Just for reference at the very, very top: a syllogism is invalid if it can possibly have true premises and a false conclusion.
I worked through a number of the 24 valid syllogisms, but I think the four in figure one, Barbara, Celarent, Darii, and Ferio, should suffice for non-tl;dr purposes. (I suspect the Trinity renders most or all of the valid syllogisms invalid, however.)
Barbara
AAA-1
Jim is my mechanic.
The mechanic on Jones Road is Jim.
Hence, the mechanic on Jones Road is my mechanic.
This is one of the most clearly valid syllogisms in my book. However, if the Trinity accurately describes reality, the following is an example where both premises are true, and the conclusion is false, which renders Barbara (which is the old "Socrates is a man" one) invalid:
God is the Father.
The Son is God.
Hence, the Son is the Father.
~~~
Here are some more:
Celarent
EAE-1
Plato is not Socrates.
The author of The Republic is Plato.
Hence, the author of The Republic is not Socrates.
The Son is not the Father.
God is the Son.
Hence, God is not the Father.
~~~
Darii
AII-1
Mercury is the closest planet to the Sun.
Ukaliali'i might be Mercury.
Hence, Ukaliali'i might be the closest planet to the Sun.
God is the Father.
The Son might be God.
Hence, the Son might be the Father.
~~~
Ferio
EIO-1
Asia is not Australia.
The most populous continent might be Asia.
Hence, the most populous continent might not be Australia.
The Son is not the Father.
God might be the Son.
Hence, God might not be the Father.
~~~
Just for comparison, syllogism AIA-1 is so invalid it doesn't even have a humanoid name:
Jim is my mechanic.
The mechanic on Jones Road might be Jim.
Hence, the mechanic on Jones Road is my mechanic.
God is the Son.
The Father might be God.
Hence, the Father is the Son.
If the Trinity is true, then Barbara, Celarent, Darii, and Ferio are hardly distinguishable from AIA-1, or any other invalid syllogism.
Sara L. Uckelman argues (I think) that such syllogisms actually are valid, and sound at that, by distinguishing between personal, formal, and essential predication. She writes
The paper is extremely technical, and I admit I have hardly a clue, but I have a hard time figuring out what it would take an orthodox Trinitarian to accept "pater est filius," even if it is an essential predication, and I'm not certain the distinction is relevant. None of the Trinitarians I brought the paper up to much took to Uckleman's conclusion.
A possible out for someone who does not want to allow that "pater est filius" is ever true is the "God's logic is not our logic" deal. I think a fair response is that that's fine, but "our logic" defines "invalid syllogism" as "a syllogism for which it is possible to have true premises and a false conclusion." If the Trinity is real, then it is possible for Barbara, Celarent, Darii, and Ferio to have true premises and a false conclusion. If that is possible, then they are invalid.
I worked through a number of the 24 valid syllogisms, but I think the four in figure one, Barbara, Celarent, Darii, and Ferio, should suffice for non-tl;dr purposes. (I suspect the Trinity renders most or all of the valid syllogisms invalid, however.)
Barbara
AAA-1
Jim is my mechanic.
The mechanic on Jones Road is Jim.
Hence, the mechanic on Jones Road is my mechanic.
This is one of the most clearly valid syllogisms in my book. However, if the Trinity accurately describes reality, the following is an example where both premises are true, and the conclusion is false, which renders Barbara (which is the old "Socrates is a man" one) invalid:
God is the Father.
The Son is God.
Hence, the Son is the Father.
~~~
Here are some more:
Celarent
EAE-1
Plato is not Socrates.
The author of The Republic is Plato.
Hence, the author of The Republic is not Socrates.
The Son is not the Father.
God is the Son.
Hence, God is not the Father.
~~~
Darii
AII-1
Mercury is the closest planet to the Sun.
Ukaliali'i might be Mercury.
Hence, Ukaliali'i might be the closest planet to the Sun.
God is the Father.
The Son might be God.
Hence, the Son might be the Father.
~~~
Ferio
EIO-1
Asia is not Australia.
The most populous continent might be Asia.
Hence, the most populous continent might not be Australia.
The Son is not the Father.
God might be the Son.
Hence, God might not be the Father.
~~~
Just for comparison, syllogism AIA-1 is so invalid it doesn't even have a humanoid name:
Jim is my mechanic.
The mechanic on Jones Road might be Jim.
Hence, the mechanic on Jones Road is my mechanic.
God is the Son.
The Father might be God.
Hence, the Father is the Son.
If the Trinity is true, then Barbara, Celarent, Darii, and Ferio are hardly distinguishable from AIA-1, or any other invalid syllogism.
Sara L. Uckelman argues (I think) that such syllogisms actually are valid, and sound at that, by distinguishing between personal, formal, and essential predication. She writes
Quote:
Originally Posted by Sara L. Uckelman "The expository syllogism Hoc essencia divina est pater. Filius est essencia divina. Igitur, pater est filius. is valid and sound if the statements are all taken to be essential predications. The paralogism arises when we interpret the conclusion as making a personal or formal predication." |
The paper is extremely technical, and I admit I have hardly a clue, but I have a hard time figuring out what it would take an orthodox Trinitarian to accept "pater est filius," even if it is an essential predication, and I'm not certain the distinction is relevant. None of the Trinitarians I brought the paper up to much took to Uckleman's conclusion.
A possible out for someone who does not want to allow that "pater est filius" is ever true is the "God's logic is not our logic" deal. I think a fair response is that that's fine, but "our logic" defines "invalid syllogism" as "a syllogism for which it is possible to have true premises and a false conclusion." If the Trinity is real, then it is possible for Barbara, Celarent, Darii, and Ferio to have true premises and a false conclusion. If that is possible, then they are invalid.
via JREF Forum http://forums.randi.org/showthread.php?t=266520&goto=newpost
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