Phil 347 Midterm 2/ Design Argument | Questions
and Verified Answers
What is another name for the cosmological argument?
Argument a priori
Which cosm. argument was first?
Plato's
Plato's cosm. argument
Everything that begins to exist has a cause distinct from itself
The universe began to exist [for reason R]
The universe has a cause distinct from itself
Why does Plato suggest that the universe began to exist? I.e what is reason R?
Everything we can access through our senses is in a process of decay
Nothing eternal is in a process of decay
Everything empirical is non-eternal
The universe can be accessed with our senses
Hence, the universe is non-eternal
2 kinds of evidence for a claim
A priori
A posteriori
A priori
Comes before experience
Intuitively evident
A posteriori
Comes after experience, based on experience
,What was Aristotle's problem with Plato's cosm. argument? What part of reason R does
Aristotle have an issue with?
Some substances that comes to be must come out of some underlying thing
So all of the things in the universe emerged from some substratum
He has an issue with premise 2 due to reason R because he thinks that everything comes out of
some substratum
What did Philoponus add to the cosm. argument?
He argued with Aristotle to provide 2 a priori arguments supporting premise 2 of Plato
Philoponus' 2 a priori arguments
1. It is impossible that there be an actual infinity of real things
2. It is impossible to form an actual infinity by succession
Cosm. argument as stated by Philoponus
1. Everything that begins to exist has a cause distinct from itself
2. The universe began to exist [for reason R] because...
2.1. It is impossible that there is an actual infinity of real things.
2.2. It is impossible to form an actual infinity by succession.
3. The universe has a cause distinct from itself
Potential infinity
Indefiniteness when you can just keep adding and indefinitely keep on adding
Actual infinity
The kind of infinity that is complete in which nothing can be added
Is God's knowledge actually or potentially infinite? (Classically)
Actually infinite
, Why can't the universe be eternal?
Because if so, the number of events (moments in time) would be an actual infinity, but actual
infinities cannot exist for real things
Why did William Lane Craig believe that the universe could not be eternal?
1. If the universe were eternal, the universe would be preceded by an actual infinity of prior
moments
2. That's impossible
3. Hence, the universe is not eternal
Why does Philoponus think that actual infinities cannot exist a priori?
Based on set theory
Set theory reasoning for actual infinities
Suppose we have an infinity of A and another infinity of set A and B.
If they were both actual infinities, the cardinality (size) of the first set = cardinality of second
set.
This is counterintuitive because there will be more in the second set intuitively
Also if we focus on set A + B and we subtracted all of B, we would end up with set A. But
somehow, after removal, it would still have the same cardinality because it's still an actual
infinity
However, this would be the case if actual infinities existed
Whole/part axiom
A subset of a set cannot have the same size as the set (when the subset and set are different)
Actual infinities and whole/part axiom
Actual infinities of real things violate the whole/part axiom
Cantor's explanation of set theory
and Verified Answers
What is another name for the cosmological argument?
Argument a priori
Which cosm. argument was first?
Plato's
Plato's cosm. argument
Everything that begins to exist has a cause distinct from itself
The universe began to exist [for reason R]
The universe has a cause distinct from itself
Why does Plato suggest that the universe began to exist? I.e what is reason R?
Everything we can access through our senses is in a process of decay
Nothing eternal is in a process of decay
Everything empirical is non-eternal
The universe can be accessed with our senses
Hence, the universe is non-eternal
2 kinds of evidence for a claim
A priori
A posteriori
A priori
Comes before experience
Intuitively evident
A posteriori
Comes after experience, based on experience
,What was Aristotle's problem with Plato's cosm. argument? What part of reason R does
Aristotle have an issue with?
Some substances that comes to be must come out of some underlying thing
So all of the things in the universe emerged from some substratum
He has an issue with premise 2 due to reason R because he thinks that everything comes out of
some substratum
What did Philoponus add to the cosm. argument?
He argued with Aristotle to provide 2 a priori arguments supporting premise 2 of Plato
Philoponus' 2 a priori arguments
1. It is impossible that there be an actual infinity of real things
2. It is impossible to form an actual infinity by succession
Cosm. argument as stated by Philoponus
1. Everything that begins to exist has a cause distinct from itself
2. The universe began to exist [for reason R] because...
2.1. It is impossible that there is an actual infinity of real things.
2.2. It is impossible to form an actual infinity by succession.
3. The universe has a cause distinct from itself
Potential infinity
Indefiniteness when you can just keep adding and indefinitely keep on adding
Actual infinity
The kind of infinity that is complete in which nothing can be added
Is God's knowledge actually or potentially infinite? (Classically)
Actually infinite
, Why can't the universe be eternal?
Because if so, the number of events (moments in time) would be an actual infinity, but actual
infinities cannot exist for real things
Why did William Lane Craig believe that the universe could not be eternal?
1. If the universe were eternal, the universe would be preceded by an actual infinity of prior
moments
2. That's impossible
3. Hence, the universe is not eternal
Why does Philoponus think that actual infinities cannot exist a priori?
Based on set theory
Set theory reasoning for actual infinities
Suppose we have an infinity of A and another infinity of set A and B.
If they were both actual infinities, the cardinality (size) of the first set = cardinality of second
set.
This is counterintuitive because there will be more in the second set intuitively
Also if we focus on set A + B and we subtracted all of B, we would end up with set A. But
somehow, after removal, it would still have the same cardinality because it's still an actual
infinity
However, this would be the case if actual infinities existed
Whole/part axiom
A subset of a set cannot have the same size as the set (when the subset and set are different)
Actual infinities and whole/part axiom
Actual infinities of real things violate the whole/part axiom
Cantor's explanation of set theory
