneself through something like the following emergency decree: Quantum mechanics forbids statements about what really exists—statements about the object. Its statements deal only with the object-subject relation. Although this holds, after all, for any description of nature, it evidently holds in a much more radical and far reaching sense in quantum mechanics.”

– Erwin Schrödinger (1931) letter to Arnold Sommerfeld, spotted in
Fuchs, C. A., Mermin, N. D., & Schack, R. (2014). An introduction to QBism with an application to the locality of quantum mechanics. American Journal of Physics, 82(8), 749–754.


The Basic Argument

“There is an argument, which I will call the Basic Argument, which appears to prove that we cannot be truly or ultimately morally responsible for our actions. According to the Basic Argument, it makes no difference whether determinism is true or false. We cannot be truly or ultimately morally responsible for our actions in either case.

“The Basic Argument has various expressions in the literature of free will, and its central idea can be quickly conveyed. (1) Nothing can be causa sui – nothing can be the cause of itself. (2) In order to be truly morally responsible for one’s actions one would have to be causa sui, at least in certain crucial mental respects. (3) Therefore nothing can be truly morally responsible.”

– Strawson, G. (1994, p. 5) [The impossibility of moral responsibility. Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition75, 5-24.]

Example social construction of knowledge in physics: the speed of light

The graph below shows historical estimates of the speed of light, c, alongside uncertainty intervals (Klein & Roodman, 2005, Figure 1). The horizontal line shows the currently agreed value, now measured with high precision.

Note the area I’ve pointed to with the pink arrow, between 1930 and 1940. These estimates are around 17km/sec too slow relative to what we know now, but with relatively high precision (narrow uncertainty intervals). Some older estimates were closer! What went wrong? Klein and Roodman (2005, p.143) cite a post-mortem offering a potential explanation:

“the investigator searches for the source or sources of […] errors, and continues to search until he [sic] gets a result close to the accepted value.

“Then he [sic] stops!”

Fantastic case study illustrating the social construction of scientific knowledge, even in the “hard” sciences.


Klein, J. R., & Roodman, A. (2005). Blind analysis in nuclear and particle physics. Annual Review of Nuclear and Particle Science, 55, 141–163. doi: 10.1146/annurev.nucl.55.090704.151521 [preprint available]

Dedekind on natural numbers

The “standard model” of arithmetic is the idea you probably have when you think about natural numbers (0, 1, 2, 3, …) and what you can do with them. So, for instance, you can keep counting as far you like and will never run out of numbers. You won’t get a struck in a loop anywhere when counting: the numbers don’t suddenly go 89,90, 91, 80, 81, 82, … Also 2 + 2 = 4, x + y = y + x, etc.

One of the things mathematicians do is take structures like this standard model of arithmetic and devise lists of properties describing how it works and constraining what it could be. You could think of this as playing mathematical charades. Suppose I’m thinking of the natural numbers. How do I go about telling you what I’m thinking without just saying, “natural numbers” or counting 0, 1, 2, 3, … at you? What’s the most precise, unambiguous, and concise way I could do this, using principles that are more basic or general?

Of the people who gave this a go for the natural numbers, the most famous are Richard Dedekind (1888, What are numbers and what should they be?) and Giuseppe Peano (1889, The principles of arithmetic, presented by a new method). The result is called Peano Arithmetic or Dedekind-Peano Arithmetic. What I find interesting about this is where the ideas came from. Dedekind helpfully explained his thinking in an 1890 letter to Hans Keferstein. A chunk of it is quoted verbatim by Hao Wang, (1957, p. 150). Here’s part:

“How did my essay come to be written? Certainly not in one day, but rather it is the result of a synthesis which has been constructed after protracted labour. The synthesis is preceded by and based upon an analysis of the sequence of natural numbers, just as it presents itself, in practice so to speak, to the mind. Which are the mutually independent fundamental properties of this sequence [of natural numbers], i.e. those properties which are not deducible from one another and from which all others follow? How should we divest these properties of their specifically arithmetical character so that they are subsumed under more general concepts and such activities of the understanding, which are necessary for all thinking, but at the same time sufficient, to secure reliability and completeness of the proofs, and to permit the construction of consistent concepts and definitions?”

Dedekind spelt out his list of properties of what he called a “system” of N. Key properties are as follows (this is my paraphrase except where there is quoted text; also I’m pretending Dedekind started the numbers at zero when he actually started at one):

  1. N consists of “individuals or elements” called numbers.
  2. Each element of N is related to others by a relation (now called the successor), intuitively, “the number which succeeds or is next after” a number. But remember that we don’t have “next after” in this game. The successor of an element of N is another element of N. This captures part of the idea of counting along the numbers.
  3. If two numbers are distinct, then their successors are also distinct. So you can’t have say, the successor of 2 as 3 and also the successor as 4 as 3.
  4. Not all elements of N are a successor of any element.
  5. In particular, zero isn’t a successor of any element.

Dedekind notes that there are many systems that satisfy these properties and have N as a subset but also have arbitrary “alien intruders” which aren’t the natural numbers:

“What must we now add to the facts above in order to cleanse our system […] from such alien intruders […] which disturb every vestige of order, and to restrict ourselves to the system N? […] If one assumes knowledge of the sequence N of natural numbers to begin with and accordingly permits himself an arithmetic terminology, then he has of course an easy time of it. […]”

But we aren’t allowed to use arithmetic to define arithmetic. Dedekind explains again the intuitive idea of a number being in N if and only if you can get to it by starting at 0 and working along successors until you reach that number. This he formalises as follows:

  1. An element n belongs to N if and only if n is an element of every system K such that (i) the element zero belongs to K and (ii) the successor of any element of K also belongs to K.

So, we get the number 0 by 6(i), the number 1 by 6(ii) since it’s the successor of 0, the number 2 by applying successor to 1, and so on until an infinite set of natural numbers is formed. This approach is what we now call mathematical induction.

There are a few issues with Dedekind-Peano Arithmetic, though – for another time…