A quip seen in a film review in last week’s Spectator magazine has given rise to this short logical analysis. The set-up line is:
(1) There is no money in poetry.
The message is that you can’t make money out of poetry, of course. The sentence is true for most people, which itself makes it contingently true, not necessarily true. But whether it is true or false, the pay-off has the same truth value as the original:
(2) There is no poetry in money.
Logic is not too fond of uncountable terms (‘poetry’, ‘money’), but the sentences can be made to conform broadly to the E-type proposition: No P are Q. It follows that if no P are Q, then no Q are P. P and Q are disjoint sets. Yet, despite the sentences having the same truth value, their respective messages seem to be different. Put another way, natural language implies more than can be inferred by logic alone.
There is a well-established distinction (P. Grice, 1967) between logical reasoning and pragmatic reasoning, whereby the latter resorts to conversational conventions, practical considerations, context, and so on. Where in logic (1) says something about money and (2) something about poetry, there is a strong sense that in conversational English both sentences say something about money.
This is reinforced by the only other type of proposition that retains its truth value upon conversion – the I-proposition: There is some money in poetry is equivalent to There is some poetry in money. Again, both sentences seem to be saying something about money.
In propositional logic, the converse of a conditional is obtained by changing around antecedent and consequent. A conditional does not imply its converse:
(3) If you write poetry, you will not make money.
(4) If you haven’t made money, you will have written poetry.
For (3) to be false, we need to find someone who has made money from writing poetry. This combination though makes (4) true, because a conditional is false if and only if the consequent is false while the antecedent is true.
The use of adverbs such as ‘conversely’, ‘on the contrary’, ‘quite the reverse’ and a few others in everyday English betrays only a distant relation to their strict meaning in logic. My Longman Dictionary gives the following example: American consumers prefer white eggs; conversely, the British buyers like brown eggs. Where is the converse relation here? What comes to mind for this example is expressions such as: ‘in contrast’, ‘while’, ‘whereas’. However, it is no use being too dogmatic about it. I understand the sentence the way it was intended, and so do millions.
(1) There is no money in poetry.
The message is that you can’t make money out of poetry, of course. The sentence is true for most people, which itself makes it contingently true, not necessarily true. But whether it is true or false, the pay-off has the same truth value as the original:
(2) There is no poetry in money.
Logic is not too fond of uncountable terms (‘poetry’, ‘money’), but the sentences can be made to conform broadly to the E-type proposition: No P are Q. It follows that if no P are Q, then no Q are P. P and Q are disjoint sets. Yet, despite the sentences having the same truth value, their respective messages seem to be different. Put another way, natural language implies more than can be inferred by logic alone.
There is a well-established distinction (P. Grice, 1967) between logical reasoning and pragmatic reasoning, whereby the latter resorts to conversational conventions, practical considerations, context, and so on. Where in logic (1) says something about money and (2) something about poetry, there is a strong sense that in conversational English both sentences say something about money.
This is reinforced by the only other type of proposition that retains its truth value upon conversion – the I-proposition: There is some money in poetry is equivalent to There is some poetry in money. Again, both sentences seem to be saying something about money.
In propositional logic, the converse of a conditional is obtained by changing around antecedent and consequent. A conditional does not imply its converse:
(3) If you write poetry, you will not make money.
(4) If you haven’t made money, you will have written poetry.
For (3) to be false, we need to find someone who has made money from writing poetry. This combination though makes (4) true, because a conditional is false if and only if the consequent is false while the antecedent is true.
The use of adverbs such as ‘conversely’, ‘on the contrary’, ‘quite the reverse’ and a few others in everyday English betrays only a distant relation to their strict meaning in logic. My Longman Dictionary gives the following example: American consumers prefer white eggs; conversely, the British buyers like brown eggs. Where is the converse relation here? What comes to mind for this example is expressions such as: ‘in contrast’, ‘while’, ‘whereas’. However, it is no use being too dogmatic about it. I understand the sentence the way it was intended, and so do millions.
I'm not sure I agree with the end of para 4. The way I read it, 1) says something about poetry and 2) about money, whether logic or conversation.
ReplyDeleteSimilarly with the I-proposition examples.
Of course, it all depends on how you say it, body language, etc...
I fully agree about the language. My thinking was that if any of these sentences is about poetry, then it states a hackneyed truth - it comes across rather flat.Think 'money', and the sentences suddenly perk up, which is why they caught my eye.In logic, the sentence 'Money is not in poetry' is about 'money' while 'Poetry is not in money' is about 'poetry'. That which a sentence is about is the subject, that which is asserted or denied of the subject is a predicate.
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