Now that I have your attention, on with validity!
Last time we chatted about ‘distribution’ of terms. If a term is distributed, then what we mean is that we’re referring to ALL members of the subject or ALL those the predicate could possibly address.
For example in the proposition No carrots are sweet, we are saying something about ALL carrots and something about ALL ‘sweetness’ as a predicate. So carrots and sweet are both distributed.
If we posit……. Some boys are strong, then the terms boys and strong are undistributed because we are talking about only some of the set of boys and only some of the set of strong things.
Why do we care whether a term is distributed or undistributed? I’m glad you asked!
Remember that we must be precise with our words. We must not give the impression of ALL if we mean only SOME. To say that ALL preteens get to stay up until midnight is a lot different than SOME do. Since terms and their quantifiers build propositions which in turn build arguments, accuracy is important.
Often people overgeneralize in order to make a point. We, the recipient of the argument, need to be aware of quantifiers (the all, some, no, some..not) or we’ll be HAD!!!
On to rule 3 of how to test whether a syllogism (argument) is valid (i.e. in the correct FORM):
Rule 3 – if a term in the conclusion is distributed (applies to ALL of a term) , then it also must be distributed in the premises. This prevents overreaching conclusions.
To determine whether a term is distributed/undistributed we label our terms by the position they occupy in each of the 3 propositions and in the syllogism itself. Here is our ‘DUDUs and UUDDs’ chart again from last time.
Subj 
Pred 

A(all) 
D 
U 
I (some) 
U 
U 
E (no) 
D 
D 
O (some…not) 
U 
D 
Some satisfying relationships are happy
Some satisfying relationships are marriages
Tf, all marriages are happy
Labeling our terms, starting ‘bottom up’ with the conclusion, we get:
Premise 1 – Some satisfying relationships(Mu) are happy (Pu)
Premise 2 – Some satisfying relationships (Mu) are marriages (Su)
Conclusion – Tf, all marriages (Sd) are happy(Pu)
S = subject term is marriages
P = predicate term is happy
M = middle term is satisfying relationships
U = undistributed
D = distributed
Rule # 3 states that if a term is distributed in the conclusion, then it has to be distributed in the premises. We find that marriages IS distributed in the conclusion; however, where the subject term marriages is located in P2, it is NOT distributed because Premise 2 is an “ I” statement (see chart above).
Therefore, we say that the syllogism is INVALID because it violates rule # 3 (of 7 altogether), committing the Fallacy of Illicit Minor (one can violate the minor or the major term.)
Just pronounce the word ‘illicit’ in a class of 8^{th}graders and you have their instant attention as they wait to hear about SEX!!!
So I have explained to my rapt class that the term ‘illicit’ means NOT allowed or unlawful. What we are NOT allowed to conclude is that every single marriage is happy JUST because SOME satisfying relationships are happy and marital ones. That conclusion goes FARTHER than the information given in premise 1 and premise 2.
Next time we will talk about a fallacy called FUM, where the middle term is undistributed.
In the meantime, as you read and listen to arguments, ask yourself if the conclusion drawn is valid or invalid according to Rule 3. If you run across an egregious and interesting example, please share!
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