Hello Anthony,
I am going to list the mounting number of propositions. I begin with the one axiom:
Axiom: All Scripture is the word of God.
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So you agree that Scripture is the sixty-six books of the Protestant Bible.
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Proposition 1: All Scripture is the sixty-six books of the Protestant Bible.
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And I'll assume that you agree that the books are the words, sentences, propositions, etc that they contain.
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Proposition 2: All the sixty-six books of the Protestant Bible are the "words, sentences, and propositions" contained in the sixty-six books of the Protestant Bible.
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All Scripture is knowledge…
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Proposition 3: All Scripture is knowledge.
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All Scripture is knowledge" has exactly the same meaning as:
"All the words, sentences, propositions, etc that the 66 books of the Protestant Bible contain is knowledge.
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Anthony’s Valid Syllogism Premise 1: All Scripture is the sixty-six books of the Protestant Bible.
Premise 2: All the sixty-six books of the Protestant Bible are the "words, sentences, and propositions" contained in the sixty-six books of the Protestant Bible.
Conclusion: All Scripture is the "words, sentences, and propositions" contained in the sixty-six books of the Protestant Bible.
Anthony’s Invalid Syllogism Premise 1: All Scripture is knowledge.
Premise 2: All Scripture is the "words, sentences, and propositions" contained in the sixty-six books of the Protestant Bible.
Conclusion: All the "words, sentences, and propositions" contained in the sixty-six books of the Protestant Bible is knowledge.
Not only is the above argument invalid, but we have three additional propositions that are not derived from the one axiom that must be accounted for. So, I guess I am not with you so far.
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If P = p1, p2, p3, p3,...pn,
then All (p1, p2, p3, p3,...pn) is X is the exact the same as all P is X.
Nothing has been added or subtracted.
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We have four different propositions. One is “All P is X,” another is “All (p1, p2, p3…, pn) is X,” another is “All P is (p1, p2, p3…, pn),” and the last one is “All (p1, p2, p3…, pn) is P.” Now to go from “All (p1, p2, p3, p3,...pn) is X” to “All P is X”, the required additional proposition is “All P is (p1, p2, p3…, pn).” If you wanted to go from “All P is X” to “All (p1, p2, p3, p3,...pn) is X,” then the additional proposition needed is “All (p1, p2, p3…, pn) is P.” And if you wanted to go to the equivalence of the two propositions, then you would have to have both of the other propositions.
Now, will you reciprocate?
(1) The implication you want to draw is not an instance of the rule of subalternation. You claim to be arguing from a universal affirmative statement to a particular affirmative statement when in fact you are arguing from a universal affirmative statement to another universal affirmative statement. You are going from "All S is P" directly to "All Q is P". There is no logic authority be it book, professor, or whomever that would say this is a valid deduction. So, what say you?
(2) The implication you want to draw would make the syllogistic argument form
Barabara unnecessary. This form allows one to go from a universal affirmative statement to another universal affirmative statement where the second universal affirmative statement is simply an instance of the first universal statement. Aristotle, Clark, and all logicians felt that this argument form was needed to make the inference valid. In other words, they did not think one could validly go directly from a universal statement to a universal instance of that statement. However, this is what you want to claim is valid. So, is everyone but you wrong?
Brian