What is Logic? (Logic 101)

[CliveStaples]

You CLAIM you have addressed what I have asked. Each time I specifically ask you to address something you reply that you have no idea what I am talking about or you don't see any relevance. You posted ONE link that I can count and that was a WIKI link. WIKI is not a reliable source of data. Many errors have been found in WIKI pages and not just on logic.

Actually, wiki is pretty reliable when it comes to mathematics.

The only thing you asked me to comment on was the reason why mathematical logic uses its particular definition for contrapositive and the principles involved in the Square of Opposition. I responded that these definitions and principles are used in mathematical logic because mathematicians and logicians are interested in the results that follow from them. I then remarked that this didn't seem relevant to the matter at hand, viz. the difference between mathematical logic and deductive logic.

Here is what I posted which you fail to address:

You are not directly addressing anything I have brought up. I mentioned concepts which ought to be universal or known in both types of logic: Mathematical Logic and Deductive logic. You seem to be holding back information or perhaps you are not aware of the terms. I do not know which. Would you acknowledge the concepts "contraposition" and "the Square of Opposition" have been altered from the original terms?
I am merely trying to show there are many distinctions between Mathematical Logic and Deductive logic. Deductive logic is pure and Mathematical Logic is geared for higher mathematics alone. Philosophers did not need higher mathematics to defeat Sophist in argumentation. Higher mathematics moves away from semantics and is basically symbol manipulation. The notion of "validity" is also different which I brought up as well. What is "validity" and why is this important in Mathematical logic? Be advised a valid argument can have all sorts of mixtures such as all false premises, all true premises, one false premise with a true premise, etc. What valid arguments cannot have is true premises and a false conclusion. This last part of validity both Philosophers and Mathematicians agree. But why is validity one of the most used words is what I am questioning despite it means much as I pointed out. Specifically why do people care about validity if "Truth" is a separate notion? Why should a newbie to logic care about validity if an argument has false premises and is still valid? I would say that just confuses the newbie. There are clear cases where validity has no practical use. It seems people associate "truth" with being "valid" and it is not the case. In Philosophy the main word is not "validity" and is not harped on about every other sentence. this seems to be the case in Math. Some of the most frequent words in math are "valid", "tautology" and "argument" which I am saying hold different contexts than Philosophers. The mathematicians changed things to suit math. Thus Mathematical Logic is in the domain of pure Math. Deductive Logic is in the domain of Philosophy.

Re-read the text again and show me where you addressed any of the sample topics that I brought up: the definition of validity, contraposition, or the square of opposition.

I don't know what you're asking me to say, here. You want me to comment on the general definitions and usage of validity, contraposition, and square of opposition? Why? How is this relevant?

I'm interested in whether you have an argument that deductive logic and mathematical logic are substantively different. So far, your examples haven't held up (namely that mathematical logic is unconcerned with semantics or symbolizing propositions). You haven't presented an argument beyond saying that "valid" and "true" aren't the same.

You mentioned them in passing but nothing in specific detail. How is that an answer? Perhaps a third party can point me to what you addressed. I see nothing direct to the things I mentioned. You writing one sentence about each of the things I mentioned would not sufficiently address anything.

I have no idea what specific detail you're looking for. Your "question" is just a request for commentary on certain technical terms. I am not interested in providing such commentary, and such provision would be irrelevant to my substantive claims--namely, that mathematical logic is concerned with symbolizing and semantics, so that these cannot be examples of subjects that deductive logic but not mathematical logic concerns.

Do you need me to define validity for you? Do you want me to demonstrate that I'm familiar with the definition of valid? Are you just looking for general comments on the relationship between truth, soundness, and validity?

The least you can do is address this part for the sake of someone new to logic and reads these posts:

I don't have to address people who are new to logic. I'm addressing the arguments you've made in this thread, namely that mathematical logic is not concerned with symbolizing or semantics.

What is "validity" and why is this important in Mathematical logic? Be advised a valid argument can have all sorts of mixtures such as all false premises, all true premises, one false premise with a true premise, etc. What valid arguments cannot have is true premises and a false conclusion. This last part of validity both Philosophers and Mathematicians agree. But why is validity one of the most used words is what I am questioning despite it means much as I pointed out. Specifically why do people care about validity if "Truth" is a separate notion? Why should a newbie to logic care about validity if an argument has false premises and is still valid? I would say that just confuses the newbie. There are clear cases where validity has no practical use. It seems people associate "truth" with being "valid" and it is not the case. In Philosophy the main word is not "validity" and is not harped on about every other sentence. this seems to be the case in Math. Some of the most frequent words in math are "valid", "tautology" and "argument" which I am saying hold different contexts than Philosophers.

Try directly addressing with details what you understand about validity and think of a person trying to learn from your writing. This should not be me versus you here. I would say a person unfamiliar with logic would think of the notion of validity makes no sense if you can have false premises and still be valid. Why should a newbie care about validity?

Is it that you can only quote authorities or can you explain what you know about logic in your own words?

I already gave a substantive remark on the discursive importance of validity. Validity is important in mathematical logic because it produces results that are of interest to people doing research in the field of mathematical logic, in the same way that differentiable functions or holomorphic functions are important in mathematical logic because they produce results that are of interest to people doing research in real and complex analysis.

[RoyBoy]

The point of me bringing up the topics I did was to show there are distinct definitions and distinct intent from Philosophy and Math. Thus the two fields are not identical, which includes Mathematical Logic is Math and not identical to Deductive logic. I specifically gave examples where the two fields differ and you choose not to address them. Are any of the concepts different in Math and deductive logic? I pointed to at least three. Where are your examples that Mathematical Logic is the same as Deductive logic? How is it you think only I hold the burden of proof?
You seem to be missing points. I never said that math does not deal with symbolizing. Math might have a small portion of semantics which you think is full blown semantics and you think I deny any semantics in math. The small amount of semantics in Math is not close to that of Philosophy. I gave a specific case. How do you translate All S is not P. You never gave a legit answer. You put your feelings in the way.

I pointed out Mathematical Logic started late compared to Deductive Logic and you some how cannot see why the topics are not identical. The two subjects have things in common but they are not identical. You seem to indicate the fallacy of composition: that both subjects have some identical parts therefore there is no distinction between deductive logic and Mathematical Logic.
This implied view is mistaken. This is a common viewpoint made by people new to logic. There are tons of people like you who think logic is Math. This was not the case 300 years ago or 500 years ago. The reason is because all people knew logic was Philosophy. After 1850 Mathematical Logic took off. Once the word Math was used people showed respect for logic because people respect the field of Math. Most people from the time of Socrates until now have disrespected Philosophy.