No logical proof of 'A' if '~A' does not entail a contradiction?

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Peter Kreeft has a good article here:
catholiceducation.org/articles/apologetics/ap0209.htm

However, I don’t exactly understand what he means when he says the following (emphasis added):

“If life after death cannot be proved scientifically, is it then intellectually irresponsible to accept it? Only if you assume that it is intellectually irresponsible to accept anything that cannot be proved scientifically. But that premise is self-contradictory (and therefore intellectually irresponsible)! You cannot scientifically prove that the only acceptable proofs are scientific proofs. You cannot prove logically or empirically that only logical or empirical proofs are acceptable as proofs. You cannot prove it logically because its contradiction does not entail a contradiction…”

What does that mean? On the surface, it seems like he’s saying that if something is unproven, its contradiction does not entail a logical contradiction. That makes sense. If I prove A, then ~A gets me *A * ~A, *which is a logical contradiction. But what’s the point of saying that? I would have to prove A first, and then its contradiction will yield a contradiction. So, changing variables for clarity, it seems like what Kreeft is actually saying is that you cannot prove B because ~B is not a contradiction. But that is not self-evident at all; it doesn’t even seem true to me. If all I have is ~B as a premise, it in no way means that I can’t prove B. I’d just wind up with a contradiction and have to get rid of ~B.

I hope that’s not too confusing. What am I missing here?
 
I think Kreeft has a bigger problem on his hands than not being able to scientifically prove that there is life after death. After all, I’ve never seen a sound, deductive argument for the existence of the immortal soul or life after death, much less am inductive scientific argument for the existence of the soul. Philosophers don’t depend solely on inductive science and would accept a good, valid and sound deductive argument for the existence of the soul. However, there has never been one…thus the default position is to believe that there is no such thing. He is not addressing the main issue here and any system he set up would have the same logical problem that he is attacking.
 
Thanks, but I’m really just concerned with the specific question I posed; I have no desire to discuss the whole article.
 
Yeah. First of all I’d like to say that there are no proofs for God. It is impossible. Kreeft has several attempts, several which are laughable, but I think one or two were ok, but there is always something little wrong with his argument, usually an assumption, that completely screws the rest up.

But… the bold part. What it seems to say in other words is: life after death cannot be proven logically, because its contradiction (there being no life after death), does not have a contradiction or cannot have a contradiction (there being life after death). So what that would mean is… either there isn’t life after death, or you cannot show that there is a life after death logcially. Because the contradiction of the contradiction would mean the thing you start off with. So if B contradicts A, then A would in turn contradict B. But he says that B doesn’t have a contradiction, so B would be absolutely true.

Again, “it” would be the idea of life after death(A), and its contradiction would be that there is life after death (B), but since B does not have a contradiction, A is not true.

Or wait… Actually…
A is saying that it is intellectually irresponsible to accept it.
B says it is intellectually responsible to accept it.

So then that would mean that it is intellectually responsible to accept it, because it does not have a contradiction.

Yeah, I think A and B pertain to it being responsible or not, not whether or not there is an afterlife. But his whole point that believing is intellectually responsible does not have a contradiction is totally based on opinion, and it certainly can have a logical contradiction as it being irresponsible to just believe. He’s basically saying, “Why not believe in God? You should because if you’re wrong, you’re screwed, and you won’t lose anything if you do believe.” Which I think is one of the worst arguments ever, and I think he’s made it several times.

But yeah, Kreeft’s full of it. It always seems like he gets confused in his own logic. Or he purposely tries to create these scenarios where you have to think a lot to get through them so much that you don’t see the flaw in them. You can prove that all acceptable proofs are scientific proofs because every single attempt at a proof no matter what it is has usually a large degree of science entailed in it. Maybe no proper science, but some sort of science. And if it has an assumption or is in some other way flawed, it is not a proof.

Hope this helps.
 
lets try it this way
  1. You say you must have proof of God or the deal is off
  2. Another person says
    (A)can you travel without using time? You say no
    (B) Can you travel to a door with out passing a half way point between you and the door? You say no
    (C) Is there an endless number of half way points* between you and the door? You say yes
  3. He says if you have given honest answers to AB&C the sum is you can never travel from here to a door. But you can actually walk from here to and through that door so which answer is false
  • given any starting point from the door, requires a number greater than zero. This number can be divided by 2 endlessly
The purpose of this and your paragraph is to crack the inclusive logic shell. It uses logic to disprove logic can be the only answer
 
Alterum said:
Peter Kreeft has a good article here:
catholiceducation.org/articles/apologetics/ap0209.htm

“If life after death cannot be proved scientifically, is it then intellectually irresponsible to accept it? Only if you assume that it is intellectually irresponsible to accept anything that cannot be proved scientifically. But that premise is self-contradictory (and therefore intellectually irresponsible)! You cannot scientifically prove that the only acceptable proofs are scientific proofs. You cannot prove logically or empirically that only logical or empirical proofs are acceptable as proofs. You cannot prove it logically because its contradiction does not entail a contradiction…”
Click to expand...
What Kreeft is doing is showing that there are no direct or indirect proofs for the claim that “it is intellectually irresponsible to accept anything that cannot be proved scientifically.” That there is no direct scientific evidence for the claim and no logical evidence for it. He also claims it self-contradictory to use something outside science to prove that it is irresponsible to accept anything outside science.

The passage you put in bold refers to a kind of indirect proof, Reductio ad Absurdum (RAA). Wikipedia has a fairly good article on it. Say you have an argument where Premise 1 (P1) and Premise 2 (P2) are supposed to prove a Conclusion (C). You can directly show how C is derived from P1 and P2 or you can show that C is true indirecctly by RAA. If C really does follow from P1 and P2, then its contradictory, ~C (“not-C”) is not possible. This is true for all valid arguments. RAA would work by using P1 and P2 and ~C and showing how it leads to a contradiction somewhere in the proof (any contradiction). This contradiction shows that ~C is false and therefore its contradictory, C, must be true.

Kreeft is claiming there is no direct or indirect proof from science against life after death (a point he makes in the next paragraph).

Sorry if it is badly expressed. Any good logic text will explain RAA–and that is what Kreeft was talking about in the bold passage above.

David
 
"There is no empirical evidence that the only kind of evidence we should accept is empirical evidence.’

Right on.
 
dsb1808 said:
…]

Kreeft is claiming there is no direct or indirect proof from science against life after death (a point he makes in the next paragraph).

Sorry if it is badly expressed. Any good logic text will explain RAA–and that is what Kreeft was talking about in the bold passage above.
Click to expand...
RAA makes perfect sense, thank you. So all Kreeft is saying is that if a ‘conlcusion’ cannot be proven from the premises, its contradiction is not a logical contradiction? (I feel like I’m missing somethng because that’s pretty obvious!)
 
Alterum,

I see you’ve already gotten some responses but with your permission I will wade in anyway.

I think what is going on here is that at the beginning of the paragraph Mr. Kreeft is trying to distinguish between three different situations:

(1) We can prove that life after death exists; we must therefore believe that it does exist and we cannot believe that it does not exist.

(2) We can prove that life after death does not exist; we must therefore believe that it does not exist and we cannot believe that it does exist.

(3) We cannot prove anything about life after death; we can therefore believe either that it does exist or that it does not exist.

In his first two sentences, Mr. Kreeft is admitting that (1) is not the case, that we cannot prove logically that life after death exists. He is saying, however, that because (2) is also not the case, we can still believe that life after death exists.

In the part that you have boldfaced, Mr. Kreeft is explaining why there is a difference between (1) and (3). The same three alternatives apply to the standard of logical proof:

(1b) We can prove that logical or empirical proof is the only acceptable basis for believing something; thus if we cannot prove something logically or empirically, we are forced to reject it.

(2b) We can prove that logical or empirical proof is not the only acceptable basis for believing something; in this case, we cannot reject something just because it cannot be proven logically or empirically.

(3b) We cannot prove anything about whether logical or empirical proof is the only acceptable basis for believing something; in this case … frankly, I don’t know what the consequences would be.

Mr. Kreeft is saying that we are in situation (2b) regarding the exclusive nature of logical or empirical proof.

I hope this helps … although when I reread it I begin to have my doubts.
  • Liberian
 
Alterum said:
RAA makes perfect sense, thank you. So all Kreeft is saying is that if a ‘conlcusion’ cannot be proven from the premises, its contradiction is not a logical contradiction? (I feel like I’m missing somethng because that’s pretty obvious!)
Click to expand...
Right, if I follow you. For a valid argument, RAA would show the contradiction of the conclusion is not possible. If that doesn’t happen, if there is no contradiction in assuming “not-C”, then the original conclusion is not valid.

Putting it “its contradiction is not a logical contradiction” isn’t quite right–what you meant is right but the expression isn’t clear enough. Better “its contradiction does not lead to a logical contradiction”–the contradiction of the conclusion (“not-C”) itself may not be a logical contradiction but in an RAA proof it will lead to some contradiction (if the original argument is valid).

It does get confusing. Try teaching it to undergraduates and your head can really spin.

David
 
Well, I’m an undergrad! 😛 (I don’t major in philosophy though, but I have taken a course in symbolic logic, and some of the same proof techniques are used in my math courses.)

Thanks for the help!
 
Alterum said:
Well, I’m an undergrad! 😛 (I don’t major in philosophy though, but I have taken a course in symbolic logic, and some of the same proof techniques are used in my math courses.)

Thanks for the help!
Click to expand...
Of course I meant no offense to undergraduates and certainly none to you. I have two sections of logic this term with about 35 students in each. Students are always coming up with some way of looking at a problem that I have never thought of before. Sometimes it feels like my head will explode before the class is over. But logic is still great fun. You might want to look at Kreeft’s Socratic Logic book in the 2nd ed. It’s not as good as John Oesterle’s classic Logic: The Art of Defining and Reasoning but Kreeft has some great exercises you might try for fun.

Good luck at school.

David
 
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