Lazy Friday (and First Order Logic)

sitting in caf’ enjoying sun, so just by the way:

Can “the company has 3 problems” be formalized in First Order language?

Picture the sentence in the context of a management presentation. My interpretation would be the following: our company has problems and 3 of them are relevant in our discussion today. Subsequently I would expect the problems to be lined up and explained. Especially I would be interested why there are 3 problems, not 2, 4 or 345. this would require the problems to be discriminated by properties. If it were not possible to discriminate them at all the “3” could not be explained and thus the sentence would make no sense.

Thus the sentence expresses the fact that there exists an expression s.t. the 3 problems can be characterized up to isomorphy, what makes it an expression about an expression and thus “the company has 3 problems” requires 2nd order language to be specified formally!(?)

So far so good/bad. I’m not yet quite sure about the above conclusion, so, any veto?

Take it easy
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Modeling Theory and Abstraction Awareness in strive for scientific rigour and relevance to information systems engineering.
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2 Responses to Lazy Friday (and First Order Logic)

1. TY says:

What you meant to “requires 2nd order language to be specified formally!”? Isn’t that says the higher-order logic statements can be encoded into first-order logic?
I think the natural words in a natural language are often appeared in higher-order logic.

• Lazy Sunday today:

Hi TY. Yes, indeed as you say, if one just talks >about< a language this is different from making statements in the language itself. However my intention (that I didn't express above) is to start with a single language, and to expand it as required.

Alternatively, one can try to join the two language levels, what can easily lead to paradoxies.

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