Angra Mainyu
Veteran Member
No. Let me establish once again, beyond any reasonable doubt (also again), that some of your key claims are false. I will further show that your logic is faulty, and that you have failed to understand some of my main arguments (of course, given our exchange in this and other threads, I predict you will fail to understand that you are in error).Speakpigeon said:I already told you I understand your argument. Your logic is not faulty here. It's your assumptions. As I already told you. And all of the argument mathematicians use to support the validity of their method of logic, those I've been able to find anyway, are similarly based on faulty assumptions. Good logic, though. Ain't it ironic? A good logic to infer a wrong logic? Yeah, can happen. Mathematicians did it.
EB
First, our premises.
Alright, let us go with that hypothesis. In particular, then, all mathematical statements are either true or false.Speakpigeon said:I think all statements are either true or false.
Let us now consider another one:
https://talkfreethought.org/showthr...gical-validity&p=668145&viewfull=1#post668145
Alright, so a deductive argument is CML-valid (i.e., valid according to classical mathematical logic, CML for short) if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.Do you know of any proper justification by any specialist of mathematical logic, e.g. mathematicians, philosophers and computer scientists, that the definition of logical validity used in mathematical logic since the beginning of the 20th century would be the correct one?
Here is the definition:
Validity
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
Internet Encyclopedia of Philosophy - https://www.iep.utm.edu/val-snd/
Thanks for your answers.
EB
So, let us go with that. Are you following so far?
I have granted for the sake of the argument one of your beliefs (namely, that all statements are either true or false), and adopted your definition of validity according to CML. So far, so good, right?
Let us now consider another one of your claims:
That is false. However, let us assume for the sake of the argument that that is true. Each implication I that is valid according to Aristotelian logic and not valid according to mathematical logic, does not take a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false (by definition of CML-validity). Hence, its form is such that it is possible for the premises to be true and the conclusion nevertheless to be false . Hence, Aristotelian logic fails to be truth-preserving, so obviously CML is a far better tool for finding mathematical truth. Aristotelian logic is a disaster (not in reality, though; your claim that " Some implications (in effect an infinity of them) are valid according to Aristotelian logic and not valid according to mathematical logic." is simply false.Speakpigeon said:No. Some implications (in effect an infinity of them) are valid according to Aristotelian logic and not valid according to mathematical logic.
Let us now consider more of your claims:
Also, you saySpeakpigeon said:What you call truths here are in fact invalid conclusions. I'm not sure there's anything interesting in doing that.Angra Mainyu said:Now, an interesting point is that under CML, an argument is valid if it is impossible for the premises to be true but the conclusion to be false. So, as long as the premises are true, CML guarantees that so is the conclusion. Given this and the above, it turns out that one consequence of having the wrong logic is that mathematicians are able to find many truths that they would never be able to find if they had the correct logic.
You have denied that CML-valid arguments always lead from true premises to true conclusions. You are mistaken, obviously, for the following reason: Suppose a CML-valid argument has true premises P1,..,Pn, and conclusion C. Now, by assumption, C is either true, or it is false. However, since the argument is CML-valid, by definition it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Therefore, given that the premises are true, so is the conclusion.Speakpigeon said:Truths that are not truths
That debunks two of your key claims. But there is more, of course. In this thread, I have given a thorough conclusive (i.e., beyond a reasonable doubt) debunking of much of your position. You may fail to see that, but here you do not only have wrong premises: your logic is also faulty. For example, your premise that "Some implications (in effect an infinity of them) are valid according to Aristotelian logic and not valid according to mathematical logic." is false. But your logic is faulty, because you fail to ascertain that that premise, together with the definition of CML-validity you accept, has the devastating consequence that Aristotelian logic is not truth-preserving. And you fail to reach that conclusion even after I have shown this to be so beyond a reasonable doubt, and repeatedly.
So, no, it is not the case that you understand my arguments. You fail to follow some of my main lines of argumentation, because your logic is faulty.