#### Absurd Theologians and Atheists

fletch_F_Fletch

fletch_F_Fletch
Total Posts:  207
Joined  25-02-2007

08 December 2008 15:16

When I assert a conditional, I am claiming that it is impossible for that antecedent to be true and the consequent to be false.

Would you agree with the following statement in of itself: To allow the consequent you assume the antecedent.

This however is the main question I would like to have answered:
Why is Silenus bound to give the same answer to both of these claims (1a) and (2a) where they both are bounded by diferent assumptions, thus different conditions?

[ Edited: 08 December 2008 15:27 by fletch_F_Fletch]

waltercat

waltercat
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08 December 2008 17:59

fletch_F_Fletch - 08 December 2008 08:16 PM

When I assert a conditional, I am claiming that it is impossible for that antecedent to be true and the consequent to be false.

Would you agree with the following statement in of itself: To allow the consequent you assume the antecedent.

It is possible that you are confusing conditional statements with the logical rule known as Modus Ponens.

A conditional statement is one of the form If ..., then ... (1a) through (8a) are all conditional statements.  In a conditional of the form “If P, then Q”, P is the antecedent and Q is the consequent.  When we assert a conditional, we assert that whenever the antecedent is true, the consequent is also true.  Or, in other words, that it is impossible for the antecedent to be true and the consequent false.  Importantly, when we assert a conditional, we assert neither the antecedent nor the consequent.

The logical rule known as Modus Ponens is represented as follows:

If P, then Q
<u>P</u>
Q

In other words, the truth of (I) If P, then Q
together with the truth of (II) P
imply the truth of (III) Q.

One way to state this is to say that when we know that a conditional is true, then, if we find out that the antecedent is true, we can conclude that the consequent is true.  This means that in order to get the consequent when all we have is the conditional itself is to assume the truth of the antecedent.

Notice that Modus Ponens is a rule that applies to a set of statements that have a given form; namely a conditional and the antecedent of that conditional (P->Q and P).

Now, again, in order to assert that a conditional is true, we do not have to know or presuppose or assert or grant that the antecedent is true.  This is because a conditional can still be true even when both the antecedent and the consequent are both false.

Why is Silenus bound to give the same answer to both of these claims (1a) and (2a) where they both are bounded by diferent assumptions, thus different conditions?

(1a) and (2a) are not both bounded by different assumptions.  Each can be asserted without assuming the existence of God (or the non-existence of God).

fletch_F_Fletch

fletch_F_Fletch
Total Posts:  207
Joined  25-02-2007

09 December 2008 07:52

Thanks for taking the time to write out your response.  Could you explain this part in more detail, if not I understand, I can take some time to look over this rule through various websites.

The logical rule known as Modus Ponens is represented as follows:

If P, then Q
P
Q

In other words, the truth of (I) If P, then Q
together with the truth of (II) P
imply the truth of (III) Q.

For Modus Ponens if you grant P and from that must follow Q then Silenus rejects (2a) on the basis of Q not P.  He believes in P, God exists, but does not believe Q must follow.  I believe your job would be to show why Q must follow.  Pertaining to (1a) the P is based on a totally different starting point, this is what I meant with presupposition, that God does not exist.  Given P in (1a) Silenus accepts Modus Ponens that Q must follow.  Now you are stating that (2a) and (1a) must both be granted if you accept one of them, Why?

Pertaining to the definition of “if” and the previous conversations we both have had.  Would you agree that to utilize “P” you must acknowledge the components of “P” to state that “Q” follows.  In (2a) and (1a) would “P” not impact how you look at “Q”?

fletch_F_Fletch

fletch_F_Fletch
Total Posts:  207
Joined  25-02-2007

05 February 2009 17:34

Who is your source?

J.L. Mackie “The Miracle of Theism” Page 115

I took some time tonight reading up on Modus Ponens.

You are claiming if Silenus accepts (1a)

(1a) If God does not exist, then there are no objective moral truths.

Silenus must also accept (2a)

(2a) If God’s nature is such that He approves of rape, then rape is morally acceptable

The P, the antecedent of the conditional claim, are completely different for (1a) and (2a).

Therefore by accepting (1a) why is he bound to also accept (2a)?  The antecedents are actually at an antithesis to one another.

I understand if the horse is dead for you.

waltercat

waltercat
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06 February 2009 09:41

It’s not that the antecedent of both are the same.  It is that the antecedent in both is false (at least according to Silenus). According to Silenus, ‘God does not exist’ is false; and ‘God’s nature is such that He approves of rape’ is false.

A conditional statement that has a false antecedent is true by definition.

fletch_F_Fletch

fletch_F_Fletch
Total Posts:  207
Joined  25-02-2007

06 February 2009 12:30

It’s not that the antecedent of both are the same.

Exactly, they are completely opposite from one another.  Modus Ponens is basically an “if-then” claim.  The “if’s” are completely different.

A conditional statement that has a false antecedent is true by definition.

Given Modus Ponens it is true if all premisis are true.  As we both stated Modus Ponens doesn’t give any bearing to whether the actual statement pertains to reality.  Modus Ponens shows if an arguement is valid.  (I’m not lecturing to you I just want you to know how I see it)  So this is important for where you state,

I am going to take this as a yes.  This means that you believe that (1a) is true.

But how can it be true?  On your account, it is impossible for God not to exist.

You have expressed so much skepticism about

(2a) If God’s nature is such that He approves of rape, then rape is morally acceptable.

And I have inferred that you object to (2a) because it is impossible for God’s nature to be other than it is.

Well, if you object to (2a) you need to object to (1a) for precisely the same reasons.

(1a)  Selinus can believe, according to modus ponens, that it is valid and true.

(2a)  Selinus holds much skepticism of (2a) as a truth claim, not in the validity of it, according to modus ponens.  He denies the truth of the claim.

waltercat

waltercat
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Joined  02-03-2006

06 February 2009 17:50

fletch_F_Fletch - 06 February 2009 05:30 PM

Modus Ponens is basically an “if-then” claim.

No.  Modus Ponens is not a claim at all.  It is a rule.

An ‘if-then’ statement is called a conditional.  Conditionals are claims.

The rule of Modus Ponens has to do with the logical relation of conditionals (and other statements). But the rule itself is not a conditional and is not even a statement.

fletch_F_Fletch

fletch_F_Fletch
Total Posts:  207
Joined  25-02-2007

08 February 2009 10:33

No.  Modus Ponens is not a claim at all.  It is a rule.

The rule of Modus Ponens has to do with the logical relation of conditionals

You really are splitting hairs.  Modus Ponens is made up of a conditional claim.  One of the logical relations, being a conditional claim, p implies q.

http://www.mnstate.edu/gracyk/courses/phil 110/110definitions.htm#ponens

Here is the quote defining Modus Ponens,

“An argument with two premises, one of which is a conditional claim and another which endorses the antecedent of that conditional. The valid conclusion of a modus ponens argument will endorse the consequent of the conditional.”

Nevertheless your point doesn’t address the below point:

(1a)  Selinus believes that it is both valid and true.

(2a)  Selinus holds much skepticism of (2a) as a truth claim, but not in the validity of it, according to modus ponens.  Basically Selinus can accept the logic of (2a) but does not have to accept it as reality.  If Selinus accepts (1a) as valid and true why is he obligated to accept (2a) as both valid and true?

[ Edited: 08 February 2009 11:15 by fletch_F_Fletch]

waltercat

waltercat
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Joined  02-03-2006

11 February 2009 08:28

fletch_F_Fletch - 08 February 2009 03:33 PM

No.  Modus Ponens is not a claim at all.  It is a rule.

The rule of Modus Ponens has to do with the logical relation of conditionals

You really are splitting hairs.

No, it is not splitting hairs.  It is very important to understand the distinction between a logical rule and a claim.  Rules like Modus Ponens and Modus Tollens are not claims.  Rather they are rules that tell us what we can infer given the truth of certain types of claims.

Modus Ponens is made up of a conditional claim.

This is misleading at best.  I don’t think it is helpful to speak of what a logical rule is “made up of.”  Rather, we should understand that Modus Ponens is a rule that tells us that when we know that a conditional is true and we also know that the antecedent of that very conditional is true, we can conclude that the consequent of the conditional is true.

One of the logical relations, being a conditional claim, p implies q.

I don’t follow you here.

Nevertheless your point doesn’t address the below point:

(1a)  Selinus believes that it is both valid and true.

It is very misleading to say that a statement is valid.  Validity s a property of arguments, not statements.  So, it is very unclear what you mean when you say that (1a) is both valid and true.  I understand what it means to say that it is true, but, as a statement, it is meaningless to say that it is valid.

(2a)  Selinus holds much skepticism of (2a) as a truth claim, but not in the validity of it, according to modus ponens.  Basically Selinus can accept the logic of (2a) but does not have to accept it as reality.  If Selinus accepts (1a) as valid and true why is he obligated to accept (2a) as both valid and true?

Again, I don’t know what you mean when you describe (2a) as valid.  (2a) is a statement, not an argument.

fletch_F_Fletch

fletch_F_Fletch
Total Posts:  207
Joined  25-02-2007

11 February 2009 12:56

This is misleading at best.

Well I don’t care either way, you can take it up with the professor from MN State and his logic course.  (1a) and (2a) make an “if-then” claim which follows the rule of modus ponens.  I know Modus Ponens, in and of itself, is not making any outside claims.  I was referring to (1a) and (2a) when I referred to them as modus ponens claims, that is why I stated your splitting of hairs.

So, it is very unclear what you mean when you say that (1a) is both valid

The word “logical” would have been a better word usage.  Again a claim formated by using the rule of Modus ponens can be logical but not actual, as we both mentioned, this leads to my ending paragraph.

So replace valid with logical and we still have my point that I would like you to address.  By accepting (1a) as true why must Selinus also accept (2a) as true?  Selinus certainly can say (2a) is logical but not true.

waltercat

waltercat
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11 February 2009 14:25

fletch_F_Fletch - 11 February 2009 05:56 PM

This is misleading at best.

Well I don’t care either way, you can take it up with the professor from MN State and his logic course.  (1a) and (2a) make an “if-then” claim which follows the rule of modus ponens.

What does it mean to say that (1a) and (2a) “follow the rule of modus ponens”???  Claims, by themselves, do not follow rules.  Rules can be applied to claims and claims can be derived from rules, but claims do not follow rules.

If you think that (1a) and/or (2a) follow from the rule of modus ponens, then you are mistaken.  Rules do not imply anything, by themselves.  Rules operate on claims.  So, in order to use a rule to derive a claim, we need some claim(s) to begin with.

Remember what I said a while ago:  You are confusing the rule of modus ponens with the notion of a conditional statement.  This is easy to do given that modus ponens operates on conditionals.  But a conditional, by itself (as both (1a) and (2a) are) is not an instance of modus ponens and cannot be derived using modus ponens without the pre-existence of certain (very specific) other claims.

I know Modus Ponens, in and of itself, is not making any outside claims.  I was referring to (1a) and (2a) when I referred to them as modus ponens claims, that is why I stated your splitting of hairs.

But they aren’t “modus ponens claims”, whatever that might mean.  (1a) and (2a) are conditionals.  Period.

Get modus ponens out of your head for a second and just look at the structure of (1a) and (2a).  They have precisely the same structure:  ‘If . . . , then . . .”  A statement with this kind of structure is called a conditional.  Now, a conditional is false just in case the antecedent is true and the consequent is false.  Thus, when the antecedent of a conditional is false, the entire conditional is true.  This is the definition of conditional that you should have learned in your course.

Since, according to Silenus, the antecedents of both (1a) and (2a) are false, (1a) and (2a) are both true.

Ok?

fletch_F_Fletch

fletch_F_Fletch
Total Posts:  207
Joined  25-02-2007

12 February 2009 08:08

What does it mean to say that (1a) and (2a) “follow the rule of modus ponens”???

(1a) and (2a) both follow the logical formate of Modus Ponens,

(1a) and (2a) have two premises, one of which is a conditional claim and another which endorses the antecedent of that conditional.  I hate to bring up wikipedia, as I can’t stand it when people claim it as authority, nevertheless this is the part where modus ponens is a conditional claim (according to wikipedia),

The first premise is the “if–then” or conditional claim, namely that P implies Q.

(1a) and (2a) function as an “if-then” premise.

Now, a conditional is false just in case the antecedent is true and the consequent is false.  Thus, when the antecedent of a conditional is false, the entire conditional is true.  This is the definition of conditional that you should have learned in your course.

On the side I never took symbolic logic as a course, this is info I’m getting through researching the Internet.  I’m not following you here, this seems really important to understand:

Thus, when the antecedent of a conditional is false, the entire conditional is true.

Why if the antecedent is false would the entire conditional be true?  Can you explain this in more detail?

(1a) and (2a) function in a manner that states “if-then”.  If the “if” is false why would this make the statement true?

Since, according to Selinus, the antecedents of both (1a) and(2a) are false, (1a) and (2a) are both true.

I believe Selinus is not stating that they are false for the same reasons.  Selinus states that (1a) is false due to it’s inability to have any ontological basis for objective morality.  Pertaining to (2a) he is stating that it is false for a different reason, Selinus believes it is false because it goes against, in his view of God, his character.

It appears you are assuming Selinus is rejecting (1a) and (2a) under the same reasons.

waltercat

waltercat
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Joined  02-03-2006

12 February 2009 11:35

fletch_F_Fletch - 12 February 2009 01:08 PM

What does it mean to say that (1a) and (2a) “follow the rule of modus ponens”???

(1a) and (2a) both follow the logical formate of Modus Ponens,

No. They don’t.  Again, (1a) and (2a) are individual statements.  As such, Modus Ponens does not apply to them.  Modus ponens is a rule that applies to a series of statements (meaning more than one).

(1a) and (2a) have two premises,

No.  Neither (1a) nor (2a) has any premises.  Only an argument has premises and neither (1a) nor (2a) is an argument.  Rather, they are statements.

A statement is sentence that is either true or false.  Examples:

The sky is blue.
Grass is purple.
Either Pluto is a planet or Neptune is a planet.
If Pluto is a planet, then Sedna is a planet.

An argument is a collection of statements one of which is the conclusion and any other are premises.

Examples:

Argument I
Premise 1:  All crows are black.
Premise 2:  Sheryl is a crow.
Conclusion:  Sheryl is black.

Argument II
Premise A: If Socrates is a man, then Socrates is mortal.
Premise B:  Socrates is a man.
Conclusion: Socrates is mortal.

Arguments I and II are each a collection of statements.  Argument I has two premises and a conclusion, as does Argument II.  Notice that the premises in Argument I differ from the premises in Argument II and the conclusion of Argument I is different from the conclusion of Argument II.

Now premise 1, by itself, is a statement.  It is not an argument.  It is a sentence that is either true or false (in this case, false—there are albino crows).  Premise A is also a statement and not an argument.  Thus Premise A does not have any premises.

There are several different types of statement.  Some statements are simple; they are composed of only one statement and no logical operators.  If a statement has one or more logical operators and or is made up of one or more simple statement, then it is said to be compound.

The five basic logical operators are negation (usually represented with a tilda (~)), conjunction (represented by the ampersand: &), Disjunction (wedge: v), conditional (an arrow: ->) and biconditional (a double arrow <->).  These operators are used to make compound statements.

A conditional statement is the kind of statement that is formed when two statements are joined together via the conditional operator.  Again, the conditional operator is captured by the English expression, ‘if ..., then ...’  The blanks (...) are to be filled in by other statements.  Because of their importance, the two statements that make up a conditional statement are given special names.  The statement that follows that ‘if’ is called the antecedent; the statement that follows that ‘then’ is called the consequent.

Thus in the following:

If it rains, then the streets will get wet.

the antecedent is ‘it rains’ (since this is the statement that follows the ‘if’) and the consequent is ‘the streets will get wet’ (since it follows the ‘then’).

So, a conditional statement does have parts: the antecedent, the consequent, and the operator itself (again, captured by ‘if ..., then…’)  But none of these parts are premises.  Statements do not have premises. Only arguments have premises.

Now, in Premise A above, the antecedent is ‘Socrates is a man’, and the consequent is ‘Socrates is mortal.’  Notice that each of these is a statement unto itself.  Thus the conditional statement, ‘If Socrates is a man, then Socrates is mortal,’ is a compound statement that is itself composed of two simple statements and the conditional operator.  But, again, the conditional statement is just a statement, it is not an argument and it does not have premises (and this means that neither the antecedent nor the consequent is a premise).

Modus Ponens is a logical rule.  Logical rules operate on collections of statements to produce new statements.  As such is it meaningless to say that a statement “follows a rule.”

one of which is a conditional claim and another which endorses the antecedent of that conditional.  I hate to bring up wikipedia, as I can’t stand it when people claim it as authority, nevertheless this is the part where modus ponens is a conditional claim (according to wikipedia),

Again, modus ponens is a rule, not a conditional claim.  And wikipedia doesn’t say that modus ponens is a conditional claim.  What it does say is that modus ponens is operative when the collection of statements contains one statement that is a conditional and another that is the antecedent of that conditional.

fletch_F_Fletch

fletch_F_Fletch
Total Posts:  207
Joined  25-02-2007

12 February 2009 14:20

I have to make this quick and won’t be back on till sometime next week.

“So, a conditional statement does have parts: the antecedent, the consequent, and the operator itself (again, captured by ‘if ..., then…’)  But none of these parts are premises.  Statements do not have premises. Only arguments have premises.”

This is exactly what I have been trying to state.  I understand my word usage were not accurate in describing my thoughts. So I will call (1a) and (2a) statements.  I jumped too far into formulating (1a) and (2a) as an argument. And this leads into your statement:

No. They don’t.  Again, (1a) and (2a) are individual statements.  As such, Modus Ponens does not apply to them.  Modus ponens is a rule that applies to a series of statements (meaning more than one).

This is where I meant that (1a) and (2a) follow the modus ponens, I was referring to the first part.  For instance (1a) could go as follows:

If God does not exist, objective moral values do not exist (1a)
Objective moral values do exist
Therefore, God Exists

Again, can you elaborate on what you said earlier,

Thus, when the antecedent of a conditional is false, the entire conditional is true.

Why if the antecedent is false would the conditional be true?

Finally, this has been my question from the beginning of this conversation:

I believe Selinus is not stating that they are false for the same reasons.  Selinus states that (1a) is false due to it’s inability to have any ontological basis for objective morality.  Pertaining to (2a) he is stating that it is false for a different reason, Selinus believes it is false because it goes against, in his view of God, God’s eternal character.  He is not denying the ontological basis for morality being in God but rather the God you describe.

[ Edited: 12 February 2009 14:22 by fletch_F_Fletch]

fletch_F_Fletch

fletch_F_Fletch
Total Posts:  207
Joined  25-02-2007

15 February 2009 19:21

Got it, while I have been focusing only on:

If God does not exist, objective moral values do not exist
(1a)

When I have been referring to the antecedent I have been referring to:

If God does not exist

When I have been referring to the conditional I have been referring to:

objective moral values do not exist

This is just the first part of modus ponens, so when you stated antecedent you were referring to the entire statement:

If God does not exist, objective moral values do not exist

Therefore I was looking at antecedents and conditionals in a micro perspective first, under just part of modus ponens.  From now on when I state antecedent I will refer to the entire first statement.  That said, now I understand or claim:

Thus, when the antecedent of a conditional is false, the entire conditional is true.