Tennant Review
Neil Tennant just reviewed my book (subscription to Philosophia Mathematica required for the link).
Tennant says:
We adverted above to an appearance of slight strain between two assertions in the work. The first of these is confidently sweeping:
. . . arithmetical truths are conceptual truths; or, at least, enough arithmetical truths are conceptual truths to enable us to account for all of our a priori arithmetical knowledge once we add in knowledge secured by inference from other truths known in this way. (p. 123; emphasis added)
But, thirty pages later the author retracts:
To account for all of our knowledge of arithmetic is a tough call, even when we allow that much can be achieved by deduction from previously known arithmetical facts. Godel’s incompleteness results are a measure of how tough a call this is. (p. 153)
There are two problems with what Neil says here about my asserting then retracting some claim. (1) The first quoted passage is not an assertion. (2) The second quoted passage is not a retraction.
(1) The passage from p. 123 appears within the scope of an ‘On the view that I’m interested in’ operator, which Tennant carefully omits to reproduce. I never claim to have established that the view in question is true. Indeed, I repeatedly stress that this is not an aim of the book.
(2) The two passages are nonetheless obviously consistent. To make things even clearer, the discussion on the very next page (p. 154) explains why I would like to maintain my optimism that the proposal on offer can account for all our a priori arithmetical knowledge even given that this is a tough call in the way just described.
I am genuinely puzzled as to why Tennant presented these passages in the way he did. (This is just one example; I had similar thoughts about many of Tennant’s other criticisms.)
The foregoing notwithstanding, I’m feeling fortunate compared to Chris Peacocke, to date the only other recipient of a review by Neil.
UPDATE: Neil tells me he has, in fact, written other reviews. I had been assuming the list on his OSU ‘publications’ page, which mentions only the Peacocke review, was complete.
I think you’re right about all of this. I see another problem with the claim that the two passages in question are in tension, in addition to the ones you identify: one might think that some, but not all, arithmetical truths are a posteriori. Then it’s obviously consistent that all a priori arithmetical truths are conceptual truths, but that some arithmetical truths are not conceptual truths.
This illustrates the important point that reviewers should always send penultimate versions of their reviews to the authors being reviewed, in order to avoid such mistakes of interpretation or argument in the published version.
I agree; I’m really surprised that some review authors don’t do this.
At Neil’s request, and to clarify, let me add that Neil did email me to ask me two questions while preparing the review. One query was to check whether a typo (a missing negation) was indeed a typo, and the other was a more substantial clarificatory question about my notion of relevant accuracy, unrelated to the stuff in this post. Neil didn’t mention that he was writing a review or send me a draft, plan or list of points at any stage.
He and I did also later communicate about the review, after it came out. I read it on the PM website and sent Neil a brief email making the above points (and a few others). He replied to the effect that he did not think he had misread me. To the best of my knowledge I did not succeed in convincing him otherwise.
Carrie,
The full context of the material (call it [MMM]) that I quoted from p.123 is “On the view that I’m interested in [MMM]. That is to say, we can know about arithmetic by examining our concepts. That is a key aspect of my view …”. So you can hardly begrudge your reader the attribution, to you at that stage, of the view that [MMM].
Moreover, with regard to your “optimism that the proposal on offer can account for all our a priori arithmetical knowledge” (to quote from your blog entry now)—an optimism which you say is expressed in your discussion on p.154—may I point out that you conclude that discussion by writing “These considerations fall short of an argument that all our arithmetical knowledge can be accounted for once we take concept grounding on board.”
So, please forgive this reader if he took you, at p.123, to be claiming that [MMM], but then took you, at p.153 (as echoed at p.154) to be retracting that claim.
I omitted the first bit of context from my quote from p.123 because it was clear that you were advancing the view that [MMM]. If I had included the preceding words “On the view that I’m interested in”, then I would also have included the immediately succeeding words “That is a key aspect of my view”.
If you do not wish your reader to make what would strike any reasonable bystander as a contextually appropriate attribution of a view to you, then you ought to be clearer about what it is that you are actually committing yourself to, and what it is that you are distancing yourself from. It’s just a basic requirement of clear philosophical exposition.
Best regards,
Neil
As I said, the book repeatedly stresses that although I am sympathetic to the view in question, I do not take it to have been established by the book’s arguments. And I am surprised at needing to point out the difference between modestly admitting that one doesn’t (yet) have a fully satisfying argument for some p to which one is sympathetic and /retracting/ p. I don’t know of either of these misreadings having been shared by any other reader, but of course I leave it to the reasonable bystanders out there to decide whether either is appropriate.
In any case, what matters to me is philosophical progress concerning the ideas on which the book focuses, not skirmishing over the reasonableness or otherwise of possible misreadings of what I wrote. Let’s hope this discussion may have helped to some extent with the former goal by helping to clarify my position for anyone else who might otherwise have read me as Neil did.