Reasons

Reasons: what is the fundamental unit of reason?

Position: Reasons fundamentalism

Action

That is the first concept I’ve identified as departing from a factual or descriptive account of reality. In its daily usage, the term denotes some intentional manifestation of an agent’s will. Colloquially, most speakers would agree that Peter’s jump is an action, whilst the rock falling is just an event.

One could easily add that an action, unlike purely physical events, also involves a mental ground. Ludwig Wittgenstein, always crafting useful images, explained action as "what is left over if I subtract the fact that my arm goes up from the fact that I raise my arm". Action can then be seen as a sort of transmission belt between a mental state and a physical event. The convention I will adopt here is to see action as a mental state in its own right.

The sequence would then look something like this: \[\text{[Desire to drink]$_{\mathbf{2}} \rightarrow$ [Action: to grab a glass of water]$_{\mathbf{2}} \rightarrow$ [Arm moving]$_{\mathbf{1}}$}\]

This concept of action makes sense in two main ways. First, it helps capture a sense in which action may exist even when the corresponding physical fact does not. Wishing to do something does not always entail that one takes the corresponding action. But also, at least in my own way of using this terminology, taking action doesn’t entail that its physical manifestation be realized. Peter may take action to jump, but then realize that having been sitting so long, his legs are numb, so nothing happens. Yet there definitely was a mental discrepancy between the simple desire to jump and the clear intention to instil bodily movement.

The second point is that action is not correlated with activity in the active/passive sense. Let’s say that Peter now encounters a bear on his hike. He needs to balance a strong impulse to run with the thought it is safer to stand still. By doing the latter, Peter is definitely taking an action by deciding to not move. It is difficult to define physical events in relative terms versus a baseline - either everything is an event or nothing is. It is then easier to define action as a mental state, rather than some physical/mental pairing.

Teleology

That term denotes the type of explanation that refers to purposes, ends or aims rather than causes. As already mentioned above, the natural sciences, like the style of fact-based metaphysics we’ve developed, have largely eschewed teleology. Although ends and aims are still haunting scientific discourse ("snakes have evolved to produce venom in order to paralyze their prey"), the reducibility of all natural sciences to physics should entail that any rigorous exposé be entirely causal.

However, one key instance of teleology that has not been waived so successfully is that of subjective minds, in particular human minds. I, like all human beings, seem to have aims in the forms of mental states: my wish to drink some coffee, my intention to go to the gym tomorrow, my fear of roller coasters. Since action has been identified as another mental state, we can also recognize that an action, usually the prelude to some physical event, is geared towards that event as its end. Agency thus seems inseparable from teleology.

The term of the art for the group of mental states that exhibit aims is that of pro-attitude (one could say that fear is an anti-attitude, or rather a tendency to be pro-not doing what one fears). None of this is too surprising, since we’ve introduced intentional mental states earlier in this book. Remember that those have an object they point to, a content, and a mode (belief, wish, fear, etc.).

Content, we’ve gone on and on about in our semantics travels. Now it seems we are to focus a bit more on the modes, which we had quickly breezed over. It seems clear that the form of directedness that’s characteristic of intentionality must be linked with the teleology of subjective mentality. Yet, all intentional states are not teleological. My seeing a chair is a perceptual state that’s directed at an object, but there is no aim involved. All in all, it appears that aims are the wont of a subset of intentional mental states, and that action is one of those mental states that can exhibit aims.

Since we’ll be manipulating mental states quite a bit, let’s equip ourselves with some symbols:

$\textsf{Bel}[x\phi]$: $x$ believes that $\phi$.
$\textsf{Des}[x\phi]$: $x$ wishes that $\phi$.
$\textsf{Act}[x\phi]$: $x$ brings about $\phi$ (by acting).

$x$ is an agent — formally, an ordinary object that we associate with mental subjectivity; for instance a human being. To say that "$x$ believes that $\phi$" is equivalent to an existence statement about the mental state "$x$’s belief that $\phi$".

Rationality

It is not obvious how rationality can be connected to this conceptual cluster. To elaborate, we will first need to agree on what that is... starting perhaps with what it’s not!

The first breeding ground of confusion seems to be the interface between rationality and logic. It is certainly encouraged by colloquial overlaps; to say that "X is acting rationally" or that "X is acting logically" is not very different in commonplace usage. However these two notions operate over different domains. Logic is about rules of inference between different propositions, and is prior to any metaphysical assumption. Rationality is broadly about the coherence between various mental states that make up a subjective mind. For instance, the "law of non-contradiction" (that some proposition and its negation cannot both be true) is a purely logical statement: \[\forall \phi (\neg( \phi \wedge \neg \phi))\] The rational equivalent would then be that a belief in $\phi$ cannot rationally be combined with a belief in not-$\phi$: \[\forall \phi \forall x (( \textsf{Bel}[x\phi] \wedge \textsf{Bel}[x\neg\phi]) \text{ is not rational})\]

It might be true, although at this stage it is still a pure guess, that all logical principles have an equivalent in terms of rationality. But not all rational principles have logical roots. Imagine that Peter doesn’t want to eat coconut, and that Peter believes (correctly) that ordering a coconut-based dish will imply his being served coconut. If Peter does order the coconut, we would conclude (absent more information) that the action was not rational. There’s nothing illogical here; what doesn’t cohere is the group of mental states involved. We could intuit the general principle that if $x$ doesn’t want $\phi$ but believes that $\alpha$ will surely lead to $\phi$, then to be rational, $x$ shouldn’t bring about $\alpha$: \[(\textsf{Des}[x \neg\phi] \wedge \textsf{Bel}[x(\alpha \rightarrow\phi)]] \wedge \textsf{Act}[x \alpha]) \text{ is not rational}\] The discrepancy between rationality and logic was only the first pitfall I had to mention. The next one is borne out of the contrast between rationalism and empiricism. These opposing numbers, which any student in Philosophy 101 is familiar with, unfortunately give the wrong idea about rationality. Rationalism is an epistemological thesis that regards a priori reasoning as the key source of knowledge, while empiricism teaches that sensory experience is. But the concept of rationality we’re dealing with in this section is much broader and absolutely compatible with both theses, regardless of apriority. To say that "Peter seeing a dog" entails that "Peter believes a dog to be nearby" is a rather obvious empirical principle, but that is also an example of rationally coherent mental states.

So, it appears that rationality is some general quality that is fulfilled by mental states considered together, or by a sequence thereof. Indeed, if intentional mental states like the ones from folk psychology do exist (beliefs, desires, feelings...), then they clearly operate within intentional systems. What we are not talking about here is the descriptive approach, that would seek to depict and explain causally why some mental state leads to another in a given mind. If such explanation is even possible, then it’s part of psychology, and at its most fundamental level of $\mathfrak{ToPM}$, the "scientific theory" of the natural (i.e. physico-mental) world.

Our talk of rationality here is instead normative. We are saying that some assemblages of mental states are good, worthwhile, obligatory in a way that we call "rational", and that others are bad, undesirable, forbidden in a way we call "irrational". Much more will be said about norms and normativity in the next subsection.

For now, we want to keep the spotlight on rationality, and more particularly to get to the bottom of that concept by isolating its base unit.

Reasons

Distancing myself from many philosophical writings that erect Reason as a singular primitive ideal, I would argue this investigation is better served by dealing with the fundamental unit, the "atom of Reason". In most contemporary accounts, that is identified as... a reason.

First let’s rebrand "Reason" as a relation between:

a fact $\text{f}$: the reason
an ordinary object $x$: the agent
a mental state $\psi$: the response
a mathematical object $\delta$: the degree

Then, the following proposition: \[\mathcal{R}[\text{f}x\psi \delta]\] reads as "$\text{f}$ is a reason for $x$ to $\psi$ with degree $\delta$".

What makes an ordinary object $x$ an agent goes well beyond this book’s scope. Suffice it to say that we know human beings to be agents; which animals or other beings are is obviously less clear-cut, not to mention the infinite realms of actual or possible agents, unfathomable to us.

The degree is also an essential notion to formalize reasoning. I have reasons to go outside in the sun, but I also have reasons to stay in the office and write. It’s clear that any human action will ultimately result from a comparison between the magnitude of a huge array of reasons. The natural incline is to consider $\delta$ as a real number: I may be 30% attracted by the sun outside but 70% deterred by my work deadline. Yet I won’t make any imposition, since we could obviously be way more creative, introducing multi-dimensional frameworks, etc. Degrees will still need to share some essential features of real numbers though, like having an order (if we can’t say if a reason is stronger than another, that seems to defeat the purpose) or some addition operation (similarly, we want to be able to tell if reasons 1 and 2 can together "out-rank" reason 3).

This lets us define the key concept of justification: $x$ is justified to $\psi$ when $x$ has more reasons to $\psi$ than to not $\psi$. We could write, very roughly, that: \[\mathcal{J}x\psi \hat{\equiv} \int_{\mathcal{D}_\text{f}} \left( \imath \delta (\mathcal{R}[\text{f}x\psi \delta]) - \imath \delta'(\mathcal{R}[\text{f}x(\neg \psi) \delta']) \right) d\mu(\text{f}) > 0\] This is a mere sketch obviously. Developing a full topology of reasons could fill a whole book. In plain English, we’ve just expressed that, going over the whole universe of facts and counting reasons to $\psi$ positively (pro rata to their degree), and reasons not to $\psi$ negatively), a positive result means that $\psi$ is justified.

A bit more technically, I may add that this sum is meant to be a Lebesgue-style integral over the domain of facts $\mathcal{D}_\text{f}$, equipped with some measure $\mu$. The expression $\imath \delta (\mathcal{R}[\text{f}x\psi \delta])$ uses the definite description operator: it is the degree of $\text{f}$ if $\text{f}$ is a reason, with the convention that if $\text{f}$ is not a reason, the outcome is $0$ ("the zero" of whatever mathematical set was picked).

Of course this amiable setup hides devilish difficulties. The reason relation is not monotonous, meaning that if $\text{f}$ is a reason, $\text{f}$ and $\text{g}$ together are not necessarily a reason. That doesn’t prevent double-counting and other infinity-prone features. The hope is that some adequate topology can be developed (or has been?) that could flesh out such a formalization.

Coming back to the reason relation, although it may not seem like it at first sight, to say that reasons are facts is quite momentous. As a reminder from previous sections, a fact is an obtaining state of affairs, so it exists if and only if the corresponding state of affairs obtains, which itself is equivalent to the corresponding proposition being true. So for instance, "John F. Kennedy died in 1997" is a perfectly valid proposition, that turns out to be false in the actual world. So there is no such fact "that JFK died in 1997". Something that doesn’t exist cannot be an argument of a relation, therefore (colloquially) "only things that are true" can be reasons.

That fits quite nicely with our linguistic intuitions. It would seem a bit strange to say "the reason for Ana to take an umbrella was that it was raining, but it wasn’t raining". We are then faced with a dilemma. We may simply say there was no reason for Ana to take the umbrella. Or we could say that the reason was her belief that it was raining. With a bit more sophistication, one could suggest the reason is, say, that she heard on the weather forecast that it was raining — but that is every bit as agent-relative as the previous suggestion, since there is no way to progress from hearing the forecast to taking the action without involving a belief about the weather. Why should that quite natural interpretation make us uncomfortable?

Say that Ed believes he’s a bird, and jumps from a tall building, to his demise. It seems equally just to say that:

Ed believed that he’s a bird, that birds can fly, and that jumping from a tall building is safe for flying creatures. From his perspective, his was then a rational decision.
Ed’s action was grounded on his belief that he was a bird. He wasn’t a bird, therefore he didn’t have a good reason to jump.

We can see that a good old analysis is warranted here, as our language is misleading us. Despite the superficial similarity, two distinct conceptions emerge:

the former example, which John Broome would call structural rationality, is a judgment over the coherence of an agent’s intentional mental states. It is a narrow, internalist concept, which doesn’t depend upon the external world beyond Ed’s subjective mind.
the latter, which Broome calls substantial rationality is wide and externalist: something can be a reason or not based on facts whose existence the agent has no accurate knowledge of.

Can we still salvage some unity and link the two concepts? I believe we can. Let’s rephrase the structural, "narrow" assessment of rationality as: "It is the case that if Ed was a bird, he would be justified to jump. Ed believed that, and in addition, believed that he was a bird. Lastly, Ed did jump. So the action was rational". It is then possible to build up rationality based on that model: \[\mathcal{Rational}[x\psi] \hat{\equiv} \begin{cases} \phi \rightarrow \mathcal{J}x\psi \\ \mathsf{Bel}[x(\phi \rightarrow \mathcal{J}x\psi)]\\ \mathsf{Bel}[x\phi] \\ \psi \end{cases}\]

In this subsection, I aimed to demonstrate the singularity of rational judgements vs the factual-descriptive mode we had become accustomed to, introduce a form of rational atomism with reasons, and provide a convincing sketch for a mathematical formalization. With that done, let’s plunge into a topic that was just grazed here: normativity.