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Peter F. Strawson famously concluded his 1950 critique of Bertrand Russell's theory of descriptions by the somewhat irrelevant remark that ordinary language has "no exact logic". Russell, in his reply, commented that on this particular point at least, he was in agreement with Strawson. Gottlob Frege premised his work with his opinion that natural languages are logically inconsistent, which provided the motivation for developing a symbolic language which we could trust to use for reasoning logically.

I couldn't find trace myself of any author arguing that, on the contrary, natural languages necessarily all have an exact logic. The current academic debate around Austin's 1961 so-called "biscuit conditionals" seems to take for granted that logic will not suffice on its own to account for the facts in this case.

There seems to be a consensus on the subject.

So my question is as follows:

Who were or are the philosophers, linguists, cognitive scientists etc. who have argued or work from the premise that natural languages have an exact logic.

Thanks for academic references.

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    There is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians Richard Montague
    – Rushi
    Sep 5, 2023 at 17:32
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    Nobody. Philosophers typically avoid arguing for something obviously false.
    – Conifold
    Sep 5, 2023 at 17:48
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    What makes you think there necessarily must be or ever have been philosophers, linguists, cognitive scientists etc. who have argued or work from the premise that natural languages have an exact logic. Must the argument be that all natural languages have logic; have some logic; have exact logic; work entirely by logic; either way, share the same logic? Can you name any natural languages that with however much logic would fit the bill? Conifold seems to stand on fairly solid ground. Sep 7, 2023 at 18:48
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    What do u mean by exact logic?
    – emesupap
    Sep 8, 2023 at 4:47
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    @RobbieGoodwin "What makes you think (...) an exact logic." Because this is implied by the notion of logic that we have since the beginning of formal logic. 2. "Must (...) share the same logic?" Logically, yes, given our notion of logic, but whether they do is an empirical question. 3. "Can you name (...) fit the bill?" All natural languages. Sep 8, 2023 at 9:23

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I think nobody has seriously argued such a thing. Given how easy it is to formulate semantic paradoxes in natural languages, it would seem to be impossible.

Leibniz did some work towards what he called a universal calculus, though it was never completed and was only published after his death. It is not a general purpose logic. And it is not clear whether Leibniz really conceived his work as trying to identify a fully general purpose logic of language.

Some philosophers in the early 20th century thought of formal logic as an attempt to create a logically perfect language, without the ambiguities and defects of natural language. Others, such as Quine, conceived formal logic as an attempt to improve natural language and to regiment it for particular purposes, rather than as something to replace natural language or stand apart from it.

Peter Strawson was responding to Russell's theory of descriptions with an alternative proposal of his own. He seems to be merely acknowledging that there are many difficulties and disagreements about how to understand linguistic expressions, including the simple definite description, and this shows that there is no definite logic of natural language. Formal logics can help, but according to Strawson they are also inevitably limited and are unable to express the full scope of what we might wish to say.

I am not sure why you are referencing the issue of 'biscuit conditionals' from John Austin. These are usually regarded as an example of a pragmatic conditional, i.e. a case where the meaning and intent in stating the conditional must be understood in terms of the pragmatics of language, rather than just the semantics. Of course, more generally we always need to pay attention to the pragmatics of language when understanding an utterance, and this only complicates the search for a logic.

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    "Given how easy it is to formulate semantic paradoxes in natural languages" It seems to me that the ambiguity in natural language is a bit of a non-starter here. Is that just a different way of stating your point?
    – JimmyJames
    Sep 6, 2023 at 21:13
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    @JimmyJames I agree ambiguity is also a major issue. Though natural languages often have ways of carefully avoiding ambiguity, it's just that they are fiddly and often ignored. When speaking of paradoxes I have in mind things like Berry's paradox or the liar paradox or Curry's paradox. These show that natural language can express things that seem to make sense but entail a contradiction. Formal languages are typically crafted to avoid this.
    – Bumble
    Sep 7, 2023 at 3:52
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Noam Chomsky posited deep structure to account for apparent differences in languages at the surface of regular usage, such as sentences having the same meaning across slightly different sentences. (I believe this later transitioned to Universal Grammar).

"Chomsky argued that the transformational processes between deep and surface structure could account for the variation observed in language use." https://www.structural-learning.com/post/chomskys-theory

He doesn't believe we will necessarily know this deep structure. But it's responsible for the similarities among and between languages. The key point being there is a logic we are largely unaware of, but underlies languages and guides their (our) surface usage. I think the fact we don't know this posited deep structure is a way to avoid linguistic and semantic paradoxes Bumble brings up.

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Richard Montague argued quite explicitely in this direction, for example in his work Universal Grammar:

There is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians; indeed I consider it possible to comprehend the syntax and semantics of both kinds of languages with a single natural and mathematically precise theory.

(Cf. Montague semantics)

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  • Welcome to Philosophy stack exchange. Do you know if Montague explained the logic of natural language conditionals, such as "If that's not Brian Ferry in person, I'm a monkey's uncle", or so-called biscuit conditionals such as "There are biscuits if you want"? Sep 7, 2023 at 15:44
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Leaving aside the question of what "exact logic" refers to (you seem to mean the certainties of formal, mathematical logic), your question still hinges upon the meaning or characteristics of a "language that has an exact logic." Would that mean a language in which all syntaxically correct propositions display "exact logic"? Ie a language in which good grammar would always ensure "exact logic"?

If that's what you mean, we can consider Chomsky's famous proposition: "Colorless green ideas sleep furiously", from his 1957 book Syntactic Structures as an example of a sentence that is grammatically well-formed, but semantically nonsensical.

It is not specific to English, obviously, but a general fact: one can construct grammatically correct yet nonsensical sentences in any human language. One could translate Chomsky's sentence above into pretty much any human language: Les vertes idées incolores dorment furieusement.

Now for your question about philosophers who would trust natural languages' inherent logic a bit too much... I cannot think of an example. Historically, I think the general tendency of philosophers has been to do the exact opposite, i.e. to mistrust natural language, as a constant source of confusion and approximations, and (sometimes) to propose their own language instead, their jargon, supposedly more precise.

I also believe this is a bit unfair.

There is a logic to language, or rather: a language has its own logic. Not exact of course, but ambiguity has its advantages.

Vagueness requires less resources than exactitude, which will in any case always remain elusive. What is required in human verbal communication is not perfect exactitude or precision (an impossible aim anyway), but only a sufficient degree of precision for the problem at hand.

If we are eating at the same table and I ask you to "pass me the salt", you will understand me just fine, in spite of the formal ambiguity of my request. I don't think I need to ask "wouĺd you grab in your hand the small metalic container in which there is some NaCl salts, move your hand towards me and release the container on the table some 40 cm in front of me so that I can easily access it without having to stand, please, because I would like to add some Na Cl salts to my dish". That'd be overly precise for the problem at hand.

All this to say that there is a reason, a logic, for why natural languages are vague and extremely flexible. It's a feature, not a bug.

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I don't think J.L. Austin would be caught suggesting anything of the kind proposed in your question. But he comes close in A Plea for Excuses:-

"...our common stock of words embodies all the distinctions men have found worth drawing, and the connections they have found worth marking, in the lifetime of many generations: these surely are likely to be more numerous, more sound, since they have stood up to the long test of survival of the fittest, and more subtle, at least in all ordinary and reasonable practical matters, than any that you or I are likely to think up in our armchair of an afternoon—the most favourite alternative method." (J. L. Austin, Philosophical Papers, p. 182)

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    @Speakpigeon Full discolure and in view of the fact that Austin invented speech acts, I have to say that I think Austin was mistaken. The brilliant and subtle distinctions that he writes about owed more, I would say, to his (and his team's) skill than to the actual shambolic, improvised and constantly changing structure of natural language (or, better, languages games). I know that remark is off-topic, but I couldn't not say it.
    – Ludwig V
    Sep 8, 2023 at 11:09
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    "the actual shambolic, improvised and constantly changing structure of natural language" How could we understand each other's prose if that was true? Today's translators can still read and understand Aristotle's language 2,300 years after the event. My mother-tongue is French and yet I don't seem to have any difficulty understanding the prose of English-speaking people. Sep 8, 2023 at 15:44
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    @speakpigeon I had in mind the idea that natural languages are a single over-arching structure. There are many structures (language games) which interact in all sorts of ways. That's when philosophy happens - that moment when we think "it must be like this, but it can't be". (I'm pushing beyond Wittgenstein, if that helps, so you understand you're getting a personal view, rather than a philosophical thesis).
    – Ludwig V
    Sep 8, 2023 at 19:02
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    @speakpigeon "Today's translators can still read and understand Aristotle's language 2,300 years after the event. My mother-tongue is French and yet I don't seem to have any difficulty understanding the prose of English-speaking people." Of course you can - after how many years of learning and practising? I know I spent over ten years learning Latin and Greek, not to mention the years that I was learning English - my mother tongue.
    – Ludwig V
    Sep 8, 2023 at 19:06
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    @speakpigeon Of course, there are some projects - Chomsky's deep grammar and logic itself - that aim to identify a single over-arching structure. Maybe, one day, all will be revealed. But I'm not holding my breath.
    – Ludwig V
    Sep 8, 2023 at 19:09
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Natural languages may be perfectly logical. It is just that their structure is very, very, very, very extremely complicated. Much too complicated for mere humans to write down rules that describe a language exactly with all exceptions mentioned. Plus the rules change all the time.

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  • "Much too complicated" Sure, but we don't need to prove formally that languages are logical. We just need to satisfy ourselves that they are in the apparently odd cases identified so far. Sep 8, 2023 at 9:32

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