Phil Homework Wk3
1. Start with All stars are bright. What 3 other propositions can you infer from this by means of the Square of Opposition?
2. Start with No tech giant is a conservative. What 3 other propositions can you infer from this by means of the Square of Opposition?
3. Start with Some (at least one) dog is vicious. What, if anything, can you infer from this by means of the Square of Opposition?
4. Start with It is false that some tiger is not tame. What, if anything, can you infer from this by means of the Square of Opposition?
5. What is the obversion of each of the following. Hint: Be careful about 5.4!
5.1 All stars are bright.
5.2 No tech giant is a conservative.
5.3 Some (at least one) dog is vicious.
5.4 It is false that some tiger is not tame.
6. What is the difference, and give an example of each, between contrary and subcontrary?
7. What is the difference, and give an example of each, between contrary and contradictory?
8. What is the valid conversion of each of the following. If it cannot be validly converted, just say “No valid conversion.”
8.1 All stars are bright.
8.2 No tech giant is a conservative.
8.3 Some (at least one) dog is vicious.
8.4 Some tigers is not tame.
9. What is the valid contraposition of each of the following. If it cannot be validly contraposited, just say “No valid contraposition.”
9.1 All stars are bright.
9.2 No tech giant is a conservative.
9.3 Some (at least one) dog is vicious.
9.4 Some tiger is not tame.
10. Assume for the sake of argument that this statement is true: All anarchists are extremists. Using the rules of the Square of Opposition, Obversion, Conversion, and Contraposition, perhaps by more than one different step, are the following statements True, False, or Undetermined? For extra credit, show how you can derive them if you think any one is True, or their contradictories if you think any one is False.
10.1 No anarchist is a non-extremist.
10.2 Some non-extremists are not non-anarchists.
10.3 No non-anarchists are non-extremists.
10.4 It is false that some non-extremists are not non-anarchists.
Here is an example of how to do a Venn Diagram for FERISON, an 3rd Figure, EIO mood syllogism.An example is:
No Republican is in favor of Obamacare.
Some Republican is in favor of health care accounts.
Some person in favor of health care accounts is not in favor of Obamacare.
Notice how this syllogism fulfills all 6 rules.
1. It has a universal premise:No Republican is in favor of Obamacare.
2. It has an affirmative premise: Some Republican is in favor of health care accounts.
3. Since one of the premises is particular (Some Republican is in favor of health care accounts) it has a particular conclusion (Some person in favor of health care accounts is not in favor of Obamacare.).
4. Since one of the premises is negative (No Republican is in favor of Obamacare.) it has a negative conclusion (Some person in favor of health care accounts is not in favor of Obamacare.).
5. The middle term is distributed at least once. (No Republican is in favor of Obamacare.).
6. If either subject or predicate term is distributed in the conclusion, it must be distributed in its premise (“A person in favor of Obamacare” as predicate of a negative proposition is distributed in the conclusion, and it is also distributed, again as predicate of a negative proposition) in the premise (No Republican is in favor of Obamacare.).
I have an example in a Word doc above, done step by step.
First in use MS-Paint to draw 3 intersecting circles.The top one will be for the middle term Republican.
In doing a Venn diagram, you have to do the universal premise first, even if it is the minor premise.Here it is the major premise and has the form Emp.That means we have to “black out” all overlap between m and p (i.e. Republican and person in favor of Obamacare).
Next we have to do the other premise, in this case the minor premise.That means I need to put an X in any sector that is m and s (Some Republican is in favor of health savings accounts).To make it easier to read, I’ll erase the msp labels in that sector.
Finally we have to check to make sure that all the classes have a member.We just made it so for s and m.But how about p?Unfortunately there are 2 sectors —s p non-m and non-s p non-m – that could fill this need; and we have no grounds on which to decide whether it’s the one or the other or both.Some books would put an X on the line that makes the boundary between these two, s p non-m and non-s p non-m.But I prefer to leave them indeterminate.If there were only one sector with p available, we would put an X in it.That happens with some of the valid syllogism forms and is essential to show the conclusion.
In any case, as we have it above, the diagram does demonstrate the conclusion of Ferison: Some s is not p (Some person in favor of health savings accounts is not in favor of Obamacare.).
3. Write 4 original, valid syllogisms, one from each of the four figures.
Write 6 original, invalid syllogisms, each of which violates one of the six rules of valid syllogism. Identify the rule violated in each case.
