Fear and Loathing
Everybody knows that we have got into a terrible pickle over the semantics of ‘if’. Theories abound, but the raw
data are recalcitrant. We add epicycles to extend the domain of theoretical fit. The data remain recalcitrant. We
wheel in ideas and devices from stock or anywhere – Gricean mechanisms, possible-worlds semantics, conditional
probabilities, assertibility, robustness. The data remain recalcitrant.
After fifty years in the salt mines1, we should be very puzzled by this. ‘If’ is a very simple word, so it ought to
announce a very simple intellectual operation. Surely, we ought to be thinking, we must have got something
fundamentally wrong. Native English speakers above the age of four have no difficulty in understanding ‘if’-
sentences. So why can’t we get any of our theories to at least map onto that understanding, never mind illuminate
it? Why are the data so recalcitrant?
V.H. Dudman, hero of the revolution, has the answers in print. ‘If’ is indeed simple, and has a simple semantics.
We fail to see this because we have made fundamental mistakes. Our picture of the relationship between logic,
semantics and grammar gets almost everything wrong. The cacophony of the ‘if’-industry is the sound of all our
chickens coming home to roost together.
A thesis of this size you don’t swallow all at once. So I introduce the leading ideas by looking at other idioms. ‘If’
Everybody knows that ‘if’ is problematic. But most seem to think that we have the so-called2 English truth-functors
well understood. ‘Although’ for instance, is unproblematic.
Nice try, no cigar. Our standard treatment of ‘although’ is likewise fundamentally flawed, and sorting out the right
story requires correcting the same fundamental mistakes. Here goes.
We teach3 that messages4 encoded by sentences like
 Her Majesty wore a cardigan, although it was very hot
Although some would say 2,300 years. Sextus Empiricus records the debate between Philo of Megara and his logic tutor
Diodorus Cronus. Philo espouses the truth-functional account and Diodorus is a precursor of Stalnaker. See William and Martha
Kneale, The Development of Logic, OUP 1962, pp.128-9.
There are no binary English truth-functors. And this because there are no binary English sentence-functors. Unless you count
the full stop. No other English particle has the requisite grammar. Therefore, no other English particle has the requisite
I do not mean, by this locution, that any of us set out to deliberately inculcate the picture I am attacking. No doubt many, most
or all find themselves in the same position as I – trying to convey a proper sense of the relationship between logic and language
despite the course we offer. I do mean that the course we offer our students invokes that picture: it is explicit in Hodges and the
University Logic Exercises, implicit in many of the works we use to supplement them.
Sometimes we forget this massively important distinction. Semantic notions are not properties of sentences but of the messages
which they encode. The message, the item a speaker wishes to get across, determines the sentence used to broadcast it, and not
the other way round. This thesis is not the upshot of some careful Philosophical Investigation, but drawn directly from the
observation that many English sentences are ambiguous. Different messages, encoded by different programs, produce the same
sentence. As a consequence, it is a fundamental error to apply semantic concepts (e.g. truth) to sentences. And I do mean
fundamental. As you will see, all the fear and loathing in Hodges can be sheeted home to this error.
are to be formalized (for want of a better word) in the propositional calculus as [P Q], where P represents the
proposition5 that Her majesty wore a cardigan, and Q represents the proposition that it was very hot. Or, as we write in
our elegant shorthand,
P: Her Majesty wore a cardigan
Q: It was very hot
We further teach that this answer is unequivocally correct, by which I mean that not even a quibble stands between it
and the right of the matter. There is no room for intellectual unease – the formalization captures all that is relevant to
But we further teach an account of why this is so. And that account is thoroughly confused. Worse, almost every
claim it makes about English ‘although’ is straightforwardly false. It goes like this:-
The Usual Story
English ‘although’ has a simple grammar. It is a binary sentence-connective. Which means that its grammatical role
is to join two sentences to make a bigger one. It generates sentences according to the phrase-marker
S conj S
And as a consequence, its grammar is exactly parallel to that of ‘’.
Further,‘although’ is one of the English truth-functors. It expresses the logical operation of conjunction. English
has many words or phrases which do this job. A short list might be
and, but, although, even though, despite the fact that, notwithstanding the fact that, etc.
These words clearly do not have exactly the same meaning. But fortunately their meanings (with the sole exception ,
apparently, of the virgin ‘and’) are composite, and all are variations on the same theme. Each makes the same
contribution to truth-conditions, as specified by the standard truth-table. And each also encodes something quite
separate - the reaction of the speaker to the conjunction.
‘But’ is selected in order to signal that the speaker recognizes a contrast between P and Q. ‘Although’ is selected in
order to signal that the speaker sees P as surprising given Q, or perhaps that the speaker agrees with P, but would wish
to introduce another consideration Q. Or something of that sort. (But nothing you could nail down precisely, and
As will transpire, this is not the philosophers’ term of art. But their usage and mine here coincide, so I postpone discussion for
certainly nothing with any propositional content. And therefore nothing which could function as either premise or
conclusion in an argument. And so irrelevant to logic 6)
And as a consequence, the semantics for ‘although’ are exactly parallel to those for ‘’, as long as you remember to
mentally add a little halo to the ‘’ to cue the appropriate reaction. ‘Although’ is ‘’ with an although flavour.
Conformably to these grammatical and semantical intuitions we ask our students to reproduce the icon
T T T
T F F
F T F
F F F
And to recite the mantra “ ‘ although ’ is a truth-functor”.
Indeed, the icon and the mantra encapsulate The Usual Story, on which, I remind you,
(i) ‘Although’ here joins two sentences with the same status.
(ii) The message thus encoded has a truth-value. It is either true or false.
(iii) The meaning of ‘although’ is composite: truth-function + special ‘although’ flavour.
These three theses are straightforwardly false. ‘Although’ does not join two sentences, it prefixes one. As the comma
reminds us. The word is prefixed to the subsidiary sentence ‘it was very hot’ to form a clause ‘although it was very
hot’ which is then embedded somewhere or other in the main sentence ‘Her Majesty wore a cardigan’. The evidence
is compelling. Word order in sentences like  is quite flexible, allowing several variants:-
[1a] Although it was very hot, Her Majesty wore a cardigan
[1b] Her Majesty, although it was very hot, wore a cardigan
[1c] Her Majesty wore, although it was very hot, a cardigan
These all encode exactly the same message. The ‘although’-clause can precede, follow or interrupt the main sentence,
and which ever way you turn it the ‘although’ sticks like glue to the subsidiary sentence. Whereas
 It was very hot, although Her Majesty wore a cardigan
encodes a quite different message. The same truth-conditions, no doubt, but a different message.
Further, the message encoded by  does not have a truth-value. It is not true or false. This is not because it has some
other status, like neither-true-nor-false, but because of its sheer complexity. The simple message
 Her Majesty wore a cardigan
no doubt does have a truth-value, but  encodes a complication of that message, a complication which cannot be
captured by a notion as simple as truth. ( Our students are on to this. They have a strong intuition that there is an
awkwardness in describing  as straightforwardly true or false. And hence a resistance to the usual truth-table).
To confirm this intuition, apply the standard tests. If a message is a candidate for truth, then it can be affirmed, it can
be denied, and it can be supposed true for further purposes (such as reasoning).
A voice of sanity. Aspects of meaning which can play no role in argument are quite rightly ignored by logic. They do not
contribute to logical structure. But that thought, if followed through, is entirely subversive of The Usual Story.
 ? It is true that Her Majesty wore a cardigan, although it was very hot
 ? It is not the case that Her Majesty wore a cardigan, although it was very hot
 ? Suppose that Her Majesty wore a cardigan, although it was very hot
In each of these, insofar as they are intelligible, the ‘that’-clause attaches only to the main sentence . It does not
extend in scope to cover the whole of . Each of  –  exhibits the same variation of order that we saw earlier in
[4a] Although it was very hot, it is true that Her Majesty wore a cardigan
[4b] It is true that Her Majesty, although it was very hot, wore a cardigan
and so on. Truth is not a property of the message encoded by .
That, I take it, is enough to dispose of theses (i) and (ii). And thesis (iii), since it presupposes both, collapses along
The Real Story
It will help to widen the perspective, as  is an example of a general pattern. The following, among others, conform
[1a] Although it was very hot, Her Majesty wore a cardigan
 Because it was very hot, Her Majesty stripped off
 Since there are no trees in Orkney, it is a desolate place
 Unless I have made a mistake, the answer is 42
 Whether or not you like them, carrots are good for you
 Despite the fact that Mike Tyson is a convicted rapist, this administration let him in
 If Brown is fair-minded, he will apologise to Magdalen.
These are English compound sentences7. Each is a compound of an independent sentence (the part after the comma)
and a subsidiary string formed from a dependent sentence (as the grammarians call it) by prefixing with a
subordinating conjunction (as the tradition calls them – but remember that they do not conjoin).
And of course the messages they encode are compounded out of an independent message and a dependent message.
To be explicit, they are encoded by the program
R1: Encode the independent message as the independent sentence
R2: Encode the dependent message as the dependent sentence
R3: Select a conjunction from the list, and prefix it to the dependent sentence
R4: Amalgamate the resulting string into the independent sentence
And now for the semantics. The component sentences are to be understood as if standing alone, and in each case the
conjunction is selected to accord the dependent message a certain status. For instance, ‘if’ accords the dependent
message the status of an hypothesis, to be treated as true whether or not it really is. ‘Unless’ is selected in order to
withdraw commitment from the independent message in the circumstances specified by the dependent message.
‘Although’ is selected to concede and discount the truth of the dependent message, and so on.
Since these are compound messages, there is a further question to resolve. What happens to the component messages
when the whole is affirmed? It varies, of course, case by case. When the encoding program selects ‘although’ or
‘because’ or ‘since’ or ‘despite the fact that’ and the like, affirmation distributes. Both the independent message and
the dependent message are affirmed outright. They are both commitments of the speaker, for differing reasons, case
All compound sentences in English conform to this pattern. All other sentences are simple – which means subject-
If the program selects ‘whether or not’ or ‘even if’, the main message is affirmed outright and the subsidiary message
is not affirmed at all.
If the programme selects ‘unless’ then neither message is affirmed outright. The main message is partially affirmed in
the sense that a partial commitment is given, a commitment which is understood to be withdrawn should the
subsidiary message turn out to be true.8
And now we can explain why  is correctly formalized as [P Q]. Anyone who affirms  thereby affirms the truth
 Her Majesty wore a cardigan
and concedes the truth of
 It was very hot.
She is therefore committed to the truth of both, and not committed to anything else.9 Hence [P Q]. Perfectly
correct, nothing missing. The end.
Or perhaps not quite the end. Let me stress the importance of that last point by taking it further. Since it is the logic
of speakers’ commitments that we are formalizing, each of the following is just as good a conjunction as , and is
likewise properly formalized by [P Q].
John is a red-haired policeman
You can have coffee or tea
Pete, Cecilia’s brother, is a wino
Helen and Kinch work at Balliol
There is no privileged position for those sentences which The Usual Story types falsely as parallel in grammar to [P
Q].10 (Indeed, a case can be made in the other direction) 11.
And, looking ahead, if the encoding program selects ‘if’, the subsidiary message is unaffirmed (because treated as a hypothesis,
whether it is true or not), and the main message is, if you like, conditionally affirmed. By which I mean that  and other ‘if’-
sentences with the same grammar are condensed arguments, as some philosophers have identified them. Anyone broadcasting
 resorts to the argument whilst withholding commitment from the premise.
Or better, not committed to anything else of logical import. For she is further committed, dialectically, to a justification or
explanation of her selection of ‘although’. She will have grounds for her choice, and those grounds are further commitments.
But they are not signalled in her output sentence, nor are they part of the message she broadcasts by it.
Apart from anything else, that grammatical structure is an artefact of our choice of notation for propositional calculus. In
Polish notation our [P Q] is written Kpq, and I take it that no-one would wish to suggest that any of the sentences we have been
discussing have a parallel grammatical structure.
Here goes. Suppose that we take the logical notion of conjunction seriously, as a genuine property of some of the messages we
broadcast. Each proffers a block of information which is in itself conjunctive. Then there is no better candidate than the
message encoded by
John is a red-haired policeman.
For it entails that John is red-haired, and it entails that John is a policeman, and it is entailed by the two taken together. Hence [P
Q]. The information has that logical form. Whereas
Tony likes power, and so does Mandy
Proffers not one conjunctive message, but two distinct messages. As a performance it is equivalent to
Tony likes power. And so does Mandy.
Some will have doubts about the last in my list, which they are accustomed to accommodate to The Usual Story. It
contains ‘and’, and surely virgin ‘and’ is a truth-functor. Of course, in
 Helen and Kinch work at Balliol
it stands between two names, not two sentences. So it cannot be a truth-functor there, since it has the wrong grammar.
But the grip of The Usual Story is strong, and many will affect to discern an underlying sentence with an underlying
phrase-marker of the approved type. , they argue, is derived by elision from the more basic
 Helen works at Balliol and Kinch works at Balliol
so that the message it encodes is ‘really’ parallel to [P Q].12 There is a minor deviation in surface structure, but
perfect fit with deep structure.
As is well known, there is now a consequential awkwardness with
 Helen and Kinch got married
or  Helen and Kinch chopped down the magnolia
which seem to have truth-conditions at odds with the developing story. No matter. Let’s add another epicycle. This
time it is Grice to the rescue rather than Chomsky. Writers argue that  is indeed fully equivalent to
 Helen got married and Kinch got married
It’s just that it would be misleading to assert  unless Helen and Kinch married one-another. Desperate13. The
unfolding mini-theory must now accommodate
 Helen and Kinch are colleagues.
Which ought to be equivalent to
 ?Helen is a colleague and Kinch is a colleague
No doubt the reader is ahead of me here. Several authors 14 now insist that problem must lie in the semantics of
Where, notice, it isn’t the word ‘and’ which is the marker of logical conjunction. It is the full stop. And here I discern the
source of the twin myths of ‘And the Truth Functor’ and ‘And the Pure’. The role of ‘and’ here is to announce the beginning
of a new message, not to signal a complication of the original one.
This is already desperate. It is completely ad hoc, and is anyway insupportable. Elision of repeated material from  yields
not  but
 *Helen and Kinch works at Balliol
So a further ad hoc manoeuvre is required. There must also be a subsequent transformation of the verb form to obtain . But
now (i) English does not do that. Transformations in depth grammar always precede elisions, which are a surface phenomenon.
And more to the crunch (ii) the required transformation could only be effected by recognizing that ‘Helen and Kinch’ is a plural
noun phrase. Whereupon  was wearing its grammar on its sleeve in the first place, and the whole story collapses.
Apart from anything else,  is clearly ambiguous. It has one interpretation which is a straightforward conjunction. (How are
the children? – Well, Helen and Kinch got married last year, and Tom’s just finished his degree...), and another which is not.
No names, no pack drill. It’s too embarrassing.
This is all just a tangle. ‘And’ is simple enough. In grammar it is promiscuous, standing as it can between nouns,
pronouns, verbs, adjectives, adverbs, prepositions and so on. In semantics it is faithful to a single pattern. The
intellectual operation it announces is integration. And what, precisely, the integration is to be will vary case by case.
Sometimes the integration will have the same effect on truth-conditions as ‘’, and sometimes it will not. There is no
need for the smoke and mirrors of underlying phrase-markers and Gricean machinery. Untutored intuition delivers
that  encodes conjunctive information and  does not. In neither case is there any need for a grammatical
endorsement of the intuition.
So much for The Usual Story about ‘although’. It is time to relate the various themes to our general picture of the
project of formalization.
Tune in next week for another episode of:
Fear and Loathing.