The Vagueness of Rigour: A Rejoinder to Alec’s Manifesto

Alec Siantonas writes in his Oriel Theology manifesto (which is probably close enough to the character of the whole to warrant the name) that a striking feature of the theology taught at Oriel is its attempted rigour, and that this rigour is part of the reason it can be though if as ‘Analytic’ theology. Now, I’m not going to try and argue that theological inquiry should not be rigorous. I am, however, going to claim that the account of rigour which seems to be applied within the Analytic tradition is itself often insufficiently rigorous; that a rigorous account of rigour would recognise that it is it a vague concept, even and especially when it is applied with all the precision which Analytic philosophy seeks to demand, and that this has certain methodological consequences. On this basis, I’ll try to suggest that if Oriel Theology is indeed rigorous, then this need not entail its being exclusively Analytic.

I’m going try to make this argument over the course of four sections. The first will be a brief historical account of the origin of the concept of rigour employed by Alec (and then Brendan) in the Analytic tradition. The second will suggest an immediate methodological problem which has plagued ‘Analytic’ rigour from its origin. The third will be a look at what the demand for clarity as a feature of rigour entails. I’ll then conclude by making some observations about what these claims, if they are true, might entail for the study of theology and philosophy, as well as for the character of Oriel Theology.

1. History

At one point in his manifesto, Alec broadly categorises Analytic Theology as a theological method of inquiry which finds its origin in the form of thought developed by Gottlob Frege. I think Alec is correct about this, though I think to Frege one can also add the names of Russell and the early Wittgenstein. Now, as I understand it, Frege, Russell, and the early Wittgenstein were primarily motivated by a desire to place philosophy on an epistemic foundation as firm as that of mathematics, for various reasons. To this end, they sought to demonstrate that mathematics and philosophy were both grounded in the same logical forms and principles; the thought ran, or so it seems to me, that if mathematics and philosophy shared the same foundation, then we could claim them to be epistemic equals possessed of the same sort of certainty.

This, it seems to me, is an intuition characteristic of much modern Analytic thought, borne witness to by certain stylistic and methodological presumptions (e.g. the tendency of Analytic writing to be cast in a certain semi/pseudo-mathematical style, a preoccupation with the possibility of deriving contradictions within systems of thought, a general belief that ideal thinking should be rigidly axiomatic (these are obviously not true of all Analytical thinkers)). And it is this historical intuition which, I believe, informs Alec’s use of the term ‘rigour’: explicitly or otherwise, he seems to me to be using ‘rigour’ with mathematics (under the guise of logic) as his paradigm. This in turn (if true) informs what he means when he says that we should be ‘offering definitions, drawing distinctions, and employing some formal apparatus’: as I’m reading him, this points towards the thought that an ideal philosophical claim has the same clarity as a mathematical proof that 2+2=4, and that a philosophical mistake should be made to be as easy to spot as in the statement ‘2+2=5’.

2. An Immediate Problem

Now, there is an immediate problem here, relating to the fact that logical arguments must be linguistic. This problem can be expressed as follows: a logical argument can only be as rigorous as the terms it employs, but the terms of language lack the ideal properties of exactness demanded by the forms of logical argument.

Let us try to clarify with a metaphor: even though the blueprint for a building might be absolutely perfect, the building itself can be no more solid than the materials out of which it is built, and even if we use the strongest materials we have, everything under the sun is eventually subject to decay. The blueprint might aim at an ideal of solidity, but in reality the building will be subject to decomposition, not to that ideal. Just substitute ‘blueprint’ for ‘expression in the language of propositional logic’ and ‘materials’ for ‘words’, and we have the intended image: for the expressions of propositional logic certainly aim at an atemporal certainty, but the words we use to flesh them out when we use them to make claims about the world are too worldly to meet this formal demand.

Now, this is not necessarily an immediate problem for mathematics: after all, its terminology is (again) the very paradigm of rigour: to carry the metaphor a bit further, the formal language of pure mathematics might as well be titanium. Philosophy and theology, however, must employ (or at least borrow) the terms of ordinary language, and these are more like play-doh: they are far too malleable and changeable for the purposes of pure logic. We can, of course, use them to express a perfectly valid argument: the soundness of that argument, however, will always be contingent upon the character of the terms employed, not the formal purity of its abstracted logical structure.

Now, this is not in the least bit a new problem or an original claim; indeed, it informs the efforts of Analytic philosophers to either develop synthetic languages closer in character to mathematics or to account for meaning in ordinary language by means of pseudo-mathematical systems (c.f. Frege, Carnap, Kaplan). I’m not going to wade into these efforts here, though I will note that several giants of the Analytic tradition (Wittgenstein, Austin, Quine, and Davidson) have argued from the basis that there is no language which escapes decay (the later Wittgenstein even argued (convincingly, in my view) that the language of mathematics, which had earlier served as his paradigm for timeless solidity, is subject to the same types of contingency as ordinary language, though in a far less obvious fashion: that even blueprints and ‘pure’ concepts are subject to time and human convention, among other things). I am instead going to note one difficulty that any effort to create a titanium language will come across, relating to the ideal of clarity in Analytic philosophy.

3. Clarity

I am taking clarity to be a requirement of rigour (one made explicit by Brendan in his response). I understand it as follows: a clear account is one which gives as accurate and perspicuous account of what it seeks to give an account of as possible (perhaps even to the point of near transparency).

I understand the problem for Analytic thought to be as follows: in taking mathematics/logic as our paradigm of rigour, we take mathematical/logical formulations of expressions as our paradigms of clarity. The clarity of mathematical/logical formulations of expressions, however, follows from the nature of their supposed objects, namely, numbers and logical functions. These are supposed to be, by nature (and here we touch upon an instructive point of contention, namely, whether numbers or logical functions have natures) the paragons of rigid and rigidly definable structure. In short, the clarity of the terms of mathematics/logic has metaphysical implications: their language(s) presuppose/follow from objects whose essence is such that they can be completely and rigidly defined (I think Alec will agree with me on this; that even the logical positivists made metaphysical claims in their semantic proclamations).

Not all things, however, are ideal mathematical objects: most importantly, there are vague phenomena, and a part of philosophy is to treat of these vague phenomena (these are both empirical claims). A clear account of a vague phenomenon, however, will (according to the understanding of clarity above) be vague; a clear account of an indefinite phenomenon will be formally indefinite (just as a clear sketch of a blurred image will be blurred).

In terms of examples, Analytic Philosophy itself furnishes a rather beautiful one: Analytic Philosophy is such a vague thing that a rigorous account of its character should be vague, as opposed to a general formal definition. Alec himself gives such a rigorous account, though even his seems to me to ignore the importance of Austin and (perhaps more tellingly) G.E. Moore for the character of the Analytic tradition, and we can also find similarly vague characterisations of Analytic thought elsewhere (c.f. Deconstruction as Analytic Philosophy, Groundless Grounds, and an anthology entitled Classics in Analytic Philosophy. The first of these even characterises an Analytic philosopher as one who has been trained to employ and recognise a particular notion of clarity!). And this is right and proper: any more precise formulation would in fact be less clear, as it would exclude things which shouldn’t be excluded by tracing sharp lines over blurred and shifting edges.

Beyond Analytic Philosophy itself, I would contend that such things as knowledge, belief, meaning, truth, existence, orthodoxy, salvation, grace, and rigour are similarly vague phenomena, such that if we are to give clear, rigorous accounts of them then these accounts must carry within them elements of vagueness. In virtue of this, I would contend that the practise of ‘offering definitions, drawing distinctions, and employing some formal apparatus’, if such practises are understood within the paradigm of mathematics, actually serve to muddy the waters of discussion; that the attempt to express a vague phenomenon by means of a titanium language will in fact distort or hide the truth, instead of reflecting it. Because of this, it seems to me that if we are to do philosophy rigorously then we should be willing to commit ourselves to the use of materials other than those demanded by the ideal blueprints of mathematical logic.

Now, the disciplines Alec refers to need not of course be practised mathematically: we can still offer definitions, draw distinctions, and employ some formal apparatus without treating mathematical propositions as our paradigms of clarity or rigour. The fun thing here, however, is that this is precisely what thinkers like Derrida and the later Wittgenstein do; namely, they treat language like play-doh on the basis that (among other things) it both is and refers to things which are subject to decay and essentially indefinite. As such, they seek to rigorously and methodically demonstrate the inherent vagueness and brittleness of our attempts at precise formulation. To put it another way, both thinkers rigorously seek to demonstrate the vagueness inherent to rigour, by rigorously seeking to show that a rigorous investigation of philosophical topics can, and in some cases must, yield vague results (out of which we can of course sometimes derive contradictions if we want to, to take one material consequence which is frequently exploited by those practising deconstruction). Their work as a whole can thus be thought of as a practical demonstration that a) philosophical and theological arguments and statements can only be as solid as the materials which philosophers and theologians use, b) that if these materials are to be true to the world then they will neither always nor often (perhaps even ever) measure up to the ideal of exactness sought by Russell, Frege, and the early Wittgenstein, and c) that if our arguments, thought, and writing are to be rigorous then they should clearly reflect these facts.

(There are arguments supporting this beyond the an appeal to the vagueness of clear accounts of vague phenomena: I’m thinking in particular of arguments for the fact that reality underdetermines convention (even mathematical and logical convention) and the effect of context on meaning. These, however, are for another time.)

4. So(,) What?

I hope that it is clear that I am not strictly trying to disagree with Alec or Brendan when they say that theology should be clear and rigorous: I’m just trying to point out one way in which the concepts of clarity and rigour that they employ need not entail a commitment to the Analytic style of thought that they’ve espoused. I am, as such, trying add a qualification to their accounts, the main import of which is, in my mind, the claim that attempts to formally define the terms of our debate at the outset by drawing rigid distinctions in the context of a given system can actually serve to distort, not clarify, what we are trying to say.

Now, the substantive import of this claim relates to the natures of the worlds that different accounts of language presuppose: for example, the language of Frege, Russell, and the early Wittgenstein (implicitly or explicitly) presupposed a world where anything true had to have an essential structure comparable to the structure of a mathematical proposition (which in their minds meant that truths in reality had to have a logical structure). The language of the later Wittgenstein and Derrida presupposes a world where such a structure is not only inessential to truth, but where the presupposition of such a structure as the basis of our meaningful utterances is inimical to our efforts to express those truths. I believe that if there is a metaphysical debate to be had (and it would be a debate), then it is probably over this question: the question of whether or not the grammar of our languages must map isomorphically onto a mathematical or logical structure given in reality if they are to be meaningful and we are to be able to use them to express truths.

The methodological import, meanwhile, seems to me as follows: that insofar as at least two different answers to the above question are prima facie defensible, neither side can lay immediate claim to either clarity, rigour, or orthodoxy as a specific or uniquely distinctive characteristic. Rigour is instead a vague term which can be truly applied to both approaches, and theology can be constructively and rigorously pursued according to both views.

(For my part, I believe that the later Wittgenstein and Derrida are right, and I believe that Frege, Russell, and the early Wittgenstein were wrong. I also believe that this can be (and has been) demonstrated. Wherever you stand, however, it seems to me any claim that clarity and rigour are the distinctive characteristics of Analytic philosophy, as opposed to other modes of thought, should be treated as dubious to say the least. I also believe that it would be lazy in the extreme to read non-Analytic  thought, theological or otherwise, and claim that it either isn’t or can’t be rigorous if it does not employ or rely on formal definitions, choosing instead to pursue clarity according to a different set of presuppositions.)

Now for the promised positive contribution: in part on the basis of the above, I would claim that, insofar as it is anything, the ‘Oriel Theology’ which Alec describes is a vague entity which can serve as a space for specific debates between (among other things) divergent foundational views, as opposed to a means for us to promote our preferred approach to those debates. I would claim that if it is to be rigorous at all then it should be rigorously committed to the exploration and development of various styles of thought and writing, such that a clear and rigorous account of Oriel Theology allows (demands, even) that there should be an equal place for non-Analytic forms of inquiry. I would also claim that if it is to be rigorous at all, then it should be rigorous enough to avoid falling into the trap of judging anyone who is reticent to begin discussions by offering up formal definitions as therefore guilty of poor thinking. In short, I would claim that if Oriel Theology is to be anything, then it should be neither an inquisition nor an ideology committed to a single set of clearly defined methodological principles, but a forum characterised by respect, curiosity, and, above all, a mutual commitment towards trying to navigate the absurdly tricky waters of theological thought.

(There is obviously more to be said re. Alec’s manifesto, not least engaging with what it means to make it as easy as possible for someone to disagree with you: another time!)

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21 thoughts on “The Vagueness of Rigour: A Rejoinder to Alec’s Manifesto

  1. Thanks Ed, good to get some dissent into the mix. I will respond to this more fully at another time (it’s 2 over here, and I’m supposed to be learning about feminism and/in philosophy at 9), but one brief thought. An important name that I use but you do not is ‘Timothy Williamson’. Much of what I say about analytic philosophy follows Williamson. Williamson, however, can hardly be charged with ignoring the vagueness of ordinary language, and similarly concludes that attempts to escape that vagueness are futile. His discussions of this topic, moreover, are paradigms of analytic rigour. This gives us at least prima facie reason to suspect that your appeal to vagueness is a red herring. But sleeps for me now.

    -Alec

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  2. Oh, I’m not arguing against the possibility of analytic rigour, or indeed its merits! Just against the idea that a specific type of rigour, namely that typically employed by analytic philosophers, is the only or predominant type, such that rigour implies or is implied by analyticity!

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  3. (I certainly wouldn’t claim that vagueness implies the impossibility of an analytic account of rigorousness, and hope I didn’t do so in the post.)

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  4. Thanks for this Ed. I agree with Alec that some dissent is very welcome; there is stuff I aggree with here as well as stuff I disagree with and will have to reflect on more. However, I would like to clarify one point. This post might give the impression that I used the term ‘bad’ in reference to non-analytic forms of thinking. I did not do this (to be clear, I’m not saying that you claim I do, but people who read this post without having read mine might think I have done so). I *think* your remark here is a reference to my discussion of McGuckin’s treatment of Nestorius’ theology. My point here was that McGuckin’s characterisation of Nestorius’ theology (which, I intimated, may also be taken as shorthand for McGuckin’s view of a ‘bad’ approach to theology) might be (on a superficial reading) seen as a criticism which can be applied to analytic theology.
    My discussion of McGuckin is particularly pertinent here, as I argue that analytic theology, rather than attempting to do away with mystery (or, in the context of this post, ‘vagueness’ is (uniquely?) well placed to identify and clarify the manner in which something is ‘mysterious’ or ‘vague’.

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  5. You are right to insist a ‘clearer’ (if I may use this term) account of rigour, and the ‘analytic’ tradition from Alec and myself. For what it’s worth, I think neither myself nor Alec (although I obviously can’t speak on Alec’s behalf here) are narrow advocates of an ‘analytic’ theology which defines itself primarily in contra-distinction to ‘continental’ theology. I put little stock in the distinction between analytic and continental philosophy. My old music teacher, when asked what his favourite type of music was, used to reply: ‘Well, as far as I’m concerned, there’s only two types of music: good and bad’. I feel much the same way. I am very fond of phenomenology, when done well; indeed, I think when phenomenology is done well, it shares many of the virtues of rigour and clarity which I classify under the heading of ‘analytic’.

    I realise here I risk either begging the question or simply being uninteresting. I am not here offering a definition of ‘analytic’ philosophy which is equivalent to ‘good’ philosophy or vice versa – indeed I am intentionally avoiding defining either at this stage. This is a discussion we can have as we go on. The purpose of this post is more to give you a sense of my attitude, as it were.

    That said, I would like to note two things I consider to be generally true of the analytic approach, which may or may not shed some light of the way I am using the term. They are not so much definitions of analytic theology/philosophy as they are observations:
    1) Thinkers in the analytic tradition (as I believer Alec suggests) tend to reject the relativistic turn of Kantian and post-Kantian thought – that is, they consider metaphysics and ontology to be legitimate fields of investigation and discourse.
    2) Closely linked to 1) [and less obviously, perhaps] thinkers in the analytic tradition tend to prefer discussion of philsophical/theological arguments on a case by case basis, and are sceptical of generalised arguments which attempt to render whole fields of discourse inoperable without the need to discuss the particular arguments contained therein. It is somewhat ironic that I should mention this a ‘virtue’ of the analytic approach as part of an, at times, sweepingly generalised discussion of the method of Oriel theology.

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  6. Sorry Brendan, I’d misread that! Will edit it out when I get the chance (though I do sometimes find your inquisitorial nature a little disconcerting!).

    I think there’s a level of truth in what you say re. mystery, and I completely agree that it’s not usually enough to just say that something is vague or mysterious then leave it at that; I do think that there is, however, an instinct towards a particular form of clarity in the character of Analytic philosophy which can tend towards attempts to define mystery in a way that compromises it (actually, the disagreement between Witt. and the Vienna circle might be instructive on that front: the former sought to be so respectful of mystery that we simply couldn’t speak of it at all, the latter took his silence for denial of its proper existence; both positions are clearly flawed (imo), suggesting the importance of finding a middle ground where we can speak clearly about mystery in a manner which preserves its character (something I think Barth does very well), just like that you say. (I’m still using outdated examples though!)

    I’m neither here nor there over whether metaphysics or ontology are legitimate fields of inquiry in the sense you mean, but I certainly think they’re worth pursuing and engaging in, not least because whatever their legitimacy they do tend to shine a light on certain fundamental presuppositions which can then make it a lot easier to understand why someone’s saying what they’re saying. I do think metaphysics itself is a very unhelpful word though: as far as I can see, debates about the nature of substance are neither very physicsy nor very meta (if metaphysics is indeed meta-physics, the same as meta-ethics, the closest thing to that name would seem to be the philosophy of science and debate over the rules governing its terminology (which even seems to me to be the material concern of Aristotle’s Metaphysics, even if it couched in terms of discerning first causes and whatnot), which I doubt is what you’re aiming at! (I think Quine gets at something like that? At least, sounds like something he’d say).

    In terms of case by case, I completely agree and completely empathise: seems like any sort of methodological claim presumes a number of non-present cases, to the extent its almost impossible to begin an inquiry without some sort of general theory, which will then (to at least some extent) determine the outcome of the investigation. I’m growing more convinced that a good way around that is to have people working according to different theories working in the same room, so that they can compare results and see which modes of thought seem most applicable when. Unfortunately we seem to have this great chasm between divergent schools of philosophy… (I completely agree when you say that the best of analytic philosophy and the best of phenomenology (and even continental) do look quite a lot like each other; but then, I think limited inc. is one of the best (and funniest) engagements in Anglo-american philosophy by an Algerian, so my opinion might be very questionable….).

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  7. (And again, just to reiterate: the argument of the post (which might, ironically, not be clear!) is just that rigour is a vague enough notion that a) it shouldn’t be limited to stereotypical contemporary analytic practises, b) stereotypical contemporary analytic practises shouldn’t be though of as intrinsically rigorous. This is not in the least to say that the analytic style referred to by Alex is therefore obviously false in all cases or that we should all start writing sentences like ‘the being of being’s being is nothing more than the being of being for being.’ (Which I think would make perfect grammatical sense in a Heidegger or a Rahner book…))

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  8. It’s mainly just the moments where you go around pointing at things and shouting ‘heresy’. Other than that, though, not at all!

    (On a more serious note, I think it’s just that you do seem to have a tendency to look for the orthodox, which whilst not bad thing, can sound like it’s dealing with a particularly specific notion of orthodoxy off the bat. For the record, I think a certain level of orthodoxy is likely important; but I think that if it’s stated as a clearly defined goal at the outset (in an Analytically rigorous sense :P) it could easily narrow things too fast and too arbitrarily.)

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  9. I agree that you don’t need analytic training to think and write with admirable clarity. Nonetheless, I don’t think it’s plausible to deny that analytic writing is generally more rigorous than writing in other disciplines that do not make significant use of some formal notation or other (not that the notation is what makes all the difference at the level of the individual text). What matters is that each of the analytic tricks I mention – offering definitions, drawing distinctions, and employing some formal apparatus – will, when competently employed, remove some of the ambiguity that would have been there otherwise, or explicate some feature of your argumentative structure that would have been implicit. In fact, analytic philosophers are trained in such a way that they use these tricks with a rare degree of frequency and competence. These tricks, moreover, can be fruitfully applied when discussing theological issues. One important potential use (to which Brendan has already pointed) is that of clarifying just what we mean when when use, in suitably awed voices, ‘mystery’ and ‘transcendence’ of God. What exactly are the limits of God-talk? What complex of factors generates these limits? What is the appropriate attitude towards speech that approaches or transgresses the limits? And so on. My overriding point here, as with the Williamson comment, is that, even when confronted with phenomena that confound our desire for perfect precision (such as vagueness and mystery), it remains (at least) as important as ever to achieve what precision we can.

    Of course, it’s possible to offer a sort of pseudo-precision that really does obfuscate the issue, as when I define ‘person’ as an entity that comes into being at the event of human conception and ceases to be at the moment of human brain death, and then attempt to pass off substantive metaphysical and ethical claims as analytic truths. But that’s an incompetent use of an analytic trick. The best way to gain competence in such matters is by example (ie, reading analytic philosophy) and by practice (ie, writing analytic philosophy).

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  10. I have only skimmed the comments, so apologies if someone else already made this point. I want to pick up and endorse Brendan’s suggestion that we should be skeptical of “generalised arguments which attempt to render whole fields of discourse inoperable without the need to discuss the particular arguments contained therein.” I think that’s right as a normative claim about how to engage with analytic philosophy. I’m pretty skeptical of attempts to undermine analytic philosophy (or analytic theology) wholesale by critiquing its “essence” or general features or whatnot. (Not saying that that’s what Ed was trying to do.)

    Of course, as a descriptive matter, I’m sure we could find examples of analytic philosophers making the very same illegitimate move that Brendan is criticizing. The point is that they shouldn’t.

    I also think that there are bigger questions here, that thread through all the posts so far, about what it is to be a member of an intellectual tradition, and what implications that has for engaging with thinkers from outside one’s own intellectual tradition. This is something I’m thinking about a lot at the moment with the book project that I’m working on.

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  11. Also, I’d be interested to hear Alec and Brendan say more about when, if ever, analytic precision becomes false precision, or at least unhelpful precision– especially in theology. I take it that this question is at the heart of Ed’s challenge, and it’s a question well-worth taking seriously.

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  12. Will read Alec’s most recent piece in a bit, so sorry. I covert anything here which is covered there!

    Just a couple of quick points: Alec, I certainly won’t disagree that there are times when analytic ‘tricks’ (though I think trick is probably the wrong word) are helpful. I would make the case, however, a) that formal definition doesn’t always remove ambiguity, and in some cases even embeds it deeper, b) that the removal of ambiguity is not always a good thing. I think I’ll write this up into a full post, but just to give the basic claims! I would also say that, from where I’m standing, the most precise account of the limits of God talk will state that the limits are indefinable; but again, another post!

    Bill: I’ll throw my hat into the ring on that one on the post I’ll write on ambiguity!

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  13. (I would also say that just as it’s a bad idea to generally denounce a particular school of thought on the basis of its ‘essence’ or general features, by that same token neither that ‘essence’ nor its general features should be used to generally support it either. On a similar theme, to Alec, I would say that Derrida’s Of Grammatology (to pick one piece, and even if it might ultimatelty be nonsense) is about as rigorous a piece of philosophical writing as there is, whilst Kripke’s Wittgenstein on Rules and Private Language (to pick one piece, even if it might ultimately be nonsense) is about as unrigorous a piece of philosophy as you’re likely to find. The point being not that Derrida’s method is always more rigorous than Kripke’s, but that (if you agree with me about the texts respective rigour, which you may well not!) the analytic tricks are not themselves guarantors of rigour. I would go so far as to argue that they don’t even necessarily increase the likelihood of rigour (though I’d need a wide survey of literature to substantiate that claim), but that just like you say, it depends on how competently (and, more importantly, appropriately) they are applied.)

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  14. ‘Does he choose salient evidence for his conclusions? Are the conclusions warranted by that evidence? Are the conclusions stated precisely enough for us to know what it would mean for us to disagree with them? Ward uses a range of strategies to make these questions too difficult for readers to answer confidently. The most identifiable of these strategies is the use of the central terms of his discussion—“belief”, “disposition”, “intentionality”—in a deeply ambiguous way, their connotations and implications shifting from page to page. Fallacies of equivocation, not to mention just plain non sequiturs, sing their siren song in every chapter.’

    From the recent Ward review. When I’m talking about rigour, I mean the opposite of what Ward is accused of. Do you really mean that it’s unclear what Kripke’s premisses are, and what inferential steps are supposed to connect them? Or do you just mean that Kripke is fundamentally mistaken about the nature of language? So long as it’s easy to home in on the mistake, then I’m not going to count Kripke as lacking in rigour.

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  15. Bill – I’ve followed your prompt and written a short post tring to clarify the conditions for good and bad precision in theological thought. I’m interested to hear everyone’s thoughts.

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  16. Also, it seems plausible enough that there should be higher-order mystery, by analogy with higher-order vagueness. Still, it would be helpful to discuss higher-order mystery with the same care that Williamson takes over higher-order vagueness.

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  17. You see, Alec, we’re using rigour in different ways; you specifically to refer to Analytic forms of argument, me to refer to arguments which seem to me to get closest to the truth of the matter. And both our uses are vague/ambiguous, insofar as mine is never going to rule out the potential validity of analytic methods, and yours can’t limit itself to analytic methods unless it wants to become completely vacuous (I.e. Saying nothing more than Analytic!).

    As it is, I’d say that Kripke’s text is manifestly unrigorous first because it takes very, very little care to ensure that it is accurately presenting the text it claims to derive (if not draw) its argument from (which is, after all, plausibly a text which argues against the rigorousness of contemporary analytic method, even if it was written in the 30s/49s) and its argument then proceeds on uncriticised presumptions of what something must be in order to be meaningful, or, in other words, an inappropriately applied formal definition. But there we go! I’ll try and get a fully fledged post about the value of ambiguity in philosophical discussion up soon.

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  18. (Sorry, that’s a ridiculously poor account of my use of the term rigour, and an example of when an analytic sensibility can come in use! More like something along the lines of: a practise is rigorous if it is consistent in its application of principles, is self-critical of the content of its principles, and/or is responsive to the nature of the subject matter at hand when deciding how to apply those principles. Again, probably more vague than you’d like, but I think that gets the matter across a bit better!)

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