I have a book on logic that I am studying. One of the examples the book uses to illustrate how to draw a conclusion from a syllogism goes like this:
All A is inside B
All B is inside C
Therefore All A is inside C
The book also has a little diagram next to this syllogism using circles. It shows a little circle (A) sitting in the middle of a larger circle (B) and an even larger circle (C) is drawn around the whole thing. The confusing part to me is that while the illustration seems infallible, and the conclusion of the above syllogism looks good, and the conclusion corresponds to the diagram of circles, the syllogism itself looks invalid.
The book teaches that the major term (term A in this case) is ALWAYS the predicate in the conclusion. But if you look at the conclusion, we see that A is not the predicate but has been snuck over to the subject side.
My question is, While the conclusion is true, the syllogism is invalid (at least I think) so how could I construct a valid syllogism to correspond to the chart with the three circles that I mentioned above?
Thanks in advance!
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This is very easy - either the book contains an error or you are misreading it. The syllogism you present is valid: if A is B and B is C then A is indeed C. This can be shown as an Euler diagram as three circles, the smallest inside the next inside the largest.
However, A is not (as you call it) the major term - it is the minor term. B is the middle term and C is the major term. The minor term (A) always ends up as subject of the conclusion, and the major term (C) always ends up as predicate of the conclusion.
The syllogism you present here is called a first figure mood: it has A as subject of the minor premise (all A are B) and C as predicate of the major premise (all B are C). Note in passing that traditionally the major premise is stated first and the minor premise is stated second (while you have stated them in a more 'natural' order) - this is significant insofar as first figure might be confused with fourth figure.
The issue of figures is important because the terms' positions in the premises vary (whence four figures), whereas the conclusion always conventionally has the terms A as subject and C as predicate. The middle term B does not enter it, merely serving in the premises as intermediary between the two others called the extremes.
See Future Logic part I, chapters 8-10, on all this.
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