What is a bridge principle in MacFarlane’s sense? Is his case for his preferred principles convincing?
1
MacFarlane (2004) outlines several principled ways in which we may take logic to guide our ‘rational change in belief,’ answering Harman’s (1984) scepticism about the possibility of any such principles. By way of a brief example, if I believe p, and I believe p → q, then intuitively I ought to believe q, or give up my belief in p or p → q. MacFarlane attempts to capture such intuitions systematically, and calls such means of capture ‘bridge principles.’ In section 2 I shall explore exactly what MacFarlane takes this to mean, in section 3 I shall outline MacFarlane’s case for his preferred principles, and in section 4 examine the preface paradox objection, and MacFarlane’s response, and the priority objection. In section 5 I shall offer responses to these objections drawing on the work of Steinberger (2015) and in section 6 conclude by accepting MacFarlane’s principles as an evaluative norm for reasoning in a social context.
2
As mentioned above, a bridge principle is a statement that takes us from some logical truth, such as A, B ⊧ C, to a normative claim about a rational agent believing A, B and C. MacFarlane (2004) gives the following form:
‘Bridge Principle: If A, B ⊧ C, then (normative claim about believing A, B and C).’ (p6).
He offers three possible parameters for the structure of the normative claim, as the type of deontic operator, the polarity of the operator, and the scope of the operator, and the possibility of a knowledge parameter (suffix k) on the antecedent logical claim, of the form ‘If you know A, B ⊧ C…’.
The scope parameter dictates how we are to apply the deontic operator to the conditional outlined above. It could apply only to the consequent (C) (if A, B ⊧ C, then you ought/may/have reason), both sides (B) of the conditional (if you ought/may/have reason to believe A, B ⊧ C, then you ought/may/have reason…) or the whole (W) conditional (one ought to see to it that if A, B ⊧ C, then…).
The deontic operator parameter outlines our level of rational normative commitment, and MacFarlane offers three options: obligation (o), permission (p) and reason (r), where obligation is thought of as indefeasible, permission grants license, and reasons thought of as defeasible (p9).
The polarity parameter is positive (+) if we have an obligation/permission/reason to believe A, and negative (-) if we have an obligation/permission/reason not to disbelieve A, where disbelieving A is equivalent to denying it, rather than failing to believe A (p8.).
MacFarlane’s Table 1 (p7) provides a complete breakdown of each possible outcome and the shorthand for each bridge principle, ordered scope, operator polarity and (optionally) knowledge, and I shall be using his shorthand from here on out. MacFarlane also proposes a modification to the general form of bridge principles in section 4 of his paper (p24), which I shall modify here for clarity:
BP*: If [you know that] schema S is formally valid, and you apprehend the inference A, B /C as an instance of S, then (normative claim about A, B and C.)
The bracketed content pertains to the knowledge variants mentioned above and on Table 1. Though BP* is not examined in MacFarlane’s initial case for his preferred principles, it can be meaningfully swapped in to replace the forms given on Table 1. For example, the BP* version of Wo+ would read: ‘If schema S is formally valid, and you apprehend the inference A, B /C as an instance of S, then you ought to see it that if you believe A and you believe B, then you believe C’ (p24). For reasons that will hopefully become clear, I shall have reason to consider the BP* version of some of MacFarlane’s possible principles, and denote them simply with a *.
3
MacFarlane’s method for arguing for his preferred principles is eliminating those principles that are implausible for one reason or another. Section 3.1 considers and rejects the C-principles, 3.2 the B-principles, and 3.3 considers the W-principles and accepts a W variant.
3.1
Firstly, MacFarlane considers and rejects all the Co and Cp variants for two reasons. Firstly, referencing Harman (1984), that in the Co or Cp variants of our bridge principles, if C is absurd, such as ‘I am a turnip,’ and A is ‘2+2 = 4’ and B is ‘2+2 = 4 → I am a turnip’, then Co+ reads:
If I believe ‘2 + 2 = 4’ and I believe ‘2+2 = 4 → I am a turnip’, I ought to believe I am a turnip.
But this is patently wrongheaded. Clearly, I ought to give up my belief ‘2+2 = 4 → I am a turnip’. Secondly, referencing Broome, the Co and Cp variants create a strange sort of ‘self-justifying’ beliefs, since A ⊧ A, then the Co and Cp variants would entail an obligation/permission to believe what one already believes (p9). For the Cr variants, MacFarlane suggests that these simply collapse into the Br variants, since if we are to hold that we have defeasible reasons for believing the logical consequences of our beliefs, then it must surely be because we think we have pro tanto reasons for the beliefs we already hold. If that is the case, Cr becomes extensionally equivalent to Br, since it will be the case that we have reasons for believing what we do, therefore we could easily rewrite any Cr principle as a Br principle.
3.2
MacFarlane simply thinks the B’s are too weak, because
‘According to the B’s logical consequence is a channel through which existing norms for belief… can be extended.’ (p10).
So, the B’s don’t tell us anything about cases when we ought not to believe the antecedent, but do anyway. Consider the turnip case for Co above, Bo+ tells us:
If I ought to believe ‘2 + 2 = 4’ and I ought to believe ‘2+2 = 4 → I am a turnip’, then I ought to believe I am a turnip.
Now, this avoids the absurdity of endorsing the thesis I am a turnip, since obviously I ought not to believe ‘2+2 = 4 → I am a turnip’, but it doesn’t give any guidance on how to revise our beliefs in the light of the logical consequences of our beliefs. Therefore, we should eliminate B-principles on the grounds of their weakness, and this seems right, since we want our bridge principles to be as strong as possible.
3.3
MacFarlane rejects the Wp’s, because ‘[L]ogical norms of belief – of reasoning in the broad sense – are surely constraints of some kind.’ (emphasis in original, p10). Wp+, for example, merely gives us permission to endorse the logical consequences of our beliefs, but does not meaningfully constrain us to do so, since permission means we may choose to do otherwise. This seems incorrect, so we should reject the Wp’s.
This leaves the Wo and Wr principle formulations. MacFarlane feels we can reject all the -k formulations because of the priority objection:
‘According to the -k variants we are subject to logical norms only in so far as we have logical knowledge. The more ignorant we are of what follows logically from what, the freer we are to believe whatever we please.’ (p12).
This certainly seems unacceptable, since we don’t want ignorance to increase our license to believe as we wish. Against Wo+ formulations, MacFarlane suggests that the excessive demands objection, from Harman (1984), will kill off any hope for Wo+. However, later in the paper, MacFarlane returns to the possibility of Wo+ in the form of what I have called Wo+*. It isn’t at all clear that he is endorsing this principle over his endorsement of Wo- and Wr+ taken together, on p13. However, as Wo+* seems to avoid the excessive demands objection (p24,); according to MacFarlane himself it avoids this objection, this would leave it with the fewest objectionable features (per the Table on page 12,) subject only to objection by the preface paradox. Since we are looking for norms of rational belief revision, it seems plausible to be looking for the strongest norms possible, indeed, this is the basis for rejecting the B variants. Therefore, I shall take him as endorsing Wo+*, and by implication rejecting the other W formulations, and ignore his apparent endorsement of a combination of Wo- and Wr+. It should be noted this may be controversial, and everything that follows is premised upon this assumption, so there may be critical discussion to be had about which principles MacFarlane is endorsing, but I shall not engage with that topic further here. Next, I shall consider two possible difficulties with MacFarlane’s preferred bridge principle, and thereby his case for it.
4
Two problems for MacFarlane’s chosen principle, and thereby his case, are the preface paradox and the priority objection. In section 4.1 I shall address myself to the former, and MacFarlane’s response, and in section 4.2 highlight how the priority objection returns for Wo+*.
4.1
In summary, the preface paradox imagines an author who has written an authoritative and well researched non-fiction book, such that the book is composed of a series of claims A1…An. Now, the author can rationally endorse claim Ai because she has done a great deal of research into each claim and has good evidence for believing it. However, as a matter of epistemic due diligence and in recognition of her fallibility, when writing the preface for the book she admits that there must be at least one error present in the book. We can take her admission from epistemic due diligence to be an endorsement of the claim that ¬(A1 ∧ A2 ∧ … An) (pp11-12). Let us assume, however, that our author is a well-informed logical agent, and that she is aware of and can apprehend the logical consequence of her assertions in the book as being (A1 ∧ A2 ∧ … An). So, Wo+* obligates our author to believe (A1 ∧ A2 ∧ … An), yet epistemic prudential reasons, and inductive reasons, surely obligate her to believe its negation. This is a problem for Wo+* as a bridge principle, since it obligates the author to endorse a consequence which we have very good reason to think is untrue.
In his earlier discussion of Wo-, MacFarlane responds to this critique and I am going to adapt it to defend Wo+*. MacFarlane argues we find ourselves roughly as follows:
You would not be (epistemically speaking) ‘entirely as you ought to be’ if you accept both the endorsement of Wo+* and induction/epistemic prudence
You ought to see to it that you accept the endorsement of Wo+*
You ought to see to it that you accept the endorsement of induction/epistemic prudence
From such a position, MacFarlane argues, we are not blameworthy, even though we have conflicting obligations, since we have a mitigating excuse (p14). MacFarlane’s position is that our excuse is:
we cannot give up our beliefs in either side of the paradox voluntarily, since it just isn’t the sort of thing we can do. Our doxastic states in the case of the paradox simply aren’t open to voluntariness in that way and
we can commit ourselves in the long term to attempting to fulfil the strictures of the norms placed upon us by going after further research and pursuing even more complete knowledge (p15).
I feel that (2) here is wrong-headed, since it simply gives us an updated version of the problem of excessive demands. Go back to our prefacing author. To avoid the paradox and comply with our norm, she must continue to research the same topic, at least in the sense outlined by MacFarlane. But, when she comes to any sort of end, she must find herself in the same position. She must be caught between endorsing what Wo+* tells us is the logical consequence of her beliefs, i.e., their conjunction, or endorsing what epistemic modesty demands and accepting that at least one of her beliefs is incorrect. This seems to imply that this process must continue ad infinitum if we are to conform to the norm as MacFarlane construes it, but surely that cannot be right either, since we must surely want to allow someone in this position to change research projects without violating the norms that logic gives us through the bridge principle? So, it appears we should abandon (2).
That leaves us only with (1), which doesn’t seem strong enough as an excuse on its own. So, it seems that MacFarlane’s response does not hold up well since it invites a new excessive demands problem. I give my response to these issues in section 5.2.
4.2
Another problem for MacFarlane’s Wo+* is that is seems to be open to the priority objection, as outlined in section 3. ‘The more ignorant we are of what follows logically from what, the freer we are to believe whatever we please,’ was MacFarlane’s reason for ruling out the -k variants, but doesn’t this also apply to the concept of apprehension? The more we fail to apprehend what follows from what, the freer we are, since we are not bound by Wo+* when we fail to apprehend. This certainly doesn’t seem desirable. I address my response to this in section 5.1.
5
So far, I have only been considering norms of reasoning as they apply to an individual reasoner, however, norms of reasoning exist in a social context and perform differing functions. In section 5.1 I appeal to this social context to avoid the priority objection, and in section 5.2 to offer some response to the preface paradox.
5.1
In (2015), Steinberger discusses three ways norms can be enacted, as directives, evaluations and appraisals. I shall focus on the last two. Evaluations are third-person standards which are ‘yardsticks,’ in that they are the standards of ‘correctness’ or ‘incorrectness’ to which agents are held. Appraisals are the third-person gradable attributions of praise and blame, that account for wide ranges of input (p11). To avoid the priority objection, we must think of bridge principles in evaluative terms, and those who fail to adhere to them should be appraised (in the sense above) by accounting for their lack of education. So, let’s imagine I am talking to someone who believes A and also believes ¬(A ∧ B), and they don’t apprehend that A ⊧ ¬¬(A ∧ B), assuming classical logic for our present purposes. In evaluative terms, they are in error, but in appraisal terms, their error is excusable, since they cannot apprehend the inference. So, from the evaluative point of view, I can judge them to be in error and therefore impute irrationality to them, and do so based on a shared, evaluative judgement, but also find them not to be blameworthy for that defect. This means we can continue to apply the principle to the ignorant in a social context, and though they are transgressing the norm, that transgression is not blameworthy. We need not demand too much from the ignorant whilst still maintaining that Wo+* is the evaluative standard to which we should all aspire.
5.2
Further to this socialised context of epistemic endeavour, I offer a possible method of responding to the preface paradox.
Let’s go back to our author. When confronted with the preface paradox, instead of feeling she must pursue her line of research until the end of her life, as MacFarlane suggests, she consults her epistemic peers (those who are equally well versed in the field as she, and as competent as she, and so on) and forms a ‘peer panel’ to assess her work. Let’s imagine our peer panel and author convene and there are premises P1 to P50 in the book, and the rest of the book is conclusions, C1…Cn+x. based on these premises. They must reach unanimous or near-unanimous assent that Pi is true for it to be ‘safe,’ else it is ‘controversial.’ This requires that peers proceed under the guidance of the bridge principle. The panel get together and discuss and reject P35-P50 as being controversial. They then work out C1…Cn, those conclusions that flow from uncontroversial premises, and Cn…Cn+x, those conclusions which flow from controversial ones. The peer panel should now have two parts of the book, premises and conclusions that are unanimously (or near-unanimously) agreed upon, and premises and conclusions that are at least somewhat up for debate. So, if the group collectively endorses {P1…P35, C1…Cn}. it seems reasonable for the author to adopt the group’s view, considering the very same epistemically prudential reasons given in the paradox. Since she is fallible, and the group is likely to be less fallible than she, then she should adopt the group’s position as her own.
Now, it might be argued that this just pushes the paradox back a step, and that the author should for epistemically prudent reasons still doubt even her peer panel’s safe conclusions, because they are also fallible, but we need not grand this. All we needed was a method for ‘breaking the tie’ between the obligations of individual epistemic prudence and the obligations of Wo+*. Epistemic prudence is a norm that requires us to account for our fallibility and our history of previous error, but we can only do so to a certain extent. By consulting our epistemic peers, it seems that as an individual reasoner, we have satisfied its demands by having a mechanism for checking our work. This seems to be the motivation behind the peer review system in academic work, and that such a check is available to our author seems to satisfy our author’s demand that she, as an individual, not be epistemically imprudent whilst not violating Wo+*. There remains the question of what to do with those statements {P35…P50, Cn+1…Cn+x}, but since these are plausible candidates for the author’s initial suspicions of error, it seems she should suspend judgment on these statements.
At this point it seems worth addressing that most individual reasoners cannot proceed like this, but that does not really matter. If Wo+* is evaluative, then we can see that most reasoners cannot resolve the preface paradox in this way, and thereby not hold them blameworthy for transgressing against the norm Wo+*. All that is required is there be some way to satisfy the obligations from the norms of epistemic prudence in principle, and the paradox seems significantly less problematic; most reasoners can be transgressing against the norm in a way that is not blameworthy, and there is in principle some way for them to avoid transgressing by satisfying epistemic prudence: consulting their epistemic peers.
6
I above considered what MacFarlane calls a bridge principle, explored his taxonomy of principles and examined his preferred bridge principle. I criticised his case with arguments of my own and offered an alternative but weaker account of how we should apply MacFarlane’s principle, suggesting that we should view MacFarlane’s principle as an evaluative norm for our reasoning, understanding that individuals may fall short, but to which we may collectively commit ourselves, ultimately accepting a modified version of McFarlane’s case.
Bibliography
Harman, Gilbert (1986). Change in View. 1st ed. Cambridge: MIT Press.
MacFarlane, John. (2004), In What Sense (If Any) is Logic Normative for Thought? Presented at the 2004 Central Division APA symposium on the normativity of logic. Available at http://johnmacfarlane.net/normativity_of_logic.pdf
Steinberger, Florian. (2015) Three way in which logic might be normative. Available at: https://floriansteinberger.weebly.com/uploads/5/7/9/5/57957573/three_ways_jp.pdf