If you meant, "If a thing is based on a profit motive, it is constitutional," which seems to be the most consistent interpretation of the wording in context (despite being a clearly false premise, c.f. antitrust law), the syllogism you present is of invalid form - in fact, it cannot be rephrased into the standard form for a categorical syllogism.
1. P -> C [premise]
2. G -> ~P [premise]
--
*. G -> ~C [*invalid*]
If, on the other hand, you meant "If a thing is constitutional, then it is based on the profit motive," then your syllogism is valid. (But I'd have to object to your premise in that case on the grounds that it's clearly false - many things the government has laws for are either neutral to or opposed to the "profit motive", again such as antitrust law.) This is an AAA syllogism with the first statement phrased oddly, viz. "all things which are not P are also not C."
1. C -> P [premise]
2. ~P -> ~C [2, contrapositive] A
3. G -> ~P [premise] A
--
*. G -> ~C [1, 3, modus ponens] A
I suspect Darl is using a slightly different meaning, that of a biconditional: "a thing is constitutional if and only if it is based on the profit motive", which would give:
1. C <-> P [premise]
2. (P -> C) & (C -> P) [def. <->]
And could therefore be turned into the second (and valid in form) argument. However, that premise is equally blatantly false.
If I were to try to formulate a logical with reasonable premises (unlike all of the above first premises, which I reject) and valid form, I would come up with the following (which needs to be expressed using first-order predicate calculus, and for which I've used E and A as substitutes for the standard predicate 'exists' and 'all' symbols):
1. Some things are both constitutional and based on the profit motive.
2. All things released under the GNU Public License are not based on the profit motive. (This premise is slightly questionable, but I grant it for the majority of cases.)
The 17th century was 1600-1699; since capitalism is usually attributed to Adam Smith, who lived from 1723-1790, it would be tricky for 17th century England to be post-capitalist.
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Apple hasn't, but other people are working on it: take a look at PyObjC.
As a logical analysis of the above...
If you meant, "If a thing is based on a profit motive, it is constitutional," which seems to be the most consistent interpretation of the wording in context (despite being a clearly false premise, c.f. antitrust law), the syllogism you present is of invalid form - in fact, it cannot be rephrased into the standard form for a categorical syllogism.
1. P -> C [premise]
2. G -> ~P [premise]
--
*. G -> ~C [*invalid*]
If, on the other hand, you meant "If a thing is constitutional, then it is based on the profit motive," then your syllogism is valid. (But I'd have to object to your premise in that case on the grounds that it's clearly false - many things the government has laws for are either neutral to or opposed to the "profit motive", again such as antitrust law.) This is an AAA syllogism with the first statement phrased oddly, viz. "all things which are not P are also not C."
1. C -> P [premise]
2. ~P -> ~C [2, contrapositive] A
3. G -> ~P [premise] A
--
*. G -> ~C [1, 3, modus ponens] A
I suspect Darl is using a slightly different meaning, that of a biconditional: "a thing is constitutional if and only if it is based on the profit motive", which would give:
1. C <-> P [premise]
2. (P -> C) & (C -> P) [def. <->]
And could therefore be turned into the second (and valid in form) argument. However, that premise is equally blatantly false.
If I were to try to formulate a logical with reasonable premises (unlike all of the above first premises, which I reject) and valid form, I would come up with the following (which needs to be expressed using first-order predicate calculus, and for which I've used E and A as substitutes for the standard predicate 'exists' and 'all' symbols):
1. Some things are both constitutional and based on the profit motive.
2. All things released under the GNU Public License are not based on the profit motive. (This premise is slightly questionable, but I grant it for the majority of cases.)
That is:
1. E(x) : C(x) & P(x) [premise]
2. A(x) : G(x) -> ~P(x) [premise]
However, there's nowhere I can go from that. There isn't a logical manipulation I can perform to get an interesting conclusion.
The 17th century was 1600-1699; since capitalism is usually attributed to Adam Smith, who lived from 1723-1790, it would be tricky for 17th century England to be post-capitalist.