# Demonstrate that the following argument is invalid

Some politicians are Democrats. Hillary Clinton is a politician. /⸫ Hillary Clinton is a Democrat.

The argument's form is:

Some A are B. x is A. /⸫ x is B. [where 'A' and 'B' stand for groups of things and 'X' stands for an individual]

• We only help with HW when you give us some context about your class, what you are supposed to use, and what you tried to answer it. Aug 26 '19 at 23:59
• The class is logic and critical thinking. I am suppose to answer the question by showing how it is invalid. I answered by saying this argument is invalid, it’s invalid because it has a bad, invalid form. The first premise is clearly true. The second premise is true: Hillary Clinton is a politician. And the conclusion is true: Hillary Clinton is a Democrat.
– user40964
Aug 27 '19 at 0:22
• But how are you supposed to "demonstrate" that it is invalid? Show that it does not fit one of the standard syllogism figures? Give a counterexample by replacing Hillary Clinton by George Bush? Draw a picture with Venn circles? Aug 27 '19 at 0:26
• You have to explain how the argument given is invalid. I figured out the answer thank you for the help.
– user40964
Aug 27 '19 at 0:30
• I do not understand if just an answer is enough or your class also requires to justify it in some particular way. Aug 27 '19 at 0:35

If one can symbolize this in first order logic one can attempt to generate a tree proof which will either show that the argument is valid or provide a countermodel.

For a symbolization, let D be the predicate "Democrats". Let P be the predicate "politician". Then we can write "Some politicians are Democrats" as ∃x(Px ∧ Dx). Since we are given that Hilary Clinton is a politician we can write that as Ph. We want to know if the conclusion Dh, that she is also a Democrat, is valid.

Most people know that Hilary Clinton is in fact a Democrat but that information is not given explicitly in the premises. To test if we can derive that information about her being a Democrat with a tree proof generator we formulate the following "(∃x(Px ∧ Dx) ∧ Ph) → Dh".

The tool provides this countermodel:

The existence of this countermodel is evidence that the argument is not valid, even though the conclusion is in fact true that Hilary is a Democrat.

The countermodel presents a non-empty domain of two members, 0 and 1. The name h is assigned to 1. All members of the domain are politicians, but only one, the 0 member, who is not Hilary Clinton, is a Democrat.

This is one way to approach the problem. However, the methods you are required to use may not permit using such tools. These tools are still useful for exploring and testing answers that you do provide.

Tree Proof Generator. https://www.umsu.de/trees/

In a valid syllogism, the middle term must be distributed in at least one premise. This example violates that rule.

The example is the syllogism IAA in the first figure (Some M are P; All S are M; thus All S are P). The middle term (politicians) is undistributed. There is nothing connecting the two premises, so together they say nothing more than each does individually.

As for the conclusion, the technical statement is, “All persons identical to Hillary Clinton are Democrats.” The subject is a set containing exactly one member.