Assessing Epistemic Modals

Draft paper, here.

After critically examining contextualism and relativism (MacFarlane's view) about epistemic modals, I propose an approach I call 'the dimensions of assessment approach'. Comments welcome.

Twenty Remarks on Necessitarianism and its Negation

Disclaimer: the following remarks are highly exploratory and are not to be read as expressing anything final. 

1. What is the status of the claim with which Lewis begins On the Plurality of Worlds? (That there are other ways the world could have been other than the way things are.) We have a tendency to hear it in the wrong key. Imagine someone who had lost a loved one saying 'Things really could have been different'. (There seems something self-deluding in this, although it is no ordinary self-delusion. You don't fix it with negation.)

2. Ayer, Carnap and others wanted to say: the necessities fall out of our linguistic/conceptual scheme. Codify 'the rules of correct English' (cf. Language, Truth and Logic) and you've codified the necessities (or a base from which they may be logically derived). But the Kripkean necessary a posteriori, semantic externalism etc. make it clear that one needs a lot more fine structure than 'rules of correct English', and that some structures are in some sense not correct, in a way which has nothing to do with internal incoherence, but rather to do with inadequacy to an external referent. 

* * *

3. 'I went to X, but could have gone to Y instead.'

How might such a proposition be used? A retrospective epistemic use. Or to point to various facts - e.g. that Y wasn't too far away, or that I was under no compulsion to go to X, or that I was seriously considering going to Y, etc. But what if I say that none of that is quite to the point? 'Sure, those things might be true, but over and above that, I'm saying that I really could have gone to Y. The world could have gone differently here, and my going to X was just how it happened to turn out.' What could this mean? (We can imagine someone being bothered, preoccupied, by the thought that things really could have gone differently.)

4. Consider these propositions:

(1) There are things which could have gone otherwise.

(2) There are contingencies.

When a philosopher asserts (1) or words to that effect, typically the reaction they want is 'of course!'. Now, this would happen sometimes, but more common among non-philosophers might be perplexity - 'what do you mean?' - and skepticism - 'but how do you know?'. (I have some experience of this.)

5. Both in and out of serious philosophy, there is a tendency to take (1) and (2) in what I would call the wrong way. Roughly: as though they described something extremely fundamental and general about reality. And yet that is not an entirely wrong-headed thought, for it is immensely important that we talk and think about non-actual scenarios.

6. It is as though, when someone pushes a statement of counterfactual possibility in a certain way, we take them to be making a very strong claim, quite beyond our ken.

7. When one hears (1) and (2) in an "inflated" way - whatever that comes to - necessitarianism can seem like the antidote: something wrong has been said, and so it should be denied. But then the denial turns out to be just as troublesome, if not more! (Now it is trivially false, instead of trivially true - like Idealism in relation to Realism.)

8. The disease is not fully containable in any one proposition. 

* * *

9. It can be very important to realize that some propositions are necessary - 'One cannot feel another's pain', 'The opium worked (if it worked at all) by means of a dormitative power'. Likewise, contingent - 'There are two sexes', 'We have one body each', 'We use the decimal system to count'. It can be very instructive to get clear about the "modal status" of these things. And of course this does not mean leaving the view that they are contingent (or necessary) and coming over to the other side, but rather: noticing something, which one might have been quite blind to. Think of the conceptual development of children - one cannot truly say that they go through a phase of believing that everyone knows the same as them, but we can see what this is getting at. In the place where we have a fundamental distinction or concept of great importance in adult life, they do not have anything to speak of.

10. So: it can be important to realize the modal status of certain propositions. But - and this is crucial - it does not at all follow from this that it is important, desirable or possible to draw a line which clearly divides all propositions according to modal status.

11. What is the modal status of 'Our conceptual scheme has moving parts'? I.e. how could anything else be a conceptual scheme? (Mind of God.) And yet the proposition easily acquires the flavour of a general fact of nature. Why? Well, lots of important facts lie immediately underneath.

* * *

12. The notion of the mind of God. It can look as though everything is an approach to this ideal, and yet we have absolutely no grip on the ideal. We (i.e. myself and most active philosophers) do not have any positive belief in the mind of God in the old sense, and all the minds we do believe in are completely un-Godly.

13. Our conceptual scheme has moving parts. But if God knows all, he doesn't need any moving parts. (Spinozistic necessitarianism, Leibniz's difficulties.)

14. So now it looks like, in a sense, the ideal conceptual scheme has no moving parts - no need to dance further with experience or reason. And yet we will always need a conceptual scheme with moving parts, and can really make no sense of anything else. Thus how could the mind of God be our ideal?!

15. From this perspective, one could imagine pantheism as a kind of scholastic solution to our present problem. (For it would block the assimilation of our mind with God's.) ('A full, non-redundant model of an object must be a duplicate of the object, or the object itself.')

16. We say things could have been otherwise - I could have walked somewhere else today. But then someone says 'but could that really have happened?' and it's like the stakes are raised somehow. But isn't this a shift to a more specialized modality?

17. "What makes you think things could have really been different, and that this isn't just a function of our ignorance?" - The first thing to say is there's no simple answer here: one can't just point to evidence. The question is symptomatic of something.

18. One pernicious kind of confusion when talking about metaphysical necessity - the modality identified, and separated from other concepts, by Kripke - is to think of it in a manner which would be appropriate for some kind of deep and remote form of retrospective epistemic possibility. This is illustrated by the notion of the Creation as an event. God did something, and it may have been reasonable to expect this to go various ways. It is important for our concerns here that such an idea is natural to some degree.

19. It is possible to feel that any kind of conceptual view of necessity, even if we grant everything to the concepts including external adequacy, somehow makes modality flimsy, shadowy - somehow still overlooks reality in some way. "The way things really could have been, concepts aside." (The notion of an inconceivable object. If such a thing is impossible, how is that not just a piece of luck? Thus it can seem that the conceptualist must rely on some kind of pre-established harmony between possible concepts and possible realities, which would of course be highly suspicious.)

20. There is a strong philosophical tendency to think of knowledge of how things must be as penetrating deeper into the world than mere contingent knowledge. As though we saw how a machine behaved, but then looked into its workings and saw that it had to behave that way. Or, we form a hypothesis about the workings based on, and in order to make sense of, the behaviour. (This gets us into difficulties, but it would be stupid to call it incorrect - or correct for that matter.)

For more on modality see here, here and here.

Toward an Understanding of De Dicto Subjunctive Necessity (draft paper)

Here. UPDATE March 2013: This document has been completely superseded by An Account of Subjunctive Necessity.

UPDATE March 2014: This latter document will in turn be superseded soon by a forthcoming blog post which will fit together with other posts.

A Plea for Conceptual Schemes

Introduction 

In 1974, Donalad Davidson published a now famous paper entitled 'On the Very Idea of a Conceptual Scheme', in which he attacked that idea and exhorted the reader to give it up. One reason Davidson set upon this idea was his evident hunch that it lay behind the pernicious, nebulous doctrine of the relativity of truth. Another, perhaps more fundamental, reason, was his desire to see the world and our understanding of it in terms of a metaphysics of sentences and objects, without employing things like concepts and propositions.

I think the idea of a conceptual scheme a highly serviceable one, and that Davidson's attack is confused. I believe that the idea of a conceptual scheme has a good deal of unrealized potential in the philosophy of modality and many other areas. My object here is simply to vouchsafe the idea from Davidson's attack. 

 

The Problem of Comparison and Neutrality

Early in his paper, Davidson makes this remark, which goes to the essence of his attack:  

[T]here is no chance that someone can take up a vantage point for comparing conceptual schemes by temporarily shedding his own.
(Davidson 1979/1984, p. 185. Page references are to the 1984 version.)

This is true, but misleading. True, because we cannot do anything by temporarily shedding our conceptual scheme - the immediate reason being is that there is no such thing as 'temporarily shedding our conceptual schemes' in the required sense (i.e. while retaining some kind of rationality or sentience). Misleading, because it seems to carry the implication that scheme-shedding would be the way we ought to proceed with a comparison, if only this were possible.

Against this, I want to insist that the only conceivable way we could compare two conceptual schemes is from within our own. We have a conception of the world (surely!). Part of that conception is the idea that there are conceptions - of the world, in the world. We are self-conscious. We think about our thinking and that of others, and when we do this we employ our conception of our own conceptions, and our conception of others' conceptions.

Of course, if we compare our conceptual scheme with another, our ideas of these two schemes will not be on a par epistemologically. This difference cannot be factored out. However, we should try to be as objective as we can, and this means trying to improve our conception of our conceptions, and those of others, and the relations between them.

Davidson, on the other hand, apparently has some idea to the effect that, as long as we are 'stuck' in our own conceptual schemes, comparison will be impossible or at the very least greatly hampered. Indeed, some notion of being stuck seems to lie at the root of this part of the confusion.


'The Dualism of Scheme and Content'

According to Davidson

[the] dualism of scheme and content, of organizing system and something waiting to be organized, cannot be made intelligible and defensible. It is itself a dogma of empiricism, the third dogma. (p. 189.)

Now, I do not want to argue with the claim that no dualism between scheme and content could be made good sense of. Rather, the point is that no notion of a dualism is called for to support the idea of a conceptual scheme.

In our ordinary ideas of 'scheme and content', I should think, it is understood that the scheme itself is potentially part of the content, and parts of this potential content - such as concepts - inhere in the scheme.

Simply put: There is no dualism of scheme and content. A distinction is not a dualism.

The idea of a dualism of scheme and content is bound up with a fundamental misunderstanding of the 'content' part of that idea, arising from a certain picture we possess of the situation, and an attitude toward this picture which most of us, in certain circumstances, are strongly inclined to take. (Cf. the notion of the thing-in-itself.) While this phenomenon is of fundamental importance in parts of philosophy, I maintain that it is not an essential part of our practical understanding of the idea of a conceptual scheme. On the contrary, and as the existence of Davidson's paper shows, it can be an obstacle.


The Problem of 'Uninterpreted Reality'

Davidson wants us to give up 'dependence on the concept of an uninterpreted reality, something outside all schemes and science'. The great unclarity here is: what do the phrases 'uninterpreted reality' and 'something outside all schemes and science' mean in this context?

As suggested in the previous section, the 'content' or 'world' term of the conceptual representation relation need not be thought of as some amorphous fundament, some uninterpreted thing-in-itself. We live in the world - in reality - and we interpret it. Reality, since we are real and interpret it, just is interpreted; there is no reality which, as a whole, is completely uninterpreted.

What about parts of reality? The particular objects, events and processes which intelligent beings talk and think about are parts of interpreted reality - parts of reality which get interpreted. Thus my desk is part of interpreted reality, as are Denmark, Donald Davidson, Beethoven's Ninth, Saturn and many other things besides.

It is quite commonly believed, in our culture, that other parts of reality are uninterpreted; if some small pebble somewhere has never been apprehended or encountered in any way by an intelligence, then this individual is, in some sense, part of uninterpreted reality. Quite obviously, this is not the sort of thing Davidson means by 'uninterpreted reality'.

We might instead take the phrase 'uninterpreted reality' to mean 'reality considered separately from any interpretational or conceptual apparatus'. Then surely this can include chairs, tables, and the rest of it. ('Considered separately from interpretational or conceptual apparatus' obviously doesn't mean 'considered without recourse to any interpretational or conceptual apparatus'.) So this doesn't seem to be what Davidson means, either.

Regarding the phrase 'something outside all schemes and science': isn't the desk I am working at now outside all schemes and science? Surely my desk is not inside a conceptual scheme, or inside science (whatever that means).
 

The following passage from Rorty, who enthusiastically embraced Davidson's critique of the idea of conceptual schemes, gives us more to work with:

The notion of 'the world' as used in a phrase like 'different conceptual schemes carve up the world differently' must be the notion of something completely unspecified and unspecifiable - the thing in itself, in fact. A soon as we start thinking of 'the world' as atoms and the void, or sense data and awareness of them, or 'stimuli' of a certain sort brought to bear upon organs of a certain sort, we have changed the name of the game. For we are now well within some particular theory about how the world is.

(Rorty 1982, p. 14.)

I deny the first assertion. The notion works like this: we use our conceptual schemes and understand there to be chairs, tables, numbers, quarks, experiences, concepts and schemes thereof. Then we form an idea of different schemes carving up the world differently. Here, our idea of the world is still our idea of the world, i.e. an idea of something which contains chairs, tables, numbers, quarks, experiences, concepts and schemes (among who knows what else).

In a strange way, Davidson and Rorty seem to make the very mistake they appear to be warning against. In saying queer things about 'uninterpreted reality', they try to identify a thing we can't say anything about. Or: they try to give the content of a notion they want to criticize, but in so doing they only embroil themselves in the confusion which bothers them. It is this confusion, I believe, which leads Davidson and Rorty to loudly and violently reject the idea of a conceptual scheme. They reached for the saw; I suggest we consider a scalpel.

Tristan Haze

References

Davidson, D. 1974. 'On the Very Idea of a Conceptual Scheme', Proceedings and Addresses of the American Philosophical Association, Vol. 47, pp. 5-20.

The above reprinted 1984 in Donald Davidson (ed.), Inquiries Into Truth and Interpretation. Oxford: Oxford University Press.

Rorty, R. 1982. 'The World Well Lost', Consequences of Pragmatism, Minneapolis: University of Minnesota Press.

Deduction and the Necessary A Posteriori

Consider: There is a cat here, therefore there is an animal here.

Assuming we want to say that this inference is valid in some sense, here are three things we might say about it:

1) It is an elliptical argument, involving an unarticulated premise, namely that cats are animals.

2) It is an enthymematic or gappy argument, involving unarticulated reasoning.

3) It is a complete argument in itself - neither (1) nor (2) is the case.

On the first approach, the deduction is clearly a priori. But this is not the only possible attitude. While the belief that cats are animals could conceivably be overturned by experience, it is arguably not a contingent fact that all the cats around are animals (cf. Kripke 1980). So rather than regarding this as part of the matter being reasoned from, we might regard it as part of the deductive apparatus.

Thus, on the second interpretation, we might regard the move from 'cat' to 'animal' as being licensed by an unarticulated principle of reasoning (which may be expressed in the form of an inference rule, or an axiom such as 'All cats are animals'). Or we might resist even this, and say that nothing is unarticulated - perhaps still allowing that the argument can be justified by the principles of reasoning which are held to be unarticulated on the second interpretation.

Note how natural these latter two approaches are; there does seem to be some sense in which the conclusion follows from the single articulated premise. Note also that the argument by itself satisfies the natural (admittedly problematic) modal characterization of validity, if we take the relevant modality to be subjunctive or metaphysical modality ("what could have been the case") rather than a priori possibility or epistemic modality ("what could be the case"): it could not have been the case that there was a cat here yesterday but no animal here yesterday.

This may suggest that, according to some intuitive and central concept of deduction, some facts about what can be deduced from what are empirical (i.e. not knowable a priori).

However, this flies rather completely in the face of previous philosophical thinking about deduction. It also raises the following puzzle: on one way of thinking about necessity, our holding it to be necessary that all cats are animals means that we have made a certain kind of connection between our cat-concept and our animal-concept (an empirically defeasible connection, held constant when describing counterfactual scenarios). But it is natural to think of this conceptual connection as partly constitutive of the content of thoughts involving these concepts - thoughts such as 'There is a cat here' and 'There is an animal here'. Thus, someone who doesn't have such a connection arguably isn't in a position to have those two thoughts at all: there would appear to be little room for them to have those exact thoughts and yet not be able to work out a priori that one implies the other.

My suggestion is that, when faced with this sort of puzzle, one should try to distinguish different ways of individuating content, some more fine-grained than others. When talking about thoughts in, e.g., the context of communication, a relatively course-grained individuation scheme is often most appropriate. When talking about the epistemology of deduction - and not just the epistemology - a more fine-grained approach is called for. (That is, an approach where what are for many purposes two instances of the same thought get treated as distinct structures.)

Insofar as this is right, the more general moral is perhaps something like: when doing philosophy, be willing to put multiple modes of content-individuation on the table - don't let one obsess you to the exclusion of all others.

Tristan Haze

Reference

Saul A. Kripke (1980). Naming and Necessity. Harvard University Press.

An Analysis of Davidson's Slingshot Argument

There is a peculiar kind of logical fallacy which, ironically, is only committed by people who have an acquaintance with formal logical theory. Fallacies of this kind arise when principles of inference from formal logic are applied inappropriately to arguments carried out in a natural language.

Here I make a case-study of Donald Davidson's famous version of the Slingshot argument against facts. The argument, in its dialectical context, is meant to show that if true statements correspond to facts, then every true statement corresponds to every fact. Davidson tries to demonstrate this conditional in order to motivate us to give up its antecedent (that true statements correspond to facts). Here is the argument:

The confirming argument is this. Let ‘p’ abbreviate some true sentence. Then surely the statement that p corresponds to the fact that p. But we may substitute for the second ‘p’ the logically equivalent “(the x such that x is identical with Diogenes and p) is identical with (the x such that x is identical with Diogenes)”. Applying the principle that we may substitute coextensive singular terms, we can substitute ‘q’ for ‘p’ in the last quoted sentence, provided ‘q’ is true. Finally, reversing the first step we conclude that the statement that p corresponds to the fact that q, where ‘p’ and ‘q’ are any true sentences. (Davidson 1969, p. 753.)

Let us go through it bit by bit.

The first apparent inference in the argument is curious. 'Then surely' suggests that reasoning is taking place here, but from what? Apparently:

Let ‘p’ abbreviate some true sentence.

But that is an instruction, not something we can infer from at all. This shows that what Davidson has supplied is not an argument, so much as a recipe for making one. And since this first step is not an inference, it can't be a fallacious inference. Still, in its slightly confusing use of a technique from logic (in this case, schematization) it gives us a small taste of things to come.

Now, following Davidson's recipe, we shall let 'p' abbreviate 'snow is white'. For perspicuity, we shall not use these abbreviations in our writings-out of the steps of the argument. (Surely this could not affect validity.) Thus our first real premise is:

The statement that snow is white corresponds to the fact that snow is white.

Now we are told we may make a substitution, yielding:

The statement that snow is white corresponds to the fact that (the x such that x is identical with Diogenes and snow is white) is identical with (the x such that x is identical with Diogenes).

The first thing to note about the above is that it doesn't obviously mean anything. This should make us suspicious. After all, we are not supposed to be merely calculating with signs here. This is supposed to be an argument - a reasoned chain of statements leading to a conclusion. How did we get to the above sentence, then? There are two things Davidson needs us to accept if we are to go along with this inference:

(1) That it is valid when arguing in English to substitute, for a sentence, a logically equivalent sentence - even when this sentence is embedded in a larger one.

(2) That 'snow is white' is logically equivalent to '(the x such that x is identical with Diogenes and snow is white) is identical with (the x such that x is identical with Diogenes)'.

In trying to assess these claims, we face a stumbling block: the lack of a clear, agreed upon notion of logical equivalence as a relation between sentences of natural languages. Some would say that 'snow is white' is logically equivalent to 'snow is white and Socrates is either mortal or not mortal'. Others would deny this, on the grounds that Socrates' existence is not implied by the original sentence. Some would say that 'John is a bachelor' is logically equivalent to 'John is an unmarried man', by the logics of bachelorhood, gender and marriage. Others would say these are perhaps analytically, but not logically, equivalent, because the equivalence does not turn on the use of "logical vocabulary".

Having made due note of this difficulty, let us observe that Davidson has no problem bringing in, out of the blue, mention of Diogenes. This gives us some handle on Davidson's intended notion of logical equivalence - enough, I think, to justify us in sweeping the difficulty under the carpet so that we may proceed to ask if (1) might be true.

That the answer is 'no' can be seen from these invalid instances:

(i) It is obvious that snow is white. Therefore, it is obvious that snow is white and [some elaborate and opaque tautology].

(ii) If you assume that the square root of two is rational, it is easy to derive a contradiction. Therefore, if you assume that [some elaborate and opaque logical equivalent to 'the square root of two is rational'], it is easy to derive a contradiction.

(iii) The statement that snow is white involves no semantic concepts. Therefore, the statement that snow is white and "grass" either refers to grass or does not refer to grass, involves no semantic concepts.

(In classical formal logic, the range of possibilities for sentential embedding is far narrower than in natural languages, and therefore no analogous counterexamples arise.)

How about (2)? For a start, can we even understand '(the x such that x is identical with Diogenes and snow is white) is identical with (the x such that x is identical with Diogenes)'? The use of the variables and brackets is, in itself, not a deal-breaker, since we can understand '(the x such that x is identical with grass) is green'. But now: on this understanding, what is the role of that which comes after 'such that' in the bracketed construction? Intuitively, the construction as a whole is a referring term, and after the 'such that' ought to go conditions relating to the variable which are met by exactly one of its possible values, thus determining a unique referent.

But then what happens if, as well as conditions involving 'x', we insert closed sentences like 'snow is white'? Well, on the intuitive idea behind the bracketed construction, this just doesn't make sense. Nevertheless, "appropriate" reference-conditions come to mind: a bracketed 'the' construction refers iff the conditions relating to the variable are met by exactly one object and all constituent closed sentences are true. To complete the semantics, we can stipulate that if such a construction refers, it refers (of course) to the condition-meeting value of the variable.

Thus we can define a new kind of referring construction, albeit a strange one. Also, it does appear that our complicated identity sentence, in light of this definition, is logically equivalent (in some sense) to 'snow is white'. Of course, this is of no use to us, since the principle whose application we wanted the equivalence for is invalid.

Before we move on: the addition of this new referring construction to our language may render previously valid principles invalid, so we must now be extra careful. (If, earlier, we had decided that (1) was true - that the unrestricted substitution of logical equivalents was valid - we would now have to go back and reconsider.)

Now, despite the fact that things aren't going very well for our argument, let us press on. We have gotten as far as:

The statement that snow is white corresponds to the fact that (the x such that x is identical with Diogenes and snow is white) is identical with (the x such that x is identical with Diogenes).

And now, citing the principle that we may substitute coextensive singular terms, Davidson has us substitute some true sentence - let us pick 'grass is green' - for 'snow is white'. (This then yields a new 'singular term', '(the x such that x is identical with Diogenes and grass is green)'.) Thus we get:

The statement that snow is white corresponds to the fact that (the x such that x is identical with Diogenes and grass is green) is identical with (the x such that x is identical with Diogenes).

And now we must ask: does the principle of substitution of coextensive singular terms hold in natural language? Notoriously, and as anyone familiar with twentieth-century philosophy of language will know, it (very arguably) does not; there are numerous contexts where such substitutions (strongly seem to) fail. (Witness the existence of intensional logics.) Here is an example of one kind of invalid instance:

Lois Lane knows that Clark Kent is Clark Kent. Therefore, Lois Lane knows that Clark Kent is Superman.

There are also well-known problems with substitution into modal contexts. Furthermore, and closer to our current context: 'the fact that Clark Kent is Clark Kent' does not obviously have the same reference as 'the fact that Clark Kent is Superman', even though the differing embedded singular terms are coextensive. And certainly the statement that Clark Kent is Clark Kent is not identical to the statement that Clark Kent is Superman. For all these reasons, we can not accept an unrestricted principle of substitution of co-extensive singular terms. Thus our last inference was invalid.

Since the final inference is a reversal of the first substitution, that concludes our step-by-step evaluation.

If there be any residual doubt about the invalidity of Davidson's argument (recipe): note that no special properties of the sentence 'The statement that snow is white corresponds to the fact that snow is white', beyond its embedding 'snow is white', are drawn upon in the derivation of 'The statement that snow is white corresponds to the fact that grass is green'. If this were really a valid way of arguing, we would also have to accept the following:

Suppose there is a chameleon, Euclid, who lives in a field of grass. Suppose further that Euclid is green because grass is green. Using Davidson's form of argument. we can infer from this supposition first:

Euclid is green because (the x such that x is identical with Diogenes and grass is green) is identical with (the x such that x is identical with Diogenes).

Then:

Euclid is green because (the x such that x is identical with Diogenes and Davidson is the author of 'True to the facts') is identical with (the x such that x is identical with Diogenes).

And finally:

Euclid is green because Davidson is the author of 'True to the facts'.

Tristan Haze

Reference

Donald Davidson. True to the facts. The Journal of Philosophy, 66(21):748–64, November 1969.

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