Categorical Logic, "Only" and "The Only"

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All good Indians are dead Indians = All G are D.
Only good Indians are dead Indians = All D are G.
The only good Indian is a dead Indian = ?

How is this last statement to be symbolized? It seems the word “The” in front of “only” makes it “All G are D.” Is that correct?

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@JCBNLA,

I would say the answer was (see below) because the addition of 'The' returns the term to a Universal, therefore:
The only G are D = All D are G.
(The only good G in the category of all G is D and because 'Only' was used then it must be that it is = All D are G.

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@igm,

Amended reply see above...

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@JCBNLA,

What you are after is equivalence, but this is a really offensive way of asking it.

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@engineer,

engineer wrote:

What you are after is equivalence, but this is a really offensive way of asking it.

I agree but put that to one side.

Although this is Categorical Logic and not Propositional Logic, is the term 'equivalence' used in Categorical Logic?

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@engineer,

I chose this bigoted statement only because it's a short and famous. I don't agree with its sentiment.

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@igm,

You wrote "The only G are D = All D are G." That means you think the word "the" in front of the "only" has no effect, that . . .

The only G are D = Only G are D.

If that's correct, then the textbook I'm reading got it wrong. So who is right? Here's what my textbook says:

Question: “The only productive and innovative scientist is the one who enjoys freedom of thought and is not afraid to risk pursuing a new idea.”

Answer: “All P are T (P represents persons who are productive and innovative scientists; T represents persons who enjoy freedom of thought and are not afraid to risk pursuing new ideas.)”

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@JCBNLA,

JCBNLA wrote:

I chose this bigoted statement only because it's short and famous. I don't agree with its sentiment.

To me, a bigoted statement, though short and famous, should never be chosen in this context. If there is no alternative, a slightly longer but uncontroversial statement must be chosen. Perhaps, the only person able to answer your question didn't because they were offended by your statement.

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@JCBNLA,

JCBNLA wrote:

If that's correct, then the textbook I'm reading got it wrong.

Given a choice of a stranger's reply, whose credentials are unknown, or a textbook, I would always choose the textbook, if my understanding of the textbook's example was a valid understanding.

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@igm,

I'm reading a textbook about ancient civilisations published between the wars.

The attituee of the writer is clearly one thst Western cibilisation is supetior to all other cultures.

It doesn't mean that what he writes about the Phoenecians has no value butit doesmeanthate erything he writes shouldnot be taken at face value.

I'm also reading a book about British comics from the 1890s onwards, the comics are peppered with the n word and other offensive terms for black people.

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@izzythepush,

izzythepush wrote:

I'm reading a textbook about ancient civilisations published between the wars.

The attituee of the writer is clearly one thst Western cibilisation is supetior to all other cultures.

It doesn't mean that what he writes about the Phoenecians has no value butit doesmeanthate erything he writes shouldnot be taken at face value.

I'm also reading a book about British comics from the 1890s onwards, the comics are peppered with the n word and other offensive terms for black people.

I'd say it's all about context.

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@igm,

It is, but saying that I wouldn't cut and paste certain terms from those sources unless it was specifically being discussed and even then I would censor some terms.

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@izzythepush,

izzythepush wrote:

It is, but saying that I wouldn't cut and paste certain terms from those sources unless it was specifically being discussed and even then I would censor some terms.

Sounds like a plan.

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Categorical Logic, "Only" and "The Only"

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