[GAWickowski]

Professor Casey,

If I understand things correctly, you state two things which seems to conflict with some references. This looks easy to resolve, but I would like your clarification.

First: You state that a valid eduction (formally) from a given proposition is exactly the same proposition, except that it is in a different form.

Second: You state that there are only four equivalent forms of a proposition that can appear.

For example: SAP is equivalent to SEP*, P*ES, and P*AS*.

According to George H. Joyce in “Principles of Logic, ” immediate inference doesn’t advance knowledge in the way a syllogism does and, hence in that sense, only “the same truth is enunciated [where] the conceptual expression undergoes transformation” (pp 92-3). https://archive.org/stream/principleslogic00joycgoog#page/n116/mode/2up

A conversion that is not done “simply,” can get us from SAP to PIS. “All men are mortal,” e.g., to “Some mortal beings are men.” Do you consider this an equivalent proposition? If so, there are more than four equivalent forms. If not, which seems obviously likely, immediate inference in this broader usage can bring us valid propositions that are not merely equivalent from that which was given as a proposition to immediately infer from. And hence, if that is the case, there must be a distinction between that which is “merely equivalent” and Joyce’s claim that these inferences are the same “truth” (or propositional content) which only undergo a change in our conceptual relationship we form of them.

Thank you very much for your comments.

[gerard.casey]

Dear George W:

Thank you for that question. Clearly, SAP and SIP are not equivalent propositions. For one thing, one is universal and the other particular, and while the truth of SAP implies the truth of SIP, the truth of SIP doesn’t imply the truth of SAP.

When I say that eduction generates equivalent propositions, I’m talking about the three kinds I deal with, namely, (simple) conversion, contraposition and obversion. I confine my account to these three because other forms of eduction (e.g. conversion by limitation – from SAP to SIP to PIS) can be arrived at by means of a combination of the three kinds of eduction I mention and the inferences deducible from the square of opposition.

My account is a somewhat simplified treatment of the subject (but not falsified!) and it is so for pedagogical purposes. Just as one can get most of the information one needs for the operation of an electronic device from about 5-10% of a manual, so too, most of what one needs from the logic we’re dealing with here can be had from a slightly trimmed account. It may take a little longer to get where we need to go but the demands on memorisation and use are significantly less.

There isn’t, then, any conflict between my account and that of Joyce.

I hope this clarifies matters? If you have any remaining doubts, please do get in touch with me.

Best wishes,

Gerard

[GAWickowski]

That’s what I figured, I just wanted to be sure.

Now that I look at my notes again, I see you mention the difference between identical versus corresponding propositions. That’s important.

I’m glad you included how you can go from SAP to SIP (via the square of opposition) and then to PIS (via conversion). Everything now seems unified, including the additional immediate inference types that Joyce wrote about.

Thank you again,
George

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