The Game of Logic eBook

This eBook from the Gutenberg Project consists of approximately 66 pages of information about The Game of Logic.

“All xm are y” contains “Some xm are y”, which contains “Some x are y”.  Or, in words, “All rainy days are tiresome” contains “Some rainy days are tiresome”, which contains “Some rainy periods are tiresome”.

Moreover, the first Premiss, besides being superfluous, is actually contained in the second; since it is equivalent to “Some rainy days exist”, which, as we know, is implied in the Proposition “All rainy days are tiresome”.

Altogether, a most unsatisfactory Pair of Premisses!

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| 0     |       |
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|   | 1 |   |   |
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|   | 0 | 0 |   |       | 1 |   |
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| 0     |       |       | 0 |   |
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Let “things” be Universe; m="medicine”;
x="nasty”; y="senna”.

All m are x; &there4 All y are x. 
All y are m.

i.e.  Senna is nasty.

[See remarks on No. 7, p 60.]

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|    ---|---    |
|   | 0 | 1 |   |
21.  |-1-|---|---|---|        -------
|   | 0 |   |   |       |   | 1 |
|    ---|---    |       |---|---|
|       |       |       |   |   |
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Let “persons” be Universe; m="Jews”;
x="rich”; y="Patagonians”.

Some m are x; &there4 Some x are y’. 
All y are m’.

i.e.  Some rich persons are not Patagonians.

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| 0     |       |
|    ---|---    |
|   |   -   |   |
22.  |---|---|---|---|        -------
|   | 0 | 0 |   |       |   |   |
|    ---|---    |       |---|---|
| 0     |       |       | 0 |   |
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Let “creatures” be Universe; m="teetotalers”;
x="that like sugar”; y="nightingales”.

All m are x; &there4 No y are x’. 
No y are m’.

i.e.  No nightingales dislike sugar.

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|       |       |
|    ---|---    |
|   | 0 | 0 |   |
23.  |-1-|---|---|---|        -------
|   | 0 |   |   |       |   |   |
|    ---|---    |       |---|---|
|       |       |       |   |   |
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Let “food” be Universe; m="wholesome”;
x="muffins”; y="buns”.

No x are m;
All y are m.

There is ‘no information’ for the smaller Diagram; so no Conclusion can be drawn.

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|   | 0 | 0 |   |
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Let “creatures” be Universe; m="that run well”;
x="fat”; y="greyhounds”.

No x are m; &there4 Some y are x’. 
Some y are m.

i.e.  Some greyhounds are not fat.

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|       |       |
|    ---|---    |
|   |   -   |   |
25.  |-1-|---|---|---|        -------
|   | 0 | 0 |   |       |   |   |
|    ---|---    |       |---|---|
|       |       |       |   |   |
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Let “persons” be Universe; m="soldiers”;
x="that march”; y="youths”.

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The Game of Logic from Project Gutenberg. Public domain.
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