10
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. ...
- 3,210
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 ...
- 22.9k
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 ...
- 22.9k
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 ...
- 6,241
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 ...
- 2,385
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, ...
- 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 ...
- 20.5k
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 ...
- 2,037
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, "...
- 12.2k
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 ...
- 139
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". ...
- 2,232
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 ...
- 31
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 ...
- 131
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 ...
- 7,311
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, ...
- 36.2k
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 ...
- 24.6k
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 ...
- 1,368
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 ...
- 19.2k
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 ...
- 18.5k
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 ...
- 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 ...
- 1,292
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 ...
- 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 ...
- 22.9k
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 ...
- 20.5k
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 ...
- 2,099
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 ...
- 23.1k
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 ...
- 11.1k
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 ...
- 23.1k
2
votes
What does the emergence of different interpretations of Wittgenstein signify?
If you want to understand the situation around Wittgenstein's work, you are going to have to study it. I put a list of resources, and introductory remarks to his work, in this post here: Introductory ...
- 20.5k
2
votes
Are the concept of time and space apriori to natural language or are they just references within natural language?
According to the empirical studies of the Natural Semantic Metalanguage (NSM) project, both time and space are core concepts, represented by several semantic primes each - core concepts of human ...
- 1,777
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