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9 votes

Does there exist a "valid" application of Gödel's incompleteness to "logical natural language statements"?

Natural language is a very slippery thing; I don't know what one would hope for exactly here. You do clarify that you're looking at "logical natural language," but it's not at all clear what that is. ...
Noah Schweber's user avatar
7 votes

Who ever argued that natural languages have an exact logic?

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 ...
Bumble's user avatar
  • 26k
7 votes

What is language? Why can I “just understand” it?

I am sorry to read that your mental health is deteriorating, and wonder how it may be related to your question. To my mind, the fact that we are endowed with capacities which we may not be able to ...
Olivier5's user avatar
  • 2,172
6 votes

Are all languages universal?

You're correct in stating that one of the current controversial issues in philosophy is determining to what extent language is in some sense universal. True language certainly, according to ...
J D's user avatar
  • 27.5k
5 votes

Is an argument in natural language as logically valid as in formal logic?

In the context of logic and reasoning, 'valid' is a property of an argument whereby the conclusion follows from the premises by necessity, or where it is impossible for the premises to be true and the ...
Bumble's user avatar
  • 26k
5 votes
Accepted

Why don't we say the "unreasonable effectiveness of language"?

The effectiveness of mathematics is not only very reasonable but also not fundamentally different from the effectiveness of natural languages. Mathematics is merely the continuation of the ...
Speakpigeon's user avatar
  • 7,968
5 votes

Who ever argued that natural languages have an exact logic?

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 ...
J Kusin's user avatar
  • 2,786
4 votes

Why don't we say the "unreasonable effectiveness of language"?

Many aspects of the usefuelness of mathematics are presumably not unreasonable: Things like arithmetic (counting, addition, multiplication etc.) or simple geometry (measurements of length, areas, ...
Toffomat's user avatar
  • 149
4 votes
Accepted

Are the concept of time and space apriori to natural language or are they just references within natural language?

Kant thought so. But Wittgenstein argues: "If I say of myself that it is only from my own case that I know what the word "pain" means - must I not say the same of other people too? And ...
CriglCragl's user avatar
  • 21.9k
3 votes

Can we define a sequence of words?

In general, are we allowed to make such definitions where on the left hand side we have a sequence of words? Yes: Names Synonyms "The president of USA plays football". we can expand it ...
wizzwizz4's user avatar
  • 2,160
3 votes

Are the concept of time and space apriori to natural language or are they just references within natural language?

If nothing else, it seems like the questions, "Where is X?" and, "When is X?" require irreducibly spatial or temporal inputs to resolve. I.e., I can't adequately answer, "...
Kristian Berry's user avatar
3 votes

Why don't we say the "unreasonable effectiveness of language"?

I think you have a different definition of "effectiveness" in mind. Mathematics is effective because it makes predictions that work. If you ask yourself "how far will this cannonball ...
Federico Poloni's user avatar
3 votes
Accepted

What is the logical function of “and/or”?

And/or is just a way to express non-exclusive or, because or is very often used as exclusive or in natural language. I would parse "A, B, C and/or D" as "(A AND B AND C) OR D". ...
kutschkem's user avatar
  • 2,290
3 votes

Natural language into propositional logic

This sentence is a conjunction of two conditionals: (D→E) ∧ (E→D) You can put it into a single connective by using CB: D↔E I was taught that "unless" is a flag for the "or" connective, so I will ...
cenicero's user avatar
3 votes

Who ever argued that natural languages have an exact logic?

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 ...
phipsgabler's user avatar
2 votes
Accepted

Where Wittgenstein argues that thinking is done in natural language?

The passage that you seek may be the following one, from the Tractatus. 4.022 Man possesses the ability to construct languages capable of expressing every sense, without having any idea how each ...
Ram Tobolski's user avatar
  • 7,411
2 votes

Questions about the relationship between Wittgenstein's Philosophical Investigations and Tractatus

The transition from Tractatus to Philosophical Investigations is a complex process. I've found very useful the analysis of Merrill & Jaakko Hintikka, Investigating Wittgenstein (1986). For sure, ...
Mauro ALLEGRANZA's user avatar
2 votes

Is an argument in natural language as logically valid as in formal logic?

A good illustration of your question and a possible answer is the ontological argument for the existence of god. The original argument was given by Anselm of Canterbury in the 11th century using ...
Jo Wehler's user avatar
  • 33k
2 votes

Language and Philosophy

There's a cardinality error in your "strong (enough for all contexts) language" project. To wit: The space of "all possible contexts" (I'd say all possible experiencings) has the ...
Rushi's user avatar
  • 3,219
2 votes
Accepted

Language and Philosophy

This answer only offers a possible alternative to the hypotheses in the question. Those hypotheses are two-fold: One assumes that one can "create a unique string for every possible context in the ...
Frank Hubeny's user avatar
  • 19.4k
2 votes
Accepted

Wittgenstein and theology

It's best not to think of this as merely 'borrowing words.' I suspect that Wittgenstein himself would have said that it's impossible to borrow a word as such; what we do instead is import rules ...
Ted Wrigley's user avatar
  • 20.1k
2 votes

Why don't we say the "unreasonable effectiveness of language"?

"To me language is the marvel. And mathematics is a language isn't it?" No. I think I understand where your confusion is coming from. You are thinking of mathematics as merely a tool of ...
Amr's user avatar
  • 417
2 votes

Why don't we say the "unreasonable effectiveness of language"?

What's so special or unique about mathematics that we keep coming back to this phrasing? Math is built on the principle of idealized precision and unambiguity. The value of 1 is precisely 1. It's not ...
Flater's user avatar
  • 1,330
2 votes

Is it rational to use disjunctive imperative sentences?

There is a lot to unpack here and I'm not sure I'll answer all of it, so apologies in advance. It is easy to conflate reason and logic and the OP mentions the disjunctive, which is a logical operator ...
Rob's user avatar
  • 706
2 votes

Formal versions of exotic logical connectives in natural language

As you say, there are many connectives in natural languages such as English, while formal logic attempts to express these in just a few. To some extent this is an inevitable tension. We want our ...
Bumble's user avatar
  • 26k
2 votes

Why is math powerful?

Your statement is basically a variation of Eugene Wigner's seeking to explain 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences'. I argue here that conservation laws in physics ...
CriglCragl's user avatar
  • 21.9k
2 votes

Why is math powerful?

In fact, math is powerful precisely because it is an "impoverished version" of natural language. By restricting what we say, we can guarantee certain properties of our overall system. For ...
emesupap's user avatar
  • 2,337
2 votes

Why is math powerful?

Good afternoon! The utility of math has many facets, but I'd list four off the top of my head. Math is abstract. And why is that important, from a psychological perspective it allows one to find ...
J D's user avatar
  • 27.5k
2 votes

Is the semantic/model-theoretic regress an infinite, vicious regress?

I think you're asking about whether the abstract idea of a "model" is well-founded. For a given axiomatic theory of logic, a model is intended to be some set of objects that satisfies all ...
causative's user avatar
  • 13.6k
2 votes
Accepted

What does the emergence of different interpretations of Wittgenstein signify?

What does the emergence of different interpretations of Wittgenstein signify? I'm going to answer the question from a different angle: the competition of interpretations have nothing to do with ...
J D's user avatar
  • 27.5k

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