Conditionals are Bad for Your Health: An Anthem

I often read that conditionals present deep philosophical problems. We’ve got to know what the real meaning of conditionals are, abstracts/forewords/grant proposals intone, and how to understand strict, material, indicative, subjunctive, counterfactual, probabilistic, suppositional readings of English sentences having the form “if…then…”, and how the modalities of tense, epistemic position, moral position fit together in them to effectively guide our practical reasoning, our decision making…to put order in our lives. What could be more important? Whitehead was wrong: Induction isn’t the scandal of philosophy, conditionals are.

And yet I don’t buy this, and neither should you. We see all manner of analyses and theories of conditionals, none of them living up to their advertised promise of explaining this supposed category of English expressions in a way that has anything to do with practical reasoning and decision making. This is because the theoretical category “conditional” in English is as pliable as a Texas congressional district.

There are many different kinds of relationships that we express with English sentences of the form “If…then…”. And when there is a risk of confusion, we turn to other devices to explicate what the item in the first gap has to do with the one filling the second. In a few situations where we use natural language technically (mathematical proof sketches, legal contracts, high-level programming languages are ready examples) we have more-or-less strict conventions for spelling out what we mean, catered to the kind of relationships we’re likely to need to express in a domain. For example,

  • In mathematical definitions ‘if’ often means if and only if, and when more details are needed, or when this convention might introduce confusion, the relationship is spelled out using a variety of other devices, such as specifying the properties of a mapping function on sets.
  • In legal contexts, by far the messiest of these examples, the use of technical conditionals is usually restricted to contracts and codes, not opinions or actual arguments (as far as I can tell). And court-tested contracts clipped and pasted into new ones, like syntactic decoupage, use variants of ‘if, then, else’ clauses, similar to a toy programming language. (On this my data is thin; corrections encouraged.)
  • In actual programming languages, there are compilers to deal with and bug reports to attend to when compiled programs produce garbage. Conventions similar to mathematics are followed, except here conditionals are typically condition-action rules to control the flow of the program, and algorithms are the items of meaning standing behind a natural language conditional like “If I click button 1, the annoying paperclip guy waves to me and goes away.”
  • In other words, in the cases in which it counts to be explicit about what a “conditional” means, we have developed technical devices and conventions for using natural language to deal with them. And in normal use? That is what conversation is for, which requires some negotiation between agents to work out a protocol for how much cooperation and precision is needed to get the message across. Precision for non-trivial information is expensive to craft, so there is natural economic pressure to accept as much imprecision as both you and your partner can tolerate; besides, if you carry precision to the limit you wind up not saying anything.

    The problem with the glut of philosophical accounts on natural language conditionals is the institutional habit of getting this relationship between natural language and formal accounts of things we do with natural language exactly backward. First screw down why you need the formal machinery, where it is that you, your machine, your business goes into the weeds with the language you’ve got. Then generate your theory to repair that problem, if nothing in stock will suit. Set up sign posts to warn passers-by of the hazard, or a school and guild if the hazards and economics line up, and introduce the tools available to deal with those hazards. And let that be that. Do not pluck sentences at random from English and expect a sensible analysis. Because parameters must be fixed, model builders will inevitably be mislead by accidental features of the example to think that the parameters they’ve fixed in their particular solution will scale and apply to a general account of “conditionals” of similar, but superficial, type. Then the corrections will follow from another blind man, feeling up the other end of this white elephant. Many trees will die. Tankers of ink spilt. Confused PhDs minted. And the western world as we know it will collapse from misallocated thought.

    This is to say that not only is the focus on conditionals hogwash, its harmful hogwash. Conditionals are bad for your health. By thinking that “if…then…” is a type of logical connective or, on more sophisticated views, approaching them with the thought that there are formal relationships between the gaps that map to the categories listed earlier, one is put in the perfect frame of mind to talk right past other people. Instead of asking what your conversation partner means, and using the full resources of natural language to try to answer, both are sent on a wild goose chase pointing and correcting one another’s grammar against intuitions about a phantom semantics. When there is a logic behind our “if…then…” talk, and often there is, people can say so, and switch to it directly, or use a pigeon-English keyed to this logic’s semantics. We can expand the variety of logics on offer by studying the implication fragments of formal languages, noble work that is actually good for your health. And useful for the guilds and schools.

    Most of the time we use English as English, and in technical contexts most of the time we use English as a metalanguage to get some grip on the general behavior of the proof, the contract, the algorithm. In doing so we need to exploit the full capacities of that natural language—and the wealth of information that is lodged in the language. But to look for the precise meaning of “if…then…” sentences appearing in normal English is in effect to cut the legs out from under you or, if you’re clever and amused by such things, out from under your opponent. It amounts to dragging you down into a weaker but unspecified language. It is the very essence of imprecision masquerading as precision. Which is unhealthy.

    To apply a formal method one has to be in a position to say what the model is supposed to do, which is not to confuse the practical assessments necessary to apply a model to a subject for the properties of that subject. (But pragmatic encroachment is a different song.) This built-in limitation is doubly important to remember when working with natural languages, since natural languages are much more flexible than formal languages. Each do very different kinds of things. Your formal model of English will throw out lots of features of English, particularly if you want that model to actually do something. If you’re a formal semanticist and only want models to point to, like specimens of meaning in a glass case, you can add attribute features to your model until your heart is content. This is important work. I’m not knocking it. But, if you want an effective guide to practical reasoning, decision making… a guide to life itself? Searching for the meaning of “if…then…” won’t do.


    Comments

    Conditionals are Bad for Your Health: An Anthem — 20 Comments

    1. Greg,

      I’m trying to understand the difference between the harmful enterprise,

      “By thinking that “if…then…” is a type of logical connective or, on more sophisticated views, approaching them with the thought that there are formal relationships between the gaps that map to the categories listed earlier, one is put in the perfect frame of mind to talk right past other people.”

      and the wholesome one,

      “We can expand the variety of logics on offer by studying the implication fragments of formal languages, noble work that is actually good for your health.”

      My suspicion: When all the details are in (particularly when we get to showing why we should care about “the implication fragments of formal languages”), the recommended, “noble” approach will eerily resemble the “harmful” one.

      Shooting from the hip while I await clarification, I will follow your lead and put forward my own (diametrically opposed, possibly simple-minded, but hopefully inspiring) slogans: Don’t despair, folks! We’re doing exactly what must be done. These are the growing pains. There’s *nothing* wrong with the search for the ultimate theory of conditionals. We have *no idea* what it would be like to do otherwise. We’re just mapping the territory at this early stage. (Don’t think decades or centuries; think millennia!) And we are – yes, we are – learning with the tumbles. The enemy is resourceful, yes. The enormity of the task does take its toll on our resolve at times. But what’s new?! Do we know any better than to seek integration, synthesis, subsumption, generality – and then more generality? [Add some silly smiling face – with a wink preferably.]

    2. Hi Claudio,

      The good I’m thinking of are mappings from various logics into other logics, or other branches of mathematics. The implication fragments of intuitionist, relevant, and linear logic into type theory; The behavior of guarded fragments of first-order logic; the theory of programming languages; relationships between mathematical models of decision. The list goes on. There are often general intuitions that motivate that drive these frameworks, to be sure, but there is no question whatsoever about what a conditional means within any of them. Or, better put, what open questions there are, are in the form of what theorems have yet to be proved about each, or whether in fact theory A maps into theory B. This type of work increases our understanding of the subject enormously.

      Also, I would add, a close look at dialogue systems are very instructive, since in effect they are exercises in effecting practical understanding by means of formal manipulations that friends of conditionals imagine a theory of conditionals to achieve. And computers don’t cheat: they do exactly what you tell them, and there is an enormous amount of information they call upon to manipuate what are in effect partially interpreted sentences. This is a very interesting area. (This might be the ugly, from one point of view.)

      The bad is starting from randomly selected bits of natural language and thinking that one of Good Works on conditionals will give you a proper semantics. And the assumption that slicing up the grammatical categories in natural language with map, somehow, to a constellation of Good Works. Or that it really does, but we just have to discover it. I’d call this a dogma. A mapping dogma, perhaps. It needs a name of some kind. The white elephant.

      Of course there is a very serious topic burried here, on which we should encourage hard work. My point is to pay attention to which end of the shovel you grab hold of. And to think a bit harder about what it is you imagine yourself to be digging for, and why.

      Or another way to put it: we should look over our shoulder at what we’ve learned from past failed attempts, which is an incredible amount, but incorporate those lessons without repeating the mistaken methodological idea that generated (most of) them.

    3. Thanks, Greg.
      I’m still baffled by your view of “the bad” and “the mistaken methodological idea”. I still don’t have a firm grip on the alternative. And, when I look at “the bad”, I still think we can use some more of it (probably much, much more). But I’ll keep chewing on it.

    4. Let me try another thought, hopefully without trying your patience. I’ll use Jon’s “Deliberations and Embedded Conditionals” post to illustrate. It is close by, fresh in mind. Recall the opening:

      Suppose you are deciding whether to do A or B, which are mutually exclusive. Suppose also that you believe the following:

      1. If p, then I should do A.
      2. If ~p, then I should do B.

      My suggestion is that we should toss a flag right here, because ‘If p, then I should do A’ is far too abstract a representation on its own. To even begin the discussion you must introduce assumptions about interpreting these sentences that aren’t necessarily true or, assumptions that are necessary to make but for which there is nowhere to represent them in this scheme.

      For example: I trust that A represents an action, but I have no idea what p is. After much typing we more or less agreed that “p holds” and your “believing that p holds” is an important distinction to untangle before going on. However, I think this is just the beginning of a very long list of attributes to untangle. There is tense, causality, my attitude toward risk, my moral position, my epistemic position, uncertainty, ignorance, default conditions on some or all of these: Attributes that have no expression in 1 and 2.

      My thesis is an empirical one, and I endorse it on my limited experiences with working on this subject and from my attempts to study patterns of failure. It is this: as you work through these attributes, the category that seems to be the subject of inquiry, “conditionals”, collapses, dissolves, does not behave well. Where many see this as a challenge, I see it as evidence of collapse and bad backbone behavior. The category itself, with its whiff of “if..then…” as type of logical operation, is an obstacle.

      And this shouldn’t be surprising. Natural language is very rich and flexible. Formal languages are very precise and rigid. Mixing the two is to invite a mess *unless* you specify the logic you are using the natural language to ape. The bad method is to use a semi-formal language to ape some logic or another, without specifying it, and then try to find this logic by studying your unconstrained intuitions about this aping behavior.

      There is another line of argument that’s run in first few sections of “Conditionals and Consequences”, a paper that I wrote with Henry and Choh Man last year. I preprint is on my research page. An argument there runs to the effect that even if linguists succeed in establishing that my empirical conjecture is false, that is, that there is in fact a stable and useful category called “conditionals” with some structure or another, the complexity of this formal object would make it entirely useless for the purposes of deliberation and inference.

    5. Greg, this is good!

      I should read your paper, of course, before venturing into the specifics of your view. In any case, I thought I’d give you the metaphilosophical background of my concerns. I hope I don’t stray too far from your interests in what follows – as I will try to bring the discussion closer to home for epistemologists (“mainstreamers”, I mean). You talk about a methodological mistake. That’s where the connection may emerge.

      There’s a view of the Gettier problem that spills into the wide open seas of grand metaphilosophizing. You will see exactly what I mean if you check out Professor William Lycan’s paper “On the Gettier Problem problem” (in Stephen Hetherington, ed., _Epistemology Futures_, Oxford UP, 2005, pp. 148-168). There, Lycan gives us his survey of the anti-Gettier Problem literature. I urge everybody to read this important paper. You will see that Lycan is not willing to give in to the doom & gloom crowd and accept either insolubility or unanalyzability or empirical inadequacy claims. (A notable omission among his targets when he considers insolubility claims is Luciano Floridi’s bombastic take “On the Logical Insolvability of the Gettier Problem”, Synthese, 2003.) That’s the good part, in my opinion. But there’s something in the way he resists that will seem just as bad to those who think, with him, that “there is nothing particularly wrong with the Gettier Problem” (that would indicate that the work on the problem is futile). In his reply to the Weinberg, Stich and Nichols (2001) view according to which “Gettier practitioners [are] pursuing only the minutiae of a concept possessed by some speakers of English” (p. 165), Lycan writes:

      “I reply: So be it… Now, I take very seriously the cynical suggestion that the Gettier concept is a philosophers’ artifact and does not represent anything possessed by ordinary people.”

      And he then makes a claim that is, for me (tortuously, perhaps), reminiscent of Frege’s description of “a [H]itherto [U]nknown form of [M]adness” (in the introduction to the _Basic Laws_):

      HUM: “No professional philosopher is qualified to make any pronouncement about the ordinary concept of anything, period…”

      (This is Lycan verbatim, p. 165. And I read him the way he himself, in note 2 of his paper, says he takes Gettier’s claim not to have taken any interest in the Gettier Problem literature: “I have no reason to doubt his word.”)

      So, we’re supposed to accept that, while philosophers claim to be providing explanations of certain phenomena based on commonsensical assumptions, they are actually only HUMming (that is, making their unqualified pronouncements…). And HUMming, of course, is some form of collective hallucination among professional philosophers.

      Now, involvement with HUM comes in degrees. Here’s an example of a very mild form of such involvement: Joe Cruz and John Pollock (1999) claim that “[w]hat the Gettier problem really shows is what a perverse concept knowledge is”. It’s a “fascinating problem”, according to them (p. 14). But they also think “it should be regarded as a side issue rather than as the central problem of epistemology”. From which, of course, we have it that the problem of how perverse the concept of knowledge is should be regarded as a side issue in the theory of knowledge. Go figure! And, while you’re at it, notice how their view of the matter is infected with HUM: Their reader is referred to Ruth Millikan’s (1984) and Stephen Stich’s (1990) “similar concerns about how contemporary epistemology treats knowledge”.

      I’m not ready to suggest that your view of what you take to be a methodological error in the discussion of conditionals is any form of HUM infection. But I thought I saw traces of a familiar form of gloom & doom there. And it was that suspicion that motivated my best impression of a general rallying the troops (my bright and sunny sloganeering in comment #1). HUM is bad! I mean, HUM is as bad as it gets!

    6. Claudio-

      This is a very quick reply to say thank you for your comments and that I want to give them more attention than I have time at the moment. My schedule is very packed for the next several days, but I hope to return to this soon.

      While it is true that arguing for a negative conclusion, particularly a meta-philosophical one is hard to keep in focus, I do hope to sharpen the point a bit and distinguish it from collapsing into a broader complaint like you mention. And precisely this kind of exchange will help. I think I had in mind Harman’s implication/inference distinction that isn’t nearly as clear as he makes it out to be, and is irritating for that reason, but, nevertheless, an extremely good tool to get people to think harder than they do about the relationship between logic and the psychological act of drawing an inference.

      His claim that there is no relationship between logic and inference is provacative and overblown, but not by that much. And I am deeply sympathetic to what I imagine his aim is pressing the point in as stark a manner as he does.

      I hope to reply soon. This is even quicker than normal. (I welcome comments from others too!)

      -Greg

    7. Thank you, Greg.

      I’m a huge fan of the Harman line myself, and I’m involved with it too in what I’m doing. But, yes, “overblown” is fair to the way he often talks about reasoning, logic, deduction and induction.

      In his 2004 book, David Christensen singles out this claim from Harman’s 1986 book and politely (maybe a little too politely) calls it a “dramatic conclusion”: “There is no clearly significant way in which *logic* is specially relevant to reasoning.”

      There is at best only incremental improvement in the following passage of Harman’s paper on “Rationality” (in his 1999 collection):

      “It is true that deductions, proofs, arguments do seem relevant to reasoning…It is an interesting and nontrivial problem to say just how deductions are relevant to reasoning, a problem that is hidden by talk of deductive and inductive reasoning, as if it is obvious that some reasoning follows deductive principles…All reasoning is inductive.” (pp. 28-32)

      WHAT?!!!!!!!!

      But, yes, there’s a precious lesson there, if you can see past the misleading bombast.

      As for being busy, there’s an angry mob of students clamoring for attention outside my office, and I’m afraid they can hear me typing!

    8. Precision for non-trivial information is expensive to craft, so there is natural economic pressure to accept as much imprecision as both you and your partner can tolerate; besides, if you carry precision to the limit you wind up not saying anything.

      Also, there’s nothing that limits that to conditionals. Tense usage, choice of pronoun, every bit of information that you intend to communicate is subject to the same consideration.

    9. Side note here: it was C. D. Broad, not Alfred North Whitehead, who referred to induction as “the glory of science” and “the scandal of philosophy.” I believe the quotation is from the end of his essay “The Philosophy of Francis Bacon” in the collection of his essays entitled Ethics and the History of Philosophy.

      Back to our regular programming …

    10. Thanks for your corrections, Tim and Aidan.

      Let’s see about sharpening my point about the role that interpretation plays in using formal methods in linguistic work on conditionals, and how this differs from attempts to regiment this interpretive step by some or another logical treatment of conditionals. This is intended to address Claudio’s worry, and perhaps Aidan’s as well. Let’s see.

      My examples are common “back-tracking” examples that linguists study, but I want to use them to highlight a methodological point.

      Consider a textbook example of a subjunctive conditional:

      (1) “If he stopped calling, then she would have told us.”

      (1) is textbook in the sense that the back-tracking effect of ‘would’ in the consequent seems to force a reading where ‘he stopped calling’ is presumed to be false. Notice that the tense of ‘stopped’ remains fixed in the sense that (1) expresses the idea that if at some point in time before now had been the moment that he stopped calling her, then she would have told us at some moment between that point and now.

      This formulation might prick the ears of tense logicians (say), and one could imagine proposals set on the assumption that (roughly) ‘would’ flips the truth value of the event in the antecedent but doesn’t mess with its tense.

      But then consider how the past-tense of the verb phrase in the sentence ‘he stopped calling’ is not preserved in

      (2) “If he stopped calling, then she would be more receptive.”

      (2) expresses the idea that she would be more receptive to him if he’d leave her alone, even into the foreseeable future. The back-shifting of ‘would’ here seems to target tense as well as truth.

      There is considerable linguistic interest to explaining what is happening in (1) and why it differs from (2), and I don’t want to go into that here. My point in raising these two examples is to highlight the general role that back-shifting plays in “conditionals”. The sentence ‘he stopped calling’ expresses different propositions depending upon whether it appears in the “antecedent” position of (1) or of (2), and this change in expression depends upon the tense of the verb in the “consequent” position. Logical connectives, note, do not back-shift. And that’s the whole point behind a function: it doesn’t back-shift.

      Still, we might think that these tense issues can be worked out since (1) and (2) do seem to follow a structure whereby the thing in the first gap of “if…then…” is presumed false, and the thing in the second gap is evaluated (roughly) under the supposition that first item is true. Perhaps that’s the main structure, and the behavior of (1) and (2) is a refinement on this picture.

      But then consider sentences:

      (3) If he had stopped calling, then she would have told us.

      which is a natural rephrasing of (1) and accords to the traditional account, but

      (4) If he had stopped calling, then she would have told us exactly what she did tell us.

      doesn’t.

      (3) is a classic counter-factual conditional: the sentence expresses that he hasn’t stop calling her, since otherwise she would have told us and she hasn’t told us that he’s stopped. The traditional account holds that the signature mark of a counterfactual conditional is when ‘would’ appears in the consequent position, which signals that the antecedent is presumed to be false. But (4) nixes this idea, since it expresses that under the supposition of his having stopped calling we would expect her to tell us and in fact she did tell us.

      My suggestion is that at this point the linguistic study of conditionals ought to make a clean and crisp break from philosophical studies and natural language processing techniques of conditionals. What linguists appear to be doing is to look at English sentences, interpret them, and then attempt to explain this interpretation by means of applying some formalism or another. And while interesting and important work, it is contentious because a theorist can think that the common structure of (1) and (2) ought to drive things, whereas another can think that (3) and (4) drives things, and another clever theorist can propose that really (2) and (4) are close pals but that there is more distance between (1) and (2) than everyone suggests. And on and on we go.

      If we restrict ourselves to looking at these proposals as devices for telling us something, indirectly, about how flexible natural language is, so be it. But if we think of these competing accounts as attempts to tell us what the interpretation of conditionals qua linguistic object actually is, this is to go looking for a white elephant

      I want to argue that this interpretive step that stands between English sentences like (1), (2), (3) and (4) and one or another formal frameworks that theorists use is a very important step. We are not reading off of the structure of the English sentences themselves.

      Some theorists talk of a speaker context, represented by possible worlds, and explain (but do not predict!) the particular back-shifting behavior in terms of an implicit quantification over those worlds that speakers intend to be relevant in order to get behavior like (1)-(4) to work out as imagined. This is to say that theorists imagine a relational structure to their interpretation of these sentences, constrained by the grammatical features of the sentences, and then try to model this within a formal language for relational structures (a.k.a. modal logic.) The second part of my objection is that even if a linguist succeeds in formulating a relational structure in some modal language or another, there won’t be any useful logical properties of this representation. Others like probabilistic machinery to explain our attitudes we take toward the item appearing in the antecedent and its relationship to the item in the second position. Again there are technical problems which force an enrichment of the framework that, even if it did succeed in overcoming the technical hurdles, would nevertheless not be at all useful for calculation.

    11. Greg,

      I’ve taken the bite you’ve offered and have choked on it. Earlier (#5), I just meant to sound a warning about the difficulty of establishing the kind of negative conclusion that you’re attracted to — the conclusion about a fatal methodological error in view of rampant disagreement — short of showing that you have a better explanation of the phenomena that is the yield of a different methodology. My warning alluded to an extreme claim made by Lycan. I suggested that you wouldn’t want to get close to that kind of claim — not unless you had an explanation for the astonishing implication that seemingly reasonable people can be afflicted with this persistent form of hallucination to be called “philosophy” for twenty-five centuries and behave as if they were making sense (progress) when discussing the *ordinary* concept of knowledge, the *ordinary* concept of “if”, etc., which Lycan didn’t offer. (Again, I can agree with almost everything Lycan says in that paper, but the remaining bit makes me lose sight of what I thought I was agreeing with!) I still have pretty much the same perplexity: Your claim about a fundamental methodological error by all (?) parties is the most ambitious claim I’ve come across w.r.t. the Vietnam of conditionals. This, of course, is not saying that you’re wrong — much less that there isn’t a whole lot to like in your post and comments on the issue. Which leads me to impose some more on you for help with the following, more specific difficulty.

      I’m thinking that I don’t know what’s wrong with William Hanson’s arguments in his paper “Indicative Conditionals Are Truth-Functional” (Mind, 100:397, 1991, pp. 53-72). I’ve searched high and low for a discussion of his arguments but I’m still empty-handed. By “high and low” I mean: There is no reference to his paper in the following works:

      D. Nute and C. B. Cross, “Conditional Logic”, in D. Gabbay et al., eds., _The Handbook of Philosophical Logic_, 2nd edn.;
      J. Bennett, _A Philosophical Guide to Conditionals_ (Oxford UP, 2003);
      D. Sanford, _If P, then Q_, 2nd edn. (Routledge, 2003; Hanson ignored in the new notes and supplementary bibliography);
      D. Edgington, “Conditionals”, in L. Goble, ed., _The Blackwell Guide to Philosophical Logic_ (2001).

      (Maybe that’s not much to indicate significance, or lack thereof, but it’s as far as I can go for the foreseeable future. I’m very nearly an amateur in these matters, and my creditors won’t let me have my fun.)

      I’m particularly disappointed to see that, having disposed of Grice and Jackson (or assuming as much), Bennett goes on to write: “The horseshoe analysis having failed, we must look further.” If I’m not much mistaken, Hanson’s arguments at least deserve a refutation.

      Now, I’m not giving CD readers a one-paragraph caricature of Hanson’s arguments here. In addition to recommending his paper to those who are attracted to your post, my purpose is to ask you: Hanson’s being right about indicative conditionals is incompatible with your being right about there being no “useful” category by the name “conditionals”, isn’t it? If we know as much about indicative conditionals as Hanson claims we do, then we certainly can use that knowledge in calculation and deliberation, can’t we?

      Lastly, I might as well take the opportunity to recommend J. F. Thomson’s masterful paper “In Defense of ‘[horseshoe]'” (ca 1963, posthumously published in The Journal of Philosophy, 1990). As Hanson notes, the kind of indirect argument put forward in Thomson’s paper can’t conclusively establish the identification of the indicative conditional with the horseshoe, but it’s undoubtedly a tremendous source of inspiration for the project. One of my all-time favorite quotations comes from it: “The logic allows it, yes. But that does not mean that we have got to do everything that the logic allows.”

    12. Thanks for suggesting Hanson’s paper, Claudio. I had not read it.

      In this paper he is assuming that there is a connective “→” for indicative conditionals, and argues that this connective has the same truth-funcitonal semantics as the “material” conditional, “⊃”. His stalking horses are Thomason’s conditional logic based on Stalnaker’s semantics, and the Relevant conditional in R.

      However, Hanson buries the lead. For in section 4, on page 64, he concedes that

      the indicative mood is not an infallible indication that a conditional is truth functional. The arguments of the preceding sections must be qualified to this extent.

      My point is this: Making this qualification is the whole ballgame for work on conditionals.

      So to compare my view with Hanson’s, I’d agree with him that many but not all English “conditionals” of indicative mood can be regarded as expressing a truth-functional relationship between the items appearing in the “antecedent” and “consequent” positions.

      Where we differ is that I think it is hopeless to ground the necessary qualifications in morphological features of English. (The most sophisticated views on the market take this point to heart; but then these accounts suffer from taking the Ramsey test too seriously, thereby making wildly wrongheaded predictions about “speaker commitments” that are involved when evaluating the truth of a conditional statement in English.)

      So my quick reply to Hanson this is this: “If A then B” is not a sentence in English, but I agree that English sentences of form ⌈ If A then B ⌉ sometimes are asserted to express that A only if B, where ‘A’ and ‘B’ map to some truth-function or another.

      I also think that English sentences of form ⌈ If A then B ⌉ sometimes are asserted to express a non-truth functional connection between A and B. “If the Lisbon bridge lights are turned on, I will see them from my house” expresses something other than either the bridge lights aren’t turned on or I will see the lights from my house.

      And ⌈ If A then B ⌉ can be used to express many other things: a conjunction of A and B, an invitation, one’s conditional intentions, and one’s uncertainty. Natural languages are flexible; and English is very, very flexible.

      I acknowledge that there is such a thing as conditional logics, each of which studies an intensional connective of some sort or another. And I think the study of these logics qua logics is very important. The mistake, however, is to think that the morphology of English is rigid enough to map different types of English “conditionals” to a constellation of conditional logics. (And perhaps this is a downside of doing translation drills into FOL and introducing students to Fitch-style natural deduction in introduction to logic, particularly if this is the only logic students are exosed to. It invites people to think in terms of “natural language friendly” logics, which leads to serious confusion.)

      I don’t think that “indicative conditionals” is a useful category for English. It isn’t the same thing as conditionals of indicative mood. You’ve got to interpret sentences of the language to get them into this imaginary philosophical category of “indicative conditionals” to even begin the debate Hanson is engaged in.

    13. Thank you, Greg. Your reply does help me see a little farther into this matter, and I hope you find something to think about in what follows.

      I’d expect us to quickly agree on these two points:

      (a) We may well be stuck in the proverbial half-full/half-empty-type situation (so familiar in philosophy). Looking at the very same data, one person sees signs of progress where the other thinks we should stop dignifying failure. Where I celebrate what I see as a step forward, you mourn for the distance to the finish line. And both views are equally legitimate and potentially helpful. The concession on p. 64 of Hanson’s paper didn’t bother me nearly as much as it bothered you. It’s consistent with his conclusion that “there is a large class of perfectly normal indicative conditionals that are indeed truth-functional” (p. 71). How much of a disappointment is that? Granted, it does make his title (“Indicative Conditionals Are Truth-Functional”) look somewhat like misleading advertising. I wish he (and the editor and referees for Mind) had toned it down a little. But we normally put up with flashy titles (like “Conditionals Are Bad For Your Health”), and we may even think it’s good to make them catchy when the author at least goes a long way toward delivering on the promise. If successful to the extent that he claims to be, Hanson makes a nice contrast with Bennett, for whom the horseshoe analysis *has failed, period* (as quoted in #12 above).

      (b) Your evidential situation has worsened — even if only a little. Without a doubt, the defense of your claim is weakened by *any* measure of apparent success in the analysis of conditionals. Never mind about *indicative* conditionals. Your original claim is about the whole category “conditionals”. The claim is better served by the bewilderment caused by that seemingly intractable beast, the subjunctive conditional, which is well-exploited in your comment #11. When it comes to Hanson’s large class of “perfectly normal indicative conditionals”, it would, without a doubt, have been *better* for your claim if you had been able to assure us that some of his arguments are fallacious. And you certainly would have so assured us, if the arguments had seemed fallacious to you. If they are not fallacious, maybe the knowledge they afford us can be useful in calculation and deliberation. The possibility does lessen the appeal of your claim.

      In addition, your reply raises some new questions for me. I’ll leave them here as they spring to mind, without trying to make them mutually independent. This will be rough, and it will be redundant. I can only hope it’s useful redundancy. I want to make sure I don’t sacrifice clarity for elegance.

      (c ) How about Aidan’s comment above (#9) to the effect that there’s nothing that is *essentially* about conditionals in your claim (apart from the obvious fact that you’ve made it *ostensibly* about conditionals)? Do you see your claim as a corollary of that familiar Fregean theme according to which grammatical form is a poor guide to logical form? Or is it meant to be something radically new?

      (d) Is your claim leading us to the compositionality-vs-holism debate? Do your claims generalize easily into a holistic view?

      (e) You write:

      ‘You’ve got to interpret sentences of the language to get them into this imaginary philosophical category of “indicative conditionals” to even begin the debate Hanson is engaged in.’

      Again, I’m haunted by the thought that we, somehow, *do* find ourselves very much in the grip of a concept of the indicative conditional. Is just reminding ourselves of our failure to come to grips with the behavior of every such conditional as philosophically conceived (just reminding ourselves of all that we have so far failed to understand about some uses of such conditionals) enough to establish anything as dramatic as your claim? Hansonian thoughts again: Haven’t we come too far to quit now? (Okay, these are the more rhetorical questions of the bunch — though not entirely rhetorical. There is this persistent perplexity: How amazing that we find ourselves collectively and reflectively transfixed by notions like the indicative conditional! It’s healthy to look into the possibility that there is some form of delusion involved, but hard to believe that there is.)

      (f) It seems perfectly reasonable to assume that there are situations in which what I mean when I say “If the Lisbon bridge lights are on, I can see them from my house” is *exactly* that either the Lisbon bridge lights are not on or I can see them from my house. Doesn’t it? I don’t see how admitting that there are those other uses in which one would mean more than that (uses in which one might, for instance, want to commit to there being some causal relation between events) gives any leverage to your claim. The theory must still allow me to express as little as I may need to express, mustn’t it? The context may well be such as to allow for reasonable doubt as to whether I mean any more than that not-p v q, and I may not be verbally skillful enough to prevent misunderstanding. (I don’t want to oversimplify the discussion of this point. This is just the roughest sketch of a familiar view. The point here is only that there is the truth-functional use.)

      (g) You write:

      ‘I acknowledge that there is such a thing as conditional logics, each of which studies an intensional connective of some sort or another. And I think the study of these logics qua logics is very important. The mistake, however, is to think that the morphology of English is rigid enough to map different types of English “conditionals” to a constellation of conditional logics. (And perhaps this is a downside of doing translation drills into FOL and introducing students to Fitch-style natural deduction in introduction to logic, particularly if this is the only logic students are exposed to. It invites people to think in terms of “natural language friendly” logics, which leads to serious confusion.)’

      The mistake part is clear enough – and hard to argue with on some interpretations. (It may just take us back to (a) above. And (a) is no catastrophe.) As for “natural language friendly” logics, isn’t that exactly what logic was about to begin with, and isn’t that what it *must* fundamentally be about? (To be honest, Greg, at first blush, that parenthetical remark sounds like what I fear I’ll hear when I cross the gates of hell! [Smiles, please!])

    14. Claudio,

      Thanks very much for your comments.

      (a) Perhaps the issue is how empty the glass is. To make it full, English has got to have properties that we now know that it does not have. In the last century we have learned an extraordinary amount about logic and natural language, and in the last few decades we’ve amassed a lot of experience applying logic to a variety of problem domains, including (but limited to) natural language. We should take stock of what we’ve learned.

      (b) My claim is that English conditionals are used to express all kinds of things, and that the categories of mood, tense, and aspect are too coarse to construct classes of “conditionals” that are imagined to be modeled by connectives or functions posited by various formal theories. You’ve still got to interpret sentences of English to get them into one of these artificial forms. Sometimes this is very clear. Other times it isn’t so clear. And the difference between clarity and unclarity does not ultimately rest on morphological features of English. So, I do not doubt that there are “if A then B” constructions used to express “A only if B”. Here is one: “If a is a member of B and B is a subset of C, then a is a subset of C.

      My point is to call attention to this interpretation gap. The picture is roughly this:

      Here is good-old first order logic, and he has some nice neighbors in the same zip code: intuitionistic, relevant, linear, default, conditional, modal, tense, hybrid, arrow, logic programming, paraconsistent, epistemic, probabilistic, and, on the other side of the tracks, the gated communities of types which includes a Church and a Curry house. And so on. This is Logicville. It is a happy place. Well run. Orderly. Norman Rockwell would paint scenes of it on a collector’s plate.

      On another continent lives natural language. It is cosmopolitan. There is dancing. Sex. Drugs. A metro. It’s a party here. Now, it isn’t that you cannot get from Logicville to the continent of natural language; you can. But there is a big bloody ocean between the two places, so you have to book passage on a plane or a boat to get from one place to the other, and it is expensive to do so. Plus, you’ve got to have a passport. And the exchange rates are murder. And they won’t let you take good meat or cheese from the continent back to Logicville. Which still disappoints me to no end.

      Philosophers, as a whole, tend to act like natural language and logic are neighbors, or live in adjoining towns. This is a mistake.

      So (g):

      As for “natural language friendly” logics, isn’t that exactly what logic was about to begin with, and isn’t that what it *must* fundamentally be about?

      No, no, no, no, no! It’s about an important fragment of mathematics. In so far as this fragment overlaps with natural language, your glass has liquid in it. In so far as it doesn’t, your glass is empty.

      ( c)(d) I’d add also that neither “and” nor “or” is truth functional in English. However, in general we use natural language “conditionals” to express a wider variety of relationships and operations than we do with “and” and “or”. So, yes, these points don’t apply simply to conditionals.

      W.r.t. Frege, the trend in linguistics over the last few decades has been to try to absorb pragmatic features into the semantics, by reifying “contexts” and “speaker intentions”. Actually, this is happening across the board, not just in linguistics. And this is very important. Studying very rich languages that effect this behavior helps a modeler to give some sense of the true costs of his abstraction of a problem into a formal language.

      But this experiment has gotten out of its cage, in so far as people think that these issues in sentence meaning need to be resolved *before* doing epistemology or epistemic modeling. This is why I classify this issue as a methodological point.

      We have learned an enormous amount about natural language, but we don’t need to *apply* this knowledge (or the techniques we’ve honed to unpick linguistic insights) to figure out our epistemic position or to assess what actions are reasonable to take given that position. On the contrary, making a fetish of natural language when considering these types of questions is exactly the wrong thing to do. It seizes obscurity from the jaws of clarity.

      (e) I think that most of the time we understand natural language just fine without recourse to logic. Or, perhaps better, this: it helps to study some mathematics to be aware of how truth-functional readings of “and”, “or” and “if..then…” work, just as it helps to know something about algebra and measures in general, and (I conjecture) our current generation will likely sort out and distill the CMU results on causation, which will help clarify what we mean when we use “if…then…” to express a connection between the first and second items filling these gaps.

      But, these are specific tools we’ve developed to add-on to natural language, not accounts that explain the meaning of constructions in natural language.

      (f) Most of our actual use of natural language “conditionals” is for asserting non-truth-functional relationships between events. Otherwise the mathematical reading of “if…then….” wouldn’t be as difficult to impart to students as it in fact is.

    15. Greg,

      I was ready to conclude that our difference of opinion was just a minor quibble between like-minded philosophers. But you’ve now given me five no’s in response to a non-negotiable claim. And there’s no part of five no’s that I don’t understand! Yet, I can’t help thinking that you’re letting the misleading title of your post punch you senseless into a corner from which no good philosophy can emerge. One can overdose on grandiloquence, you know. It’s known to happen to best of us. (Remember the author of the _Tractatus_?) You’re sounding more and more like a historian. The more historical you go, the less exciting you become from a philosophical point of view. We like history too, of course. All right, we love it. But there’s a precious philosophical point getting lost in the rough and tumble of this discussion. It’s almost buried now under the thick layers of history that you’re wrapping yourself in. With that, I can’t cooperate. I’ll pursue that point for another mile.

      Here’s a true story we can use. I pick up a copy of Discover magazine and glance at the “Letters” section. I see readers reacting to a report on the perils and costs of a manned flight to Mars. A confident Mr. H, of Small Town, Missouri, pithily opposes the idea as follows:

      “If Mars were inhabitable, then it would make sense to send humans there, but it isn’t, so it doesn’t.”

      (As you can see, Mr. H would gladly accept the weakening of his conditional. He clearly wouldn’t be bothered. He would trust the refurbished argument all the same.)

      In reply, a Mr. C, dubbed “deputy chief scientist at NASA’s Space Life Sciences division”, a supporter of the manned flight proposal, has no difficulty accepting Mr. H’s premises and rejecting his conclusion. Habitability is not decisive, Mr. C briskly notes — and then proceeds to trample over Mr. H’s lifeless body.

      I’m sure you understand Mr. H’s plight. He thought he had *conclusively* established that a manned mission would be folly. He put all his logical might to the task. He might very well have agreed to disagree with anyone who rejected either of his premises. Anyone can do that. Moreover, the impressive Mr. C might have come up with evidence that Mr. H doesn’t have. Had C produced the new evidence, H might have easily changed his mind. But C granted the premises! H surely expected the all-mighty Logic, that pillar of Western civilization, to do what it is supposed to do. “Is C an imbecile?” — you can imagine a befuddled Mr. H asking himself. Next, he will certainly refrain from concluding that the impressive C is an imbecile. Confusion will deepen. Mr. H will grow obsessive, discombobulated, anti-social, unsure of his sanity. He may turn suicidal.

      I can help Mr. H. And you know exactly how. I’ll take him on a guided tour of Logicville. We’ll take a long stroll on Main Street, where I’ll tell him about Philo and Frege. Then, we’ll be ready for that obligatory stop for tourists coming to the Greater Logicville area, the Gricean Lounge in Pragmaticsville, right next to Thomson’s Fish & Chips. We’ll have a coffee with Walter Sinnott-Armstrong, James Moor and Robert Fogelin (“A Defence of Modus Tollens”, Analysis, 1990). Roy Sorensen may show up later. Tim Williamson may drop by. A rehabilitated Mr. H will have seen the error of his inferential ways. He’ll go back to his continental community a new man, no longer subject to humiliation. He’ll be ready for a career in philosophy too (his head abuzz with good problems).

      Is there anything you can do for Mr. H, anything consistent with the claim that conditionals are bad for Mr. H’s health? Sorry! Just noting that

      “In so far as this fragment overlaps with natural language, your glass has liquid in it. In so far as it doesn’t, your glass is empty.”

      or noting that “most of the time we understand natural language just fine without recourse to logic” is not good enough. I suppose you would say that Mr. H just got lucky, because our glass has liquid in it this time. Is that it? Would that mean that conditionals are sometimes good for Mr. H’s health?

      You write:

      “[T]his experiment has gotten out of its cage, in so far as people think that these issues in sentence meaning need to be resolved *before* doing epistemology or epistemic modeling.”

      But who’s sitting and waiting? Anybody in epistemology? I’ve always thought that epistemologists were getting ready to seize control of Logicville! We call our beachhead “Pragmaticsville”. (Good to see we can count on you when our orders finally come!)

      I also have a problem with your history of Logicville. It has to do with the Rockwell joke.

      Let me use a popular metaphor. (This one is for you, Keith DeRose, with my regards.) Frege was the Beatles. Russell was Bob Dylan. In reply to Frege’s “I wanna hold your hand”, Russell had no choice but to come up with a bitter “You’ve got a lotta nerve to say you are my friend”. He looked deep into the eyes of the beast. It wasn’t just the concepts of class and predicate at stake (as if that weren’t bad enough). He put the concept of truth under siege too. He was in a position to write “Logic Is Bad For Your Health”. Frege gave him a written permission to do so. Instead, he put all those years (between the _Principles_ and _Principia_) into trying to find a philosophical launch pad for that flying bathtub, the ramified theory of types. He could have left Logicville burning and become the king of continentals. Instead, he taught us to accept complexity and chin up. (“There must be some way out of here, said the joker to the thief…”) Does that look like a Rockwell character? Logicville is no Rockwell landscape at this point. Was it ever? Frege warned that grammatical form is misleading. Do we really need any sobering up?

      Sometimes it sounds like you would advise the authorities on the continent to sever diplomatic ties with Logicville, impose a trade embargo. That would be a bad mistake. We’ve thrived on imports from Logicville. You’ve emphasized the dancing, the sex, the rock’n’roll, all the good stuff that the continent is known for. You forgot to mention the bloodbath on the streets, the zaniness, the worship of idiocy, the gullibility, the predators of the innocent, the snake oil peddlers. Here’s a story of continental horror by Robert Fogelin ( _Walking the Tightrope of Reason_, pp. 36-38):

      “I once found myself in a room of advanced thinkers where I was the sole person with a good word to say about the law of noncontradiction. As a result, I was subjected to a great deal of ridicule and abuse. I tried to explain…that, in rejecting the law of noncontradiction, they were, in all likelihood, not rejecting the principle itself but instead rejecting a false picture that they mistakenly associated with it. They would have none of this — hell-bent on performing a slam-dunk against logophallocentric Western rationalism, they would accept no such temporizing compromise. In exasperation I finally employed what is called an impolite ad hominem. I asked whether the organizers of the conference were applying for future funding from the National Endowment for the Humanities. When some indicated that they were, I asked if it would make any difference to them whether the answer to their request was no rather than yes, and if so, why? Not surprisingly, this produced a reaction of rage.”

      As Fogelin notes, he was lucky on that occasion:

      “None of this will move anyone who genuinely opts for silence or for madness…[M]any so-called postmodern thinkers exist quite beyond the reach of intellectual embarrassment…”

      We’re keeping Jerry Lee, of course. And we’re definitely not giving up on the sex. But don’t forget Mr. H. For my part, I’m keeping both, Hanson and Wheeler. I have no doubt that both are good for *my* health. But, when it comes to helping Mr. H, I’ll be telling him about Hanson *first*. Then, after I see his answers to those exercises, I may tell him about Wheeler. I hope you understand.

    16. Thanks again for you comments, Claudio.

      It is a mistake to think that logic must fundamentally be about natural language. It is about the language of mathematics. Logic can be used to represent all kinds of things, including some (but not all) natural language arguments. But it must follow the same rules of use that are in place for applying other branches of mathematics to non-mathematical domains. Bad philosophy, not to mention bad science and bad engineering, follows from ignoring the basic principles for applying formal methods.

      The most charitable reading of H, which is apparently C’s reading given his reply, is that Mr. H thinks that habitability is a necessary condition for sending astronauts to Mars, and NASA’s C says that it isn’t.

      We *can* rearrange H’s sentence into a logical form that expresses this relationship. We *cannot* find all of the grounds for this reasonable encoding in the morphology of English “if…then…” sentences. This is the main point.

      My other remarks were attempts to explain how we got to the state that we are in with respect to logic and language. There is a built-in limitation in how logic is taught to undergraduates in most places. It is a pedagogical trick to “linguistify” logic for introductory students, and it is probably one that I will also continue to use until I think of something better that students will tolerate. And there are very sophisticated *uses* of logics by linguists, too. My worry is that students exposed to the simple introduction who then see these tricked-out linguistic models, armed with a bit of Grice, might then think that this is the core business of logic. And it isn’t.

    17. Thank you for your patience, Greg. It’s been a very enjoyable and informative discussion for me.

      Let me just take the opportunity to add a quick PS.

      I’ve thrown the name “Grice” around in what may seem like a happy-go-lucky manner to some readers of Wayne Davis’ _Implicature_ (Cambridge UP, 1998). I should add that, to my mind, the *historical* Grice does not survive the onslaught of Davis’ arguments. But I also think there’s an important non sequitur in that book. Here’s what Davis thinks he is entitled to claim:

      “With the blinders off, we can see that the most familiar facts about implicature have not even begun to be explained. The goals of science have not been achieved. The illusion of understanding provided by the Gricean theory has only served to stifle inquiry… I raise many fascinating questions about implicature, requiring systematic historical and sociolinguistic research for their solution, which did not and could not arise when the Gricean theory held sway.” (p. 3)

      I’m not pursuing the matter. I just want to add that I think Davis’ anti-Grice case is very good. But I can’t see that it is nearly as good as he claims in that passage.

    18. I enjoyed the exchange, Claudio. It was nice to try out a few different lines of argument on this topic.

      A post script on contextual features: some may see positive evidence for recent trends in epistemology in my remarks on the interpretation gap between “if…then…” sentences and one or another logical conditional, or even one or another interpretation of conditional probability. A broad trend in applied logic is to create semantic representations of features that were once pragmatic features, after all, which shows up in linguistics, game theory, epistemic modal logic, dialog systems, and is a pillar under the growing field of multi-agent systems…which arguably is the new name for ‘Symbolic AI’. “Contextualism” is a child of many fathers.

      But I would caution against getting too carried away with errecting heavy philosophical positions, particularly in epistemology, on this shift of the semantic-pragmatics border. It is a terrific technical device that has many good uses, but it doesn’t get around this interpretation gap that is behind the point on conditionals. Tasking this type of view with explanatory tasks makes otherwise reasonable choices appear arbitrary, since we’ll be looking for mechanisms in the framework to explain why this structure is the right one instead of that one.

      The slogan I mentioned in another thread is worth repeating, if only to help keep one’s eye on the prize: we are primarily interested in questions about our epistemic position, not questions about how we talk about our epistemic position.

    19. “The slogan I mentioned in another thread is worth repeating, if only to help keep one’s eye on the prize: we are primarily interested in questions about our epistemic position, not questions about how we talk about our epistemic position.” (#19)

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