Young Ludwig and Old Ludwig walk into the pub.

Young Ludwig: OK, the first round is on me. What do you fancy?

Old Ludwig: That looks like a lot of choice. I might need some help. I am completely German, and in Germany we only have five types of beer.

Young Ludwig: Mr Bartender, tell us a bit about the beers you have on offer.

Bartender: It would be my pleasure. As you can see, we have seven beers on tap today. This first one is called “Finest Hour”, it’s a classic British Bitter. Sorry about the bulldog and Churchill stuff on the label, Meine Herren, I know it was a long time ago but we do still obsess a bit about the war. The rest are all IPAs.

Old Ludwig: Six IPAs? Wouldn’t it make more sense to have a little more variety?

Bartender: They are all quite different from one another.

Young Ludwig: They are? You’d better give us some more guidance, then. Tell us a bit about “Finest Hour”.

Bartender: This is what we call a “session beer”: it’s only 3.5% ABV, which means you can drink two or three of them in a “session”. It’s got a mellow, biscuit-malty base, with pleasant, moderate aromas of flowers and fruit from nice English hops, but the overriding character is its robust bitterness. There’s something called an International Bitterness Unit, or IBU, which measures how many bittering compounds there are in your beer. The scale for most beers starts at about five and goes up to maybe 80 or so. This one clocks in at 40, which means it is noticeably bitter.

Young Ludwig: Hence the name of the style.

Bartender: I suppose so, yes. Next we have “Viceroy”, that’s an English IPA.

Old Ludwig: What does “IPA” stand for?

Bartender: It stands for “India Pale Ale”.

Young Ludwig: I thought you said it was English.

Bartender: The “India” bit refers to the fact that it was one of the most popular types of beer to have shipped out from breweries in Britain to faraway colonies like India. Remember what I was saying about IBUs? That unit measures the number of parts per million of isomerised alpha acids in a beer. Alpha acids are chemical compounds, called humulones, found in hops. When you boil them for a long time, their chemical structure changes into an isomer that is soluble. These are what give beer its bitter flavour. A handy side effect is that they are bacteriostatic – in other words, they stop bacteria from reproducing. India Pale Ales are brewed with a bigger dose of bittering hops than a Bitter would be, as this used to help keep the beer from going off on its long journey to the colonies. For the same reason, it tends to be a bit stronger than a Bitter, too. Viceroy here is 6.5% ABV and registers 60 IBUs.

Young Ludwig: I see. “Pale” speaks for itself. What about “Ale”?

Bartender: That refers to the type of yeast used to ferment the beer. Ales are fermented with a yeast that likes to work at around 20°C, and which floats about in the beer as it is doing so. We call these “top-fermenting” yeasts. The other main type of beer is lager, the sort of thing they drink in your part of the world: this is fermented with a yeast that likes to be cold and sits at the bottom of the beer.

Old Ludwig: “Bottom-fermenting” yeasts?

Bartender: Exactly.

Young Ludwig: All right, I get this. “India”, “Pale” and “Ale” are like three elemental propositions, which are logical depictions of three elemental facts: one, bitter and strong; two, pale in colour; three, fermented with top-fermenting yeast. So “India Pale Ale” is like a molecular proposition governed by truth-functional logical connectives: it must be the logical picture of its correspondent state of affairs in the real world – a beer that is bitter, strong, pale and top-fermented – to be truthful. Should any state of affairs in the real world differ from the elemental propositions, “India”, “Pale” and “Ale”, then the molecular proposition is a contradiction and impossible to be true.

Bartender: I’m not sure it’s that simple.

Old Ludwig: Me, neither.

Young Ludwig: Well, let’s test the theory. Tell us about these other “IPAs”.

Bartender: So, this third one is called “West Coast”, it’s an American IPA.

Young Ludwig: Let me guess. The same as an English IPA but just a bit bigger, brasher and more in-your-face?

Bartender: That might be a bit racist. But yes, you could say that. Let’s be fair and say that the “American” bit refers to where the hops come from. “West Coast” is only slightly higher than “Viceroy” on the IBU scale, at 70, and it’s exactly the same strength, at 6.5%. The American hops make a difference to the aroma: this one is more citrusy and tropical than “Viceroy”, which is more floral and herbal, but also with a citrussy zest.

Young Ludwig: It’s an ale, right?

Bartender: Oh yes, it’s an ale.

Young Ludwig: There we go. We’re still in the realm of truth, then. It’s strong, bitter, pale and an ale.

Bartender: True enough. What about this fourth one? It comes with a rather grand name: “Destroyer of Worlds”.

Old Ludwig: Crikey!

Bartender: Indeed. It earns it. This is a Double IPA. It’s not quite twice as strong as a standard IPA but it comes close, at 10.5% ABV. It is also crazy on the bitterness scale, at 120 IBUs. Having said that, it is still recognisably fresh, fruity and light in character like “West Coast”.

Young Ludwig: Strong, bitter, pale and an ale. What can be said at all can be said clearly.

Bartender: Yes, perhaps. But things might start to get a bit murkier with these last three, in more ways than one. This one is called “Hop Guzzler”. They call it a “Session IPA”.

Young Ludwig: Hold on a minute. Earlier you said a “session beer” was one with low ABV that you could drink two or three of in a session. I’m not sure I’d want to polish off three pints of “Destroyer of Worlds”.

Bartender: No, you wouldn’t. But “Hop Guzzler” is only 3%. It’s quite bitter, though, with 50 IBUs.

Young Ludwig: But that sounds exactly the same as “Finest Hour”, the one on the first tap.

Bartender: Arguably, yes. And you’re not the only one to remark upon that. The lobby group, The Campaign for Real Ale, insists that “So-called IPAs with strengths of around 3.5% are not true to style”. Martyn Cornell, a respected beer historian, wrote back in 2013 that old-style low-strength IPAs are “not really distinguishable from ordinary bitter”, and he also thought that, to be “sessionable”, a beer should be restrained, and not “dominate the occasion and demand attention”. That suggests a session beer shouldn’t have a big, complex hop aroma, anymore than it should have a high ABV. I think that makes sense: a session beer should be accompanied by talk about football, say, not talk about the beer.

Young Ludwig: We are drifting into the arena of the contradiction.

Bartender: Or the “Oxymoronic Category Fail”, as Cornell put it.

Old Ludwig: If a craft beer could talk, we could not understand it.

Young Ludwig: But there’s no excuse for that. Like I said earlier, what can be said at all can be said clearly, and whereof one cannot speak, thereof one must be silent. The limits of my language are the limits of my world. For these beers to exist, we must have the corresponding words for them. And these beers do appear to exist. I need to think a bit more. What’s up next?

Bartender: On tap number six, we have “DDH Club Tropicana”. This is what is called a New England IPA.

Old Ludwig: More letters! What’s “DDH”?

Bartender: It stands for “Double Dry-Hopped”. With these beers, the hops – and there are lots of them – tend to go in after the boil is over, which brewers call “dry-hopping”. The “double” simply denotes that this process is done twice during the fermentation period. The outcome is an intensely aromatic beer: the fruity, resinous, citrussy aromas from hops come from very volatile compounds that evaporate quickly during the boil, so adding hops after the boil preserves more of them in the finished beer. It also means that more of the hops’ polyphenols get into the finished beer, which lend it a persistent haze. Brewers of this style tend to like this quality, and they often use high-protein malts such as oats and wheat that also leave polyphenols in the beer, so that the two sets of polyphenolic compounds bind together to make the beer especially hazy, or even opaque, like fruit juice. “DDH Club Tropicana” is a virtually opaque example, and it clocks in at 7% ABV.

Young Ludwig: All right. This is pale, for sure, albeit opaque. It’s also an ale, and it’s strong. But a question occurs to me. Earlier on you said that bitterness comes from isomerising hop alpha acids by boiling them for a long period of time. But the hops in this beer haven’t been boiled.

Bartender: So where does the India Pale Ale bitterness come from?

Young Ludwig: Right, exactly.

Bartender: This one isn’t very bitter, for precisely the reasons you adduce. Its IBU count is a mere 30. I have seen a couple of examples with zero IBUs, or as close as to make no odds.

Young Ludwig: But if “India”, “Pale” and “Ale” are elemental propositions depicting the facts of high strength & bitterness, pale colour and top-fermentation, “India Pale Ale” is a non-truthful, or contradictory molecular proposition if the facts include low strength (as they do for “Hop Guzzler”), low bitterness (as they do for “DDH Club Tropicana”), dark colour or bottom-fermentation.

Bartender: Wait until you hear about the beer on tap seven. That one’s called “Darkness Visible”. It’s a Black IPA.

Old Ludwig: A Black IPA?

Bartender: It’s big on IBUs, coming in at 80, and while it looks like a Stout or Porter, the dark malt flavours of chocolate and coffee are toned down somewhat in favour of fruity hop aromatics. Indeed, this one has been dry-hopped.

Old Ludwig: Coffee and mango? Sounds horrible. If ever there were a contradictory molecular proposition…

Bartender: It’s an acquired taste, I suppose.

Young Ludwig: More to the point, it patently isn’t pale! These are contradictions. Untruths.

Bartender: Steady on. Do you mean trade description violations?

Young Ludwig: Possibly. But certainly violations of propositional logic.

Old Ludwig: Perhaps propositional logic is wrong?

Young Ludwig: Wrong? What do you mean, wrong? Explain how there can be fact such as a “Black India Pale Ale”.

Bartender: I might be able to help there. Although earlier I said that “IPA” stood for “India Pale Ale”, no-one calls these beers “India Pale Ales” anymore. It’s just “IPA”. I’m not sure if I follow your terminology, but perhaps “IPA” has become an independent elemental proposition, something quite distinct from the molecular proposition of “India Pale Ale”? Maybe an “IPA” needn’t be Indian, pale or an ale, at all?

Young Ludwig: So what would this proposition depict?

Bartender: I’m not sure. Anything that isn’t Miller Lite?

Old Ludwig: I don’t think it matters whether we describe these beers using the word “IPA” or the words “India Pale Ale”. What matters is merely the fact that these words are used in certain ways in the language games pursued by brewers, pubs and beer drinkers. For a large class of cases in which we employ the word “meaning” it can be explained thus: the meaning of a word is its use in the language.

Young Ludwig: But do we not then face a situation in which words are detached from the reality they depict, floating free of the world as it is?

Bartender: That does seem a bit radical. I was merely suggestng that “IPA” had floated free of the words “India Pale Ale”.

Old Ludwig: You speak about reality, but your questions about the beers we have to choose from refer to words – so I have to talk about words. Then you say: “The point isn’t the word, but its meaning”, and you think of the meaning as a thing of the same kind as the word, though also different from the word. “Here the word, there the meaning.” But you already know that this kind of vertical conception of logical truth is illusory, if I understand what you are saying about molecular propositions. To insist that “India Pale Ale” describes a beer that is strong, bitter, pale and top-fermented is the same as insisting that 2+2=4, and just as tautologous, just as senseless. It does not give us knowledge about meaning or reality because to know a tautology is to know nothing.

Young Ludwig: Go on.

Old Ludwig: Remember that duck-rabbit picture I showed you once? We both remarked on the eerie effect it had: it was, in fact, never a duck-rabbit, but only ever a duck or a rabbit. We agreed that these were two entirely different pictures, even though they involved the self-same lines on the self-same page, with no changes at all. Well, sometimes “India Pale Ale” depicts a beer like “Hop Guzzler”, and sometimes it depicts a beer like “Viceroy”. When the language game changes, the rules change, too. What was it you once said about ladders?

Young Ludwig: I said that you have to throw away the ladder I provide, after you have climbed up on it. “My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them.”

Old Ludwig: “Senseless”, exactly. That was the term I used already. One might properly say that these propositions you describe, these grammatical relations, are “autonomous”. Therefore, faced with puzzles such as how to make a choice of beer based only on the names and style descriptions attached to those beers, we do well to remember that these puzzles are not to be solved by the application of etymological fallacies about shipping beer to the colonies, nor other misconceived notions regarding the relations between words and reality, but rather by interrogating the relations within language, within an autonomous grammar, through the pursuit of language games.

Young Ludwig: So what you are saying is that we should welcome nonsenses such as “Session IPAs” and “Black IPAs”?

Old Ludwig: Most certainly. The Black IPA may taste disgusting, but it teaches us a valuable lesson: it teaches us to pass from a piece of disguised nonsense to something that is patent nonsense, the better to recognise the inherent senselessness, or tautology, of all logical propositions.

Bartender: All right, gents. What’ll it be, then?

Young Ludwig: A half of “Destroyer of Worlds” for me.

Old Ludwig: I’ll take a pint of “DDH Club Tropicana”.

The bartender pours the beers and sets them on the bar. Old Ludwig takes out his mobile phone, snaps a photograph of his beer and posts it onto Instagram.

Old Ludwig: Hashtag IPA!

Young Ludwig: So, Mr Bartender, what’s this glitter beer I keep hearing about?