Counterfactual causality, what is the point?

Abstract: A theory of causality, a root concept, must strive to converge its ontological and teleological directions. The counterfactuals used by Paul Noordhof unfortunately failed in this attempt. They form a good description of cognition, highlighting its biases. Going further requires looking at the complex dimension.

Part 1: Two-way causal representation

Causality is one of the root concepts of our conceptual edifice. All our mental activity is based on it. Unconsciously: if such a mosaic of colored dots appears in my field of vision, I know that my companion is in front of me. And consciously: at some discreet variations of her expression I guess if she is happy or dissatisfied, and can trace the chain of causality that led to this mood.

However, the reliability of this causal chain is variable. The arrival of a photon on my retina modifies a rhodopsin molecule and triggers a nerve impulse: scientifically sound causality. The identification of my partner: rather solid too, but I could have to deal with a disguise specialist, or suffer from a neural alteration that would make me confuse her with another person. As for guessing the mood and its origin, my causal projection can completely miss its target.

First direction: causal judgment

“Causality” is therefore in fact “causalities”, relations of different force. They are the property of our downward look, our judgment on things, which allows us to weave the scene of the world and predict it. These causalities are never ontological causality, the relationship between things in essence. Because it is impossible to replace them. We only do this through representations. Already it is difficult to understand our own acts, composed in part at inaccessible levels. We do not have the full consciousness of it and we compensate for it, as for the rest, by representations of our intimate functioning.

Second direction: pseudo-ontological causality

The essence of a photon is inaccessible. It is characterized by a model: grain of light endowed with a certain energy, devoid of duration. The model makes it possible to construct a pseudo-ontological causality. Let’s keep in mind that we didn’t have access to the essence of the photon. But it seems quite satisfied with its model, enough to behave as we hope. The pseudo-ontological causalities designed by science are the most reliable, once the models are confirmed. Up to the rhodopsin molecule and the triggering of nerve impulses, we are in a “tight” causal chain.

The chain relaxes when the data is interpreted by neural networks. Many options are possible. Our mind avoids chaos by favoring certain options, which are sought in the data. They are actually approximations of reality, because different datasets trigger the same interpretation. The causal chain has loosened. Neurons manage uncertainty with false certainties.

Return to conscious judgment

This causality is no longer ontological but teleological. We went back to the first direction, to the judgment. Reversal that comes from the crossing of levels of reality: the organization of one level is correlated with that of the previous one but not strictly caused by it. They are separated by an approximation. The causal chain is broken by the existence of an independent causality, at the higher level, which is sought in the lower level. This is the teleological effort: a fragment of intention.

Of course the independence of higher/emerging causality is relative. It was formed on the most common stabilities of the lower level. It is a preference rather than a true independence, which is maintained within certain limits. We define ourselves as a collection of desires. Nevertheless, they are enough to dissociate us from the strict causality in which the photon is enclosed. It is impossible to predict our behavior from the sets of photons that hit our retinas, even though they are our main source of information about the world.

Ontological causality for the real and teleological for the mind

Our mind manufactures (pseudo)ontological causalities for uncomplicated things, especially inert matter. Their behavior is very stereotypical and it is quite easy to be guided. By dint of obstinacy, matter even manages to impose strange causalities on us, which amaze us at first, such as quantum mechanics. It is therefore very involved in our ontological mental constructions. I call this part of the mind, attached to matter, the Real pole (the non-self). Its representations form the upward look, or how reality is organized from matter to produce the complexity of the world and in particular of the living.

Our desires, and the self-image they form, are the part I call the Spirit pole (the self). The causalities fabricated there reflect our intentions, the need to control the world to satisfy our desires. It is the downward, teleological, intentional look that manufactures causal certainties where they are often fragile. Their value deviates from those of ontological/ascendant causalities, which bring us together, while the descendants divide us. Nevertheless, it is through descending causality that we modify the imperturbable march of the world, that we change it so that it corresponds to us.

Now that we have clearly separated these two causal directions (ascending-descending), and shown their independence, let’s see what the philosophers say about them. The most consensual vision is currently the counterfactual theory of causality. Paul Noordhof defended it exhaustively in ‘A Variety of Causes‘ in 2020. I refer to this book for comment.

Part 2: What is a counterfactual?

David Hume, father of modern discussions of causality, wrote in 1748: « We may define a cause to be an object, followed by another, and where all the objects similar to the first are followed by objects similar to the second. Or in other words where, if the first object had not been, the second had never existed. » Noordhof points out in the footsteps of David Lewis that the two sentences actually contain two very different ideas: the first translates a regularity of the structure of the world, a simple causal sequence. The second implies a dependence of the effect on the cause. The effect cannot exist without the cause. So there is an advance of the sequence and Hume surreptitiously injects it with a temporal property. It is even a direction of time, a temporal arrow, because the effect follows the cause and cannot precede it.

The dependence of the effect on the cause is a subjective conditional: “If A had not been, then B would not have been“. The italic part of the conditional is its ‘antecedent’, the underlined part its ‘consequence’. The antecedent can be positive or negative, as the consequence. That is, the entire conditional is: “If A had (or had not) been, then B would have (or would not have been) “. This subjective conditional is called in philosophy ‘counterfactual‘, a contraction of ‘contrary-to-fact conditional’. It’s hardly intuitive. Noordhof explains that the antecedent is presumed to be ‘contrary to the fact’ (in the sense of ‘not expected’) and the consequence is what holds. Sometimes the presumption is false—the antecedent is not contrary to the fact. The counterfactual is then rather ‘subjective conditional with true antecedent’. But for Noordhof it doesn’t make a difference.

The counterintuitive side of the term ‘contrary factual’ responds – which Noordhof confirms – to the need to differentiate a cause from a simple fact attached to another in a sequence. The two facts look at each other and agree or contradict. The counterfactual contains causality and the refusal of causality, it is in this sense that we must understand ‘counter’.

The counterfactual is a causal opinion

This decryption is a little tedious and I am sorry about it, dear reader. But it is essential to follow up on the first part of the article. You now understand unambiguously that counterfactual theory is a downward theory, essentially teleological. It decides causality instead of objects. The counterfactual is a tool of the Spirit pole to analyze the world. An epistemological tool among others, preferred by the philosopher. The Real pole, on the other hand, will rather choose upward theories, those that leave objects the knowledge of the relationship they have together. They themselves define their causality. Tool preferred by scientists. Thus the counterfactual alone cannot be a complete theory of causality. It is with this restriction that one must read Paul Noordhof’s book.

Noordhof himself confirmed this choice. He indicates that the mere attachment of one fact to another in a sequence is not sufficient to fully render the concept of causality. Causality, for us, is the imperative “if this had not happened, it would not have happened”. The counterfactual immediately reflects this imperative side. But we have seen that it is our intentional Spirit pole that needs it. The Real pole doesn’t care. The structure of reality is, without the need for our presence; and if it takes place, it does so without qualms. The ‘pros’ and ‘cons’ have no meaning to it.

The counterfactual awakens a controversy

This is why counterfactual theory is not adopted by all philosophers. Some see it as a semantic construct, which is right. Language is the formalism borrowed by the downward look to represent the world. Noordhof protests that it doesn’t matter if counterfactuals are semantic, they are true because the essence of things contains causality that brings them truth. That’s right as well. But there is a translation, a semantic filter.

The two philosophical positions are not contradictory. They reflect the two directions of look, upward and downward, which must converge for a relationship of truth to the world. The double look extinguishes the controversy, but also extinguishes Noordhof’s claim to make the counterfactual a complete theory of causality. Scientists in particular will not find their way around. Favoring the upward look, they mock the judgments of the Spirit pole. Things are elements connected by equations, which do not care about our opinions. It is by getting rid of our opinions that we get closer to them. An opinion serves to make them go where they would not want to… provided that they have been understood, in their proprietary causality.

Part 3: Counterfactual Theory under test

Here is the summary of the counterfactual theory (Noordhof, p.144):

For any actual, distinct events e₁ and e₂, e₁ causes e₂ (if and) only if there is a (possibly empty) set of possible events Σ such that
(I) e₂ is probabilistically Σ-dependent on e₁, and,
(II)’ for any superset of Σ, Σ*, (where Σ is included in Σ*), if e₂ probabilistically Σ*-depends upon e₁, then every event upon which e₂ probabilistically Σ*-depends is an actual event,
(III) e₂ occurs at one of the times t for which the mean value for p(e₂ at t) is x and x >>y —y is p(e₂ not at t).

In words: A cause, e₁, is something which (independently of its competitors) both makes the chance of an effect, e₂, very much greater than its mean background chance in the circumstances (that is, the chance without any of the competitors) (clause (I)) and actually influences the probability of the effect in this way at the time at which the effect occurred (clauses (III)) via a complete causal chain (clause (II) and the way in which probabilities are assessed).

This probabilistic presentation is far removed from the causal certainties we experience. Should we be ironic about the fact that the theory supposed to reflect our intuition completely loses it (at least that of the layman)? Not. Let us remember that intuition is precisely what is proposed to our consciousness without it understanding its workings. It is normal that its decryption seems complicated. That is not the problem. It is within the limits of theory. It brilliantly explores how our neural networks construct causality, but is not an ontological theory. At least it is ontological only from the levels of mental representation, not those of physical reality. It is a lemma of causality conceived by our mind, a theory of cognition and not of physical reality.

Noordhof’s approach could not do better. The downward look starts from multiple individual minds and Noordhof struggles with the need to group them into a fundamental theory of reality. It fails, on the one hand by maintaining categories of causality —that of individual entities and that of properties— and on the other hand, categories of elements involved —objects, events, facts, properties—. He refers to them as ‘ontological categories’, which is a serious confusion. All we can know about the ontology of these elements is information. Nothing else. The categories are teleological.

In summary in Noordhof’s theory, the experienced cause looks for how it occurred. ‘How the initial state becomes the result/cause’ is not processed.

Part 4: Going further

Counterfactual theory sees a fusion of causalities. This is the characteristic of the downward look. It does not independently see the levels of reality, from elementary particles to macroscopic objects. It sees the result of their superposition, analyzed by the mind using the tools capable of interacting with this result: language for social relations, sensory sensors for objects, measuring instruments for biological and molecular levels, etc. Because interactions occur between complex entities. There are a multitude of levels where causality is exercised in relative independence from neighboring levels.

I kayak

Let’s take an example: ‘I’m rowing, my kayak is moving forward’. In this simple, fusional causality, there is a host of correlations. Let’s go down this scale of complexity. ‘Why am I rowing?’ Reason branches out into goals of physical maintenance, self-image, planning and simple physical pleasure. Saying “I like to row” merges a great depth of neural codifications, each responding to its own causality. My reason established, muscle realization involves additional neural coordination. My gesture is more or less efficient. If it is too disturbed the kayak does not advance anymore. Let’s go down to the physical correlations. The paddle is a solid material facing a liquid medium. In a certain temperature range, it penetrates and the water opposes a partial resistance. The kayak advances in reaction. The solid states of the paddle and the liquid state of the water are themselves related to specific molecular interactions. Etc.

A reductionist claims that all these causes are reducible to the laws governing elementary particles. We could ask him how these laws are ultimately more fundamental than those that overhang them. It’s useless, because reductionism, in the example of my kayak, capsizes! We do not know how to predict the properties of water from the laws of particles. We observe its varied states, we can correlate them with the movements of the particles, but we can not take their quality out of the equations. However, it is the qualitative state of liquid that then makes it possible to design its dynamic model. Rupture between two causalities, even if they are closely intertwined.

Fortunately the world is very regular

In the end, to say that the advance of the kayak is caused by my reason for rowing is a huge approximation of the downward gaze, which agglomerates a host of intermediate causes, all likely to distort counterfactual causality. This is rare on a daily basis and it is the regularity of the world that keeps our approximations consistent. Replacing causal regularity with counterfactuality, as Noordhof would like to do, requires means that the descending gaze does not possess. To be certain that “If A had not been, then B would not have been”, it is necessary to place oneself in the lowest foundation from which the ascending gaze begins, and to observe finely the organization of the causes from this elementary level, through a multitude of models.

Even by doing so, our causality will go through breaks in reality, at the quantum, chemical, biological levels. Arriving at the mind, it became fusional, “certain” only by concealing its approximations. It is more accurate and honest to say that the mind observes causal regularities than counterfactuals.


Counterfactuals are not applicable to the complexity of the world, our downward gaze being only a small individual lens. I have only once found the word ‘complexity’ in Noordhof’s book, in the introduction, to point out that “natural phenomena differ radically in type and complexity”. In this case, how can we conceive of a theory of causality that obliterates this dimension?

The examples chosen by Noordhof do not take this into account, so he mixes causalities completely alien to each other. Using fusional causality indiscriminately is even dangerous in some areas. It is with counterfactuals that some psychiatrists have been able to say: “If gene A had not been, psychopathy B would not have been”, and advocate for the eradication of gene A by eugenics. An aberration that ignores the multitude of physiological and psychological levels intermediate between gene and behavior.

In other words, Noordhof’s theory, which is cognitive, has the advantage of highlighting our cognitive biases. His mistakes are those that make us take erroneous paths, inflated with intuitive certainties that we take for realistic.

Where to use counterfactuals?

More modestly, can counterfactuals be used to examine one level of reality independently of others? Certainly. Causality is a mode that is jointly determined by related elements, in relative independence of their constitution. In terms of structuralism, their information is integrated. The counterfactual applies perfectly to such a set: “If the state A of the integrated elements had not been, then the state B of the integrated elements would not have been”.

It is of course possible to hope for a metaphysics of complexity, which makes it possible to unify these levels of causality. Could the counterfactual then become universal? No, because this metaphysics has already begun to recast the notion of time in a way very different from the postulates used by counterfactual theory. The directional arrow does not exist at the fundamental levels of reality. It appears as one rises in the levels of complexity, with thermodynamic entropy, then biological and mental. This direction is not a fundamental property of reality in itself, only of the organization it has chosen for itself.

At the very top of the complexity, we are equipped with a marked time arrow. The causes are jostling, all sips of imperative necessity. A different view, which must coincide with that of our tiny subatomic workers on themselves.


A Variety of Causes, Paul Noordhof, 2020

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