## sub-set proposition and convertible proposition

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### sub-set proposition and convertible proposition

Ἰησοῦς ἐστιν ὁ λόγος

Is the above statement a sub-set proposition or a convertible proposition ?
Οὐαὶ οἱ λέγοντες τὸ πονηρὸν καλὸν καὶ τὸ καλὸν πονηρόν, οἱ τιθέντες τὸ σκότος φῶς καὶ τὸ φῶς σκότος, οἱ τιθέντες τὸ πικρὸν γλυκὺ καὶ τὸ γλυκὺ πικρόν
Isaac Newton
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### Re: sub-set proposition and convertible proposition

Isaac Newton wrote:Ἰησοῦς ἐστιν ὁ λόγος

Is the above statement a sub-set proposition or a convertible proposition ?

It is essentially convertible. Grammatically it is convertible because Ἰησοῦς is a proper name and λόγος has the article. Semantically it is convertible because I don't think that John has anything else much to say about ὁ λόγος other than that it is Jesus.
Markos
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### Re: sub-set proposition and convertible proposition

Hi Marcos,

Markos wrote:
Isaac Newton wrote:Ἰησοῦς ἐστιν ὁ λόγος

Is the above statement a sub-set proposition or a convertible proposition ?

It is essentially convertible. Grammatically it is convertible because Ἰησοῦς is a proper name and λόγος has the article. Semantically it is convertible because I don't think that John has anything else much to say about ὁ λόγος other than that it is Jesus.

I'm inclined to believe that both nouns are not convertible since they are not completely interchangeable. For otherwise we could not say that ὁ λόγος was at one point not "flesh."

I'm looking at the sentence as a sub-set proposition with ὁ λόγος as the PN.. Here's GGBB, p.44,

"In instances where one substantive is articular and the other is a proper name (or where both are articular), word order may be the determining factor."

Since in the above sentence Ἰησοῦς precedes ὁ λόγος , it is the subject...Also , as far as I can tell, even if both substantives are proper nouns, it is not a grammatical requirement that they be convertible.
Οὐαὶ οἱ λέγοντες τὸ πονηρὸν καλὸν καὶ τὸ καλὸν πονηρόν, οἱ τιθέντες τὸ σκότος φῶς καὶ τὸ φῶς σκότος, οἱ τιθέντες τὸ πικρὸν γλυκὺ καὶ τὸ γλυκὺ πικρόν
Isaac Newton
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### Re: sub-set proposition and convertible proposition

χαῖρε καὶ σύ, φίλε!

It seems to me that most convertible propositions are not WHOLLY interchangeable. If you wanted to, you could rate convertible propositions. I would say this is an 8 or a 9. You might say it is a 3 or a 4. Anything below a 1 would be a subset proposition.

John would agree, would he not, that Jesus is the Word and that the Word is Jesus?

I'm inclined to believe that both nouns are not convertible since they are not completely interchangeable. For otherwise we could not say that ὁ λόγος was at one point not "flesh."

The logos was indeed at one point not flesh. Jesus was indeed at one point not flesh.
Markos
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### Re: sub-set proposition and convertible proposition

Hi Marcos,

Markos wrote:χαῖρε καὶ σύ, φίλε!

It seems to me that most convertible propositions are not WHOLLY interchangeable. If you wanted to, you could rate convertible propositions. I would say this is an 8 or a 9. You might say it is a 3 or a 4. Anything below a 1 would be a subset proposition.

Wallace in GGBB defines a convertible proposition as follows:

[the] convertible proposition...indicates an identical exchange. That is to say, both nouns have an identical referent. The mathematical formulas of A=B, B=A are applicable in such instances. A statement such as "Michael Jordan is the greatest basketball player in NBA history" means the same thing as "the greatest player in NBA history is Michael Jordan." There is complete interchange between the two (p. 41).

An 8 or 9 or even a 99.999∞ would be a sub-set proposition.

John would agree, would he not, that Jesus is the Word and that the Word is Jesus?

I don't think he could say Jesus = the Word and the Word = Jesus . The most he could say is that Jesus is [is of essential predication, not of identity] the Word [ because the Word is not necessarily Jesus.].

The logos was indeed at one point not flesh. Jesus was indeed at one point not flesh.

If Jesus and logos were interchangeable,the following statement would logically have to be false:

Jesus is the Logos made flesh. But it is true... And I'm sure we could find more such enigmas..
Οὐαὶ οἱ λέγοντες τὸ πονηρὸν καλὸν καὶ τὸ καλὸν πονηρόν, οἱ τιθέντες τὸ σκότος φῶς καὶ τὸ φῶς σκότος, οἱ τιθέντες τὸ πικρὸν γλυκὺ καὶ τὸ γλυκὺ πικρόν
Isaac Newton
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