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I'm after the proper method for constructing semantic values of whole sentences out of the semantic values of individual words. There are also a few individual words I'm curious about as well.

If we were to take the sentence: Some snake smokes

[[Some]]= λf · [λg · 1 iff ∃x such that f(x)=g(x)=1]

[[Snake]= λx · x is a snake

[[Smokes]]= λx · x smokes

Now I have scrawled in my notes that

[[Some Snake Smokes]]= ([[some]] [[snake]]) [[smokes]]

but I'm not sure how to work from that template and write it as a lambda abstraction.

Additionally, I was curious about the semantic values of the following words:

[[is]]= λx · I know theres some ambiguity about this one and I'm unsure where to start.

[[that]] (I hope that I can play today) = ?

[[or]] (Maurice or Jacob is green)= ?

[[day]]= λx · x is a day I'm pretty sure about this one but just wanted to double check

Thank you!

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  • Worth noting that 'That' and 'Or' both have multiple meanings; you may want to expand on which meanings you mean.
    – JeffUK
    Oct 8 '17 at 9:00
  • Correct; "is" is ambiguous: it can be "it belongs to" (like: "one is a natural number"), "it is a subset of" (like in: "men are animals"), identity ("Joyce is the author of Ulysses").
    – Mauro ALLEGRANZA
    Oct 8 '17 at 14:18
  • I don't think there's just one answer to this. Assigning semantic values to sentences in a natural language is not a trivial thing. In fact, there are some that argue it cannot be done. There are constructed languages which can be read as English but have a proscribed semantic meaning. Attempo Controlled English (ACE) is one such example.
    – Cort Ammon
    Nov 8 '17 at 0:41
  • I am confused why you would want to do this and what happens even if you did? You do realize that propositions don't work like this, right? If you were into making a short hand language this might last for a while but how would you cover every contextual definition. Some words have a slang or cultural context as well as an academic context for instance.
    – Logikal
    Dec 5 '17 at 1:35
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You can do what you want in the framework of Heim & Kratzer's Semantics in Generative Grammar; 'some' is treated in section 6.4 as you describe it.

[[some snake]] = [[some]]([[snake]]) = λg . ∃x such that x is a snake and g(x) = 1

Some of the other words raise some complicated questions.

Heim & Kratzer treat 'is' as a copula as vacuous in section 4.2. So, the entry is λf . f (it maps type e,t functions to themselves).

If 'that' introduces an intensional context then it's beyond the scope of an introductory book. See http://web.mit.edu/fintel/fintel-heim-intensional.pdf (PDF).

If 'or' is conjoining clauses then it is straightforward to treat it as a truth functional connective. It takes truth values to functions from truth values to truth values: it takes 1 to a function that takes both 0 and 1 to 1, and 0 to a function that takes 1 to 1 and 0 to 0. The other case is discussed in Heim & Kratzer section 7.2.2.

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The problem with your approach is that it is impossible to properly assess meaning without context.

As Setargew Fantaw puts it,

the human brain, unlike computers, interprets things on the basis of information that the context of perception provides. When using language or performing any task, we do it within a context. When we hear a certain sentence, we capture its meaning because it is uttered in certain context. Otherwise, were we to hear them free of any context there would always be ambiguities. Sentences are heard "in the appropriate way because the context organizes the perception; and since sentences are not perceived except in context they are always perceived with the narrow range of meanings the context confers" (Hubert Dreyfus).

Without context, all sentences will be ambiguous; we can't know if

Some snakes smoke

refers to actual snakes, or to Brazilian soldiers in WWII, or something else.

So, the meaning of a sentence seems to be an emerging property, that is not contained in the mere sum of its parts.

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  • Hi Luis thank you for your response, for the purposes of the class I'm taking I think we just take things literally-- there is no context, for example, I am asked to give the semantic value of the sentence [[some philosopher smokes]] with only the phrase and the individual semantic values to work with must like the example I gave in my question.
    – Lucy Toru
    Oct 9 '17 at 0:29
  • The problem with logic classes is that they remove "propositions" from actual context, mistakenly assuming such removal is a neutral operation, that has no effect on their meaning. Such assumption is false, and accounts for many of the problems with philosophy. Logic classes are like a kind of morgue for sentences, where they are subjected to procedures that are analogue to forensic anatomy procedures. But while coroners understand that they are analysing corpses, not living people, logicians fail to make the distinction. :)
    – Luís Henrique
    Feb 14 '18 at 22:56

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