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Sun 18 Sep, 2011 05:08 pm

A thing X is a sufficient cause of a thing Y if and only if X exists implies Y exists. A thing X is a necessary cause of a thing Y if and only if Y exists implies X exists. These definitions are commonly accepted.

Now, suppose things H and J exist. Then H exists implies J exists since hypothesis and conclusion are true. So, H is a sufficient cause of J by definition. Also, J exists implies H exists since hypothesis and conclusion are true. So, H is a necessary cause of J by definition. Using conjunction introduction, H is a necessary and sufficient cause of J. This proves that anything that exists is a necessary and sufficient cause of anything that exists.

Is this true? If not, find the flaw in the argument. What do you think about this?

@browser32,

browser32 wrote:

Now, suppose things H and J exist. Then H exists implies J exists since hypothesis and conclusion are true.

Illogical conclusion, incompatible with your own construct.

@browser32,

...either you change the definition of exist or you change the definition of cause...the general idea is good the terms chosen are n´t !

@browser32,

browser32 wrote:

What do you think about this?

I think you are trying to determine just exactly how many angels can dance on the head of a common pin.

@browser32,

browser32 wrote:

A thing X is a sufficient cause of a thing Y if and only if X exists implies Y exists. A thing X is a necessary cause of a thing Y if and only if Y exists implies X exists. These definitions are commonly accepted.

Now, suppose things H and J exist. Then H exists implies J exists since hypothesis and conclusion are true. So, H is a sufficient cause of J by definition. Also, J exists implies H exists since hypothesis and conclusion are true. So, H is a necessary cause of J by definition. Using conjunction introduction, H is a necessary and sufficient cause of J. This proves that anything that exists is a necessary and sufficient cause of anything that exists.

Is this true? If not, find the flaw in the argument. What do you think about this?

False. Although sufficient and necessary conditions are indeed true, we still need to discern whether or not H implies J for sufficient conditions, or vice versa for necessary conditions. You have the logical form down, and I would agree with you on this, but that does not mean that we can take two arbitrary existents and say, "Well since so-and-so exists and another so-and-so exists, they are both necessary and sufficient for each other". You are confusing logic with experience. Think about it.