ABSTRACT
The Granny, Uncle and Spider arguments are unusually simple: two premises (input) and a conclusion (output). But even these need tidying if we want to make their forms absolutely clear. For example:
My Granny's rich! Everybody who has a Rolls Royce is rich, and she has one, so she's rich!
puts the argument's conclusion first. Then we have the two premises; then the conclusion again. This is very common in ordinary conversation. So is putting the conclusion first and not repeating it:My Granny's rich! Everybody who has a Rolls Royce is rich, and she has one!
Anyone who can follow the argument knows that what comes after the conclusion (conversationally) is in fact what the speaker accepts to start with and gives as reasons for drawing the conclusion. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203061350/f5ce7580-7c0c-4392-aeab-0c1bd683fe20/content/fig14_B.jpg" xmlns:xlink="https://www.w3.org/1999/xlink"/> It makes no difference in which order we take the two premises; logically speaking, both go into the machine together. But the conclusion follows from them. Logically, both conversational versions are identical in form to:Everyone who has a Rolls Royce is rich My Granny has a Rolls Royce __________ My Granny is rich.
(The line means 'THEREFORE'.)
Here the written order of statements follows the logical order.Must we also rewrite the Uncle argument (as I put it in Chapter 1) if we want to show its statements in their logical order? If so, do it.
What about the Spider argument?
https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203061350/f5ce7580-7c0c-4392-aeab-0c1bd683fe20/content/fig15_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>|
Insects have eight legs |
[FALSE] |
|
Spiders are insects |
[FALSE] |
|
THEREFORE |
|
|
spiders have eight legs. |
[TRUE] |
