For the following argument, (1) reconstruct it as a standard form categorical sy
ID: 3471724 • Letter: F
Question
For the following argument, (1) reconstruct it as a standard form categorical syllogism with exactly three terms, (2) identify the three terms, (3) provide the mood and the figure, (4) use either the Rules method or the Venn diagram method to determine validity (if you use the Rules method, identify which Rules method you are using and indicate how the argument fares with regard to each rule; if you use the Venn diagram method, construct a proper Venn diagram for the argument), and indicate validity.
a) Some metals are rare and costly substances, but no welder’s materials are nonmetals; hence some welder’s materials are rare and costly substances.
Explanation / Answer
Answer a)
Step 1: breaking into premises and conclusion and symbolising:
P1: Some metals are rare and costly substances.
P2: No welder's materials are nonmetals.
C: Some welder's materials are rare and costly substances.
P1: Some M are R
P2: No W are nonM => All W are M (obverse)
C: Some W are R
Step 2: Translating into standard form
S= W
P= R
M= M
P1: Some M are P (major premise)
P2: All S are M (minor premise)
C: Hence, Some S are P
Step 3: identifying the Mood and figure:
the given argument is of the type IAI – 1
Step 4: proving Validity using Boolean Logic
Thus, the given argument is invalid as it breaks the rule about having both the middle terms ad distributed and it actually has an undistributed middle term.