A'ight this one is gonna be a quick and short one. There are four figures of a syllogism, characterized by the 4 different combinations the middle term can take in respect to the minor (subject of the conclusion) and major term (predicate of the conclusion). Sometimes it gets hard to remember which one is which, so here's a quick tip for ya.
Sign convention - P (predicate of conclusion/major term/major premise). S (subject of conclusion/minor term/minor premise). M (middle term)
The four figures of syllogisms are -
Now observe the positions of the M (middle term) in each of the syllogisms. Those specific positions are referred to by their corresponding numbers, i.e. the first position of the M - M being diagonal to each other is called the 1st figure of syllogism and the second position is called the 2nd figure of syllogism and so on.
Now the way to remember them.
Notice the pattern? Notice this shrug emoji? ¯\_(| ͜ |)_/¯ We are going to simplify this to --
\ || / this. The \ represents the pattern of placement of M in the first figure and similarly, the / represents the 4th figure. So they are easy to remember. Now the second figure has the placement of M towards the right side in a vertical fashion, that's where the placement of the first | is on the \ || /, towards the right side of the first \. Similarly, the second figure has the placement of M towards the left side in a vertical fashion, that's where the placement of the second | is on the \ || /, towards the left side of the last /.
Let us take an example -
All men are humans.
No humans are dogs.
Therefore no dogs are men.
Figuring out the predicate of the conclusion/major term (men), the subject of the conclusion/minor term (dogs), and the middle term (humans) we can write this as --
P -- M
M -- S
--------------
∴ S -- P
We see that the position of both the Ms form a right-leaning diagonal i.e. / By our \ || / drawing we know that this sign / comes in the 4th position, therefore this is a 4th figure syllogism.
Taking another example -
All artists are egoists.
Some artists are poor.
Therefore some poor are egoists.
Figuring out the predicate of the conclusion/major term (egoists), the subject of the conclusion/minor term (poor), and the middle term (artists) we can write this as --
M -- P
M -- S
--------------
∴ S -- P
Here we see that the position of both the Ms form a left-sided straight line i.e. | By our \ || / drawing we know that this left-sided straight sign | comes in the 3rd position, therefore this is a 3rd figure syllogism.
Closing Tip
If you are having a problem remembering the position of the 2nd and 3rd figure because both the || vertical lines are close together, try using an x in between like this, \x||x/, and notice the position of | with regards to the x. Right to the x, x|, meaning right-sided vertical line and thus 2nd figure, and if the left side of x, |x, then left-sided vertical line, meaning 3rd figure of syllogism.
Hope this helps. Any questions? Ask below
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