Christopher Blake-Turner's "Reasons, basing, and the normative collapse of logical pluralism"

 

Introduction

I've recently switched my focus back towards the philosophy of logic from the philosophy of maths as I have a paper on logical pluralism that I'd like to re-work and submit somewhere over the summer. My paper, in part, draws on Christopher Blake-Turner's co-author work with Gillian Russell (who I believe was the supervisor of his recently completed doctoral thesis). Given that (1) I like his previous work, (2) that I have a preference for reviewing the work of early-career philosophers and (3) that I prefer to review recent work when I saw that Blake-Turner has a forthcoming paper in Philosophical Studies, it seemed like a natural target for a review.

The paper is very interesting and of generally high quality. My biggest "macro" criticism is that it feels like two papers, not one. The material about the basing of reasons stands largely independently from the material about the collapse problem, neither really affects the other, though both contribute towards his wider claim that those interested in the relation between normativity and logic ought to acquire a more nuanced conception of the kinds of normative relations available.

Interestingly, I also disagree with a great many of the details in the paper. What I liked was the broad strategy of the paper and, where I disagreed with details, there was usually a work-around to be found (but not always). I like the creativity of the paper, even if I disagree with some of the execution.

The paper responds to a well-known objection to logical pluralism that states that logics have to do genuine normative work and that there can only be one logic that does this (i.e. the logic that captures all and only the deductive inferences that an agent should or must make). In this paper, Blake-Turner offers a way of rejecting this by offering a more nuanced conception of "genuine normative work".

His idea is that the argument only goes through if one holds that the normative work a logic must do must be absolute, in the sense that it relates to what one ought or must do. For instance, for a logic L to do genuine normative work perhaps it has to be the case that if X follows from Y in L, then if agents believe X, then they must believe Y (or must believe Y, if their attention is drawn to it). But this is an unnecessarily strong normative condition. Blake-Turner argues that by weakening this condition, the argument fails to go through.

The collapse argument:

Blake-Turner formulates the collapse argument like this:

• P1: Logics must do genuine normative work
• P2: Exactly one logic does genuine normative work
• C: There is exactly one logic

Personally, I prefer to think of the argument as follows:

• P1: Logics must do genuine normative work in order to be correct.
• P2: Exactly one logic does genuine normative work.
• C: There is at most one correct logic (i.e. logical pluralism is false)

Two comments on this:

First, a lot of people in the literature use the term "logic" as a success term. i.e. there are logics (which are, by definition, correct) and there are logic-like mathematical structures that are not logics. It's odd that this is how the terms are often used in the literature as this is not how we speak in practice. Priest's famous book is called "Introduction to non-classical logics" not "introduction to non-classical logic-like mathematical structures, some of which are potentially logics"! I prefer to use the term, not as a success term, but in line with a term like "theories". There are successful and unsuccessful theories, but both are theories. There are successful and unsuccessful logics, but both are logics. This is largely terminological. In most of his paper, Blake-Turner follows my usage.

Second, I've weakened the conclusion to really focus on the anti-pluralist nature of this argument. As it stands, a logical nihilist (someone who thinks there are no correct logics) would have to reject P2 of Blake-Turner's formulation. If "logic" is being used as a success term, then there are no logics at all, even if there are some logic-like mathematical structures that do genuine normative work (these structures might fail to be logics for other reasons). Nevertheless, the nihilist can help themselves to a weaker version of the collapse argument in line with my own formulation. I see the collapse objection only as a limit on the number of (correct) logics there can be, not as a direct argument for monism.

On either formulation, Blake-Turner's response is the same. He rejects P2.

By Blake-Turner's analysis, the case for P2 has three parts. One premise (call this the normative premise) states what it is for some logic to do genuine normative work. A second bridges some logical facts (typically about entailment) to some normative facts (call this the bridge premise) and the third argues that only one logic fulfils this. For instance:

All-or-nothing (normative premise): A logic does genuine normative work iff it makes a difference to what an agent is entitled or obligated to do.

Oughts from Validity (bridge premise): A logic L makes a difference to what an agent is obligated to do iff, if X entails Y in L, then for any agent A, if they believe X, then they are obligated to believe Y.

The third part of this mini-argument comes from a particular view of logical pluralism, namely that of Beall & Restall (case-based logical pluralism)

The idea of case-based logical pluralism is as follows. An argument is valid iff in every case* where the premises are true, so is the conclusion. Case, so argues Beall & Restall, is ambiguous and there are many acceptable ways of making the term specific. Corresponding to each way of specifying a meaning of "case" is a correct logic.

Blake-Turner takes this further and deals only with versions of pluralism that follow a hierarchical form. i.e. the pluralist endorses a strongest logic that endorses all but not only those inferences that are present in at least one of the pluralist's other logics.

Beall & Restall do endorse a class of logics that follow this structure, but I'm unsure if this is incidentally or if it's a consequence of their position. I'd be interested in hearing from Blake-Turner as to why he accepts this restriction, as it seems unnecessarily weakening for the pluralist.

But if the correct logics do form a hierarchy like this, then only the strongest can do genuine normative work, by the above premises.

Given any particular argument either (1) the weaker logics agree with the stronger logics in which case the weaker logics make no difference to what the agent ought to do or (2) the stronger logic trumps the weaker logics, in which case they still make no difference.

Either way, only the strongest correct logic matters for what the agent ought to do.

Blake-Turner concedes that this does follow from his view of pluralism plus All-or-nothing and Oughts from Validity. I'm not sure if that's necessarily true. There might be room for a Pluralist to push back and say that in case (2) (disagreement between the logics) the stronger logic doesn't trump. Whilst the strongest logic might be stronger, that doesn't mean that it's got priority. It might be that in cases of disagreement, the facts about logical correctness alone aren't enough to determine what an agent ought to believe. They have to reason by at least one of the logics, but they have a choice as to which one. (or, perhaps, certain pragmatic or contextual factors will decide which logic is best here).

Blake-Turner's move is to reject All-or-Nothing and Oughts from Validity as too demanding. He suggests three ways of broadening one's normative horizons and adopting weaker premises.

Reasons over Oughts

Blake-Turner offers three ways of adjusting Oughts from Validity and All-or-Nothing.

The first of these is the most relevant to the collapse objection. Blake-Turner suggests using the (pro tanto) reason relation in place of the obligation relation. All-or-nothing and Oughts from Validity are replaced as follows:

Ecumenical Normative Work (normative premise): A logic does genuine normative work if and only if it makes an ecumenical normative difference: a difference to what an agent is entitled to do, obligated to do, or has reason to do

Reasons from Validity: A logic L makes a difference to what an agent has reason to do iff, if X entails Y in L, then if an agent believes that X, then they have a reason to believe that Y.

Blake-Turner has two arguments for why one ought adopt these principles.

The first is that, generally, reasons do a lot of work in a lot of philosophical domains and so it's not unreasonable to think that they'd also play a central role here. I take this to (1) not be intended a decisive argument in favour of the position and (2) to more be supporting the claim that there's nothing wrong with adopting these principles, rather than committing people to them. Seen in those lights, I think that's fair enough.

His second argument is problematic. He argues that the preface paradox gives reason to abandon Oughts from Validity. The preface paradox is an apparent case of a failure of conjunction introduction. If one considers all of a long list of claims one endorses (e.g. a book one has written), one believes in each one individually. When one takes their conjunction, one ought not believe this as the chance of at least one of your beliefs being wrong is quite high (even if you don't know which one that is). Oughts from Validity seems to have a counterexample in this case.

I don't take the preface paradox all too seriously. It's always seemed to me to just be a failure to factor in degrees of belief to one's definitions. Oughts from Validity is a statement about full beliefs. The agent in the preface paradox case either (1) genuinely has full beliefs (perhaps unjustifiably) so is committed to the conjunction or (2) actually has partial beliefs. One might call these beliefs because, generally, high-value credences function like a full belief, but this breaks down in this case. But in this case, Oughts from Validity doesn't apply. The response to abandon Oughts from Validity in response to this paradox is an overreaction, in my opinion.

So I don't really buy Blake-Turner's positive case for his principles, but I don't really think he needs one. These are prima facie plausible principles and the burden is on the proponent of the collapse argument to explain why he's wrong, not on him to defend the principles.

Blake-Turner argues that all this escapes the collapse objection in the following way. As above, there are two cases: when the logics agree and when they disagree. Blake-Turner analyses these cases as follows (with suitable Beyonce´ analogies that I can entirely get behind!).

Suppose A already has reason to go with B to a concert (e.g. because of a promise) and this reason is enough to ensure that A is obligated to do so (e.g. because there are no additional opposing reasons). A then learns that Beyonce´ will be playing at this concert. Naturally, A likes Beyonce´. The facts about Beyonce´ have made no difference to what A must do but have made a normative difference. They've provided additional reason for A to go. Reasons can over-determine obligations.

As with Beyonce´ concerts, so with logics. That A's strongest logic endorses an inference is enough for A to have the relevant sort of obligation about their beliefs, but that doesn't mean that A's additional logics can't provide an additional reason to believe and hence make a normative contribution.

Where the logics disagree, even if the strongest logic always trumps, it might be the case that the weaker logics disagreeing provides some (weaker) reason against believing. In Beyonce´ concert terms, suppose A has promised to go to a party with B but gets Beyonce´ tickets for the same night. A is obligated to go to the party, so the Beyonce´ tickets make no all-or-nothing normative difference but nevertheless are a reason against going to the party. Similarly so for logics.

This is a broadly persuasive story but I think there is a major issue that needs to be resolved, perhaps the most major issue in the paper. Apparently, separate reasons can often do the same normative work.

Suppose A discovered that (1) a musician they like is playing at a concert. Unknown to them, this is Beyonce´. This would be reason for them to go. Suppose A discovered that (2) this concert is a concert where Beyonce´ and only Beyonce´ will be playing, this would also be a reason to go. Suppose, for the sake of weights of reasons, that every musician A likes, A likes equally well.

Both (1) and (2) are reasons for A to go to the concert. But, taken together, they provide no more reason than each other. Though, in a sense, separate reasons, they are thin relative to one another (one might equally say that they are separate sentences expressing the same reason, this is merely a linguistic dispute). If A learned (1) or (2) separately, then this would do genuine normative work. But if A already knows either (1) or (2), then learning the other does no additional Normative work. One might even argue for a priority of (2) over (1). That (2) is the reason that really does the normative work and the (1) is subsidiary to that.

I'll say that two reasons do the same normative work iff they are like (1) and (2) in the relevant respects. I'll say that they do different normative work if they both do normative work alone and each still does normative work when taken together.

Suppose L1 and L2 are correct logics obeying Blake-Turner's hierarchical structure. L1 is stronger than L2. If L1 and L2 agree on an inference, do the reasons they provide do the same normative work or different normative work?

I confess I'm not sure what the pluralist is committed to here. I think this connects to why the Pluralist's logics form a hierarchy. If this is just an incidental fact of the position and the stronger L1 does not have priority over L2, then I think it's plausible to say that they do different normative work. If the hierarchy is a deeper feature generated by the position, then L1 is not only stronger than L2 but, in some sense, has priority over it. In this case, it looks like the reasons are really doing the same normative work and Blake-Turner's response doesn't go through.

A similar problem can be identified in cases of disagreement with the facts about L1 acting as a defeater for the facts about L2.

Overall, I'm broadly optimistic for this approach but there's some serious work that needs doing to establish that the reasons provided by L1 and L2 are genuinely independent of one another.

Other ways of broadening one's normative Horizons

Blake-Turner offers two other connected ways of changing the normative requirements on correct logics.

The first of these is built around an idea called basing. The idea of basing is that one can hold beliefs in virtue of others (elsewhere, I call this one's grounds for believing). This potentially has some connection to whatever normative work it is that logics do.

According to this idea, it's not enough for an agent A simply to believe that Y if they believe that X and X entails Y one some correct logic. If A believes that Y but not because of its connection to X, rather for some other reason (e.g. A likes the sound of Y), then A has not fulfilled their logical obligations. A needs to believe Y in part in virtue of their belief that X. We get the following principles:

Based oughts from validity: A logic L makes a difference to what an agent is obligated to do iff, if X entails Y in L, then for any agent A, if A believes that X, then A is obligated to believe that Y and to base this belief in part on X.

Based reasons from validity: A logic L makes a difference to what an agent has reason to do iff, if X entails Y in L, then for any agent A, if A believes that X, then A has reason to believe that Y and to base this belief in part on X.

This also allows for normative principles that are based on invalidity rather than validity. This is Blake-Turner's final idea.

Based oughts from invalidity: A logic L makes a difference to what an agent is obligated to do iff, if X entails Y in L, then for any agent A, A is obligated not to believe Y in part on the (deductive) basis that X.

Based oughts from invalidity: A logic L makes a difference to what an agent has reason to do iff, if X entails Y in L, then for any agent A, A has reason not to believe Y in part on the (deductive) basis that X.

These are interesting contributions and seem like plausible ideas. I have two comments.

The first is that, whilst interesting, these adjustments make no real contribution to solving the collapse argument. All of that work is done by the idea of explaining normative work in terms of reasons. This is what I mean in the introduction when I say that this was really two papers. The idea that basing is important to the normative contribution logics make is an interesting one, but it's irrelevant from the collapse argument. It builds towards Blake-Turner's wider move of approaching normativity in logic with a more nuanced understanding of normativity, but that's a wider aim, not something that's relevant for the narrower aims of this paper.

Second, adding this requirement might yield some strange consequences. Take any monotonic logic (i.e. that if X is a subset of X' and X entails Y, then X' entails Y). If that logic is correct, then everyone ought/has reason to base all of their beliefs that are entailed by some of their beliefs on all of their beliefs. Proof of this is simple: Let Y be a belief of A's that is entailed by some of A's beliefs X. Let X' be the union of X with any other beliefs of A's. By monotonicity, X' entails Y. So by based oughts/reasons, A ought/has reason to base their belief that Y in part on all of their beliefs.

Blake-Turner recognises this and tries to get out of it with the based-invalidity versions of the bridge premises. This does remove the reasons/obligations that arise given monotonicity but does not go far enough. This principle is still not enough to say that an agent is wrong to base their beliefs in this way. I might suggest the following fix.

What matters for the (deductive) basis of one's beliefs is not entailment, per se, but rather non-redundant entailment. The idea of non-redundant entailment is simple. X non-redundantly entails Y iff X entails Y and no subset of X entails Y. If one adjusts the bridge premises to use non-redundant entailment, rather than entailment simpliciter, then this will avoid this issue.

Summary

I'm broadly supportive and optimistic about Blake-Turner's project here. A lot of the general ideas have some promise and are interesting. That being said, I think there are issues with his views as they stand. Fixable issues, but issues nonetheless. The most substantive of these is the issue relating to different reasons doing the same normative work. That issue is, I think, solvable, but will require some non-trivial work relating to exactly how correct logics do normative work. Overall, the paper is good and I certainly recommend reading it.

For anyone wishing to read this article it can be found via these links:

• https://link.springer.com/article/10.1007/s11098-021-01638-9
• https://philpapers.org/rec/BLARBA

Christopher Blake-Turner is soon to be Assistant Professor at the University of Alabama at Birmingham, having recently finished his PhD from UNC Chapel Hill (congratulations, Doctor Blake-Turner).

I welcome comments or friendly criticism below, or you're welcome to email me at gareth.pearce@univie.ac.at

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