23. If an Attribute occurs in both Premisses, the Term containing it is called 'the Middle Term'. For example, if the Premisses are "some m are x" and "no m are y'", the class of "m-Things" is 'the Middle Term.'
If an Attribute occurs in one Premiss, and its contradictory in the other, the Terms containing them may be called 'the Middle Terms'. For example, if the Premisses are "no m are x'" and "all m' are y", the two classes of "m-Things" and "m'-Things" may be called 'the Middle Terms'.
24. Because they can be marked with CERTAINTY: whereas AFFIRMATIVE Propositions (that is, those that begin with "some" or "all") sometimes require us to place a red counter 'sitting on a fence'.
25. Because the only question we are concerned with is whether the Conclusion FOLLOWS LOGICALLY from the Premisses, so that, if THEY were true, IT also would be true.
26. By understanding a red counter to mean "this compartment CAN be occupied", and a grey one to mean "this compartment CANNOT be occupied" or "this compartment MUST be empty".
27. 'Fallacious Premisses' and 'Fallacious Conclusion'.
28. By finding, when we try to transfer marks from the larger Diagram to the smaller, that there is 'no information' for any of its four compartments.
29. By finding the correct Conclusion, and then observing that the Conclusion, offered to us, is neither identical with it nor a part of it.
30. When the offered Conclusion is PART of the correct Conclusion. In this case, we may call it a 'Defective Conclusion'.
2. Half of Smaller Diagram.
Propositions represented.
__________
------- -------
| | | | | |
1. | | 1 | 2. | 0 | 1 |
| | | | | |
------- -------
------- -------
| | | | | |
3. | 1 | 1 | 4. | 0 | 0 |
| | | | | |
------- -------
------- -------
| | | | | |
5. | 1 | 6. | | 0 |
| | | | | |
------- -------
-------
| | |
7. | 1 | 1 | It might be thought that the proper
| | |
------- -------
| | |
Diagram would be | 1 1 |, in order to express "some
| | |
-------
x exist": but this is really contained in "some x are y'."
To put a red counter on the division-line would only tell
us "ONE OF THE compartments is occupied", which we
know already, in knowing that ONE is occupied.
-------
| | |
8. No x are y. i.e. | 0 | |
| | |
-------
-------
| | |
9. Some x are y'. i.e. | | 1 |
| | |
-------
-------
| | |
10. All x are y. i.e. | 1 | 0 |
| | |
-------
-------
| | |
11. Some x are y. i.e. | 1 | |
| | |
-------
-------
| | |
12. No x are y. i.e. | 0 | |
| | |
-------
-------
| | |
13. Some x are y, and some are y'. i.e. | 1 | 1 |
| | |
-------
-------
| | |
14. All x are y'. i.e. | 0 | 1 |
| | |
-------
---
| |
15. No y are x'. i.e. |---|
| 0 |
---
---
| 1 |
16. All y are x. i.e. |---|
| 0 |
---
---
| 0 |
17. No y exist. i.e. |---|
| 0 |
---
---
| |
18. Some y are x'. i.e. |---|
| 1 |
---
---
| |
15. Some y exist. i.e. |-1-|
| |
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