Logic

It's been a while since a logic class. In fact, I am do to take another this fall.

I would suggest doing some background research. I find the site above to be a good reference.

Your question pertains to propositional logic as it is called today.

"In an argument we pass from one or more propositions called premisses to another proposition called the conclusion. This combination of premisses and conclusions constitutes the argument's structure." (Aristotle)

There is an easier and modern interpretation.

PROPSITIONS AND CONCLUSIONS
An argument? or a deductively sound argument.. has three parts.
1.One or more premises that support evidence for the conclusion.
2.A conclusion
3.A connection linking the premises to the conclusion logically.
4.EXAMPLE

So take for example.

All ducks are mammals. All mammals are warm-blooded. Thus all ducks warm blooded.

Put yourself in the position of a lawyer.

All ducks are mammals and all mammals are warm blooded are the evidence you need to convince the judge that the only logical outcome of these statements is could be is that all ducks are warmblooded.

So you are right? 1 +1 =2, but it is premises = conclusion, not premises+premises = conclusion



OPERATORS


With the previous example, let's translate it to symbolic logic.

D --> M, M -- > W |- D-->W


D=ducks
M=mammals
W=warmblooded


In order to understand Aristotle and his logic, you need to understand the inference rules of logic.


There are four sentence operators. The only one I'm using is a conditional (-->) which is denoted as an arrow. There are different symbols for a conditional, such as a sideways horseshoe, but this is easier to understand.


The conditional operator rule means this; If A Then B. All this means is that when translated, A necessarily (another important topic) means B. If a duck, then warmblooded. Pay attention to If, then, as this is the call sign of a conditional.

HOW DUCK = WARMBLOODED
Take the previous example.

D --> M, M -- > W |- D-->W


When doing symbolic logic, which is intended in logic, The calculation looks like this
1.D --> M
2.M -- > W |-
3.D-->W HS, 1,2


In line one, we have the first sentence, all ducks are mammals


In the second line, we have the final proposition, all mammals are warmblooded.


The symbol that comes after ( |-) this is call a turnstyle, which means "therefore"


When solving logical problems, you only have the first two lines. But how do we get D-->W?, or more precisely, that ducks are warm blooded?

THERE ARE EIGHT GENERAL INFERENCE RULES
To get D-->W, we need to know and memorize the inference rule Hypothetical syllogism. This just means that in the system of logic, you can evoke this "law" to solve the equation.
Hypothetical syllogism means this. A--> B, B -->C, thus A -->C. Because A leads to B and B leads to C, we can cut the nonsense out of the middle, as it is wasted logic, thus getting A -->C.
So on line three, we can infer D-->W by HS (hypothetical syllogism) in lines 1 and 2.

Interestingly enough, hypothetical syllogism was until modernday called Aristotelian syllogism. But this is very important. Don't look to Aristotle to explain formal logic. It sounds impressive, but you'll never make any sense from it unless you know formal logic first. You are confused because he does not elaborate on the codified laws of logic. Logic isn't meant to be abstract the way other philosophy is, its supposed to embrace the conceptual ideas of mathematics? cold and methodical, with definite answers within a closed system.

Also note that Logic is a closed system, which mean that within logic, the sky could be red and unicorns could be outside your window if it is logically supported.

MY ADVICE.
First study and memorize fundamental elements of logic, such as conditional, negations, etc.
Then study translation of words to logical symbols, because translating the sentence wrong is like saying 2+5= 100, because you misinterpreted 5 from 98.
Then study inference rules
Then move on to more concepts that streamline the inference rules.

Let's recap to see if i understand it:

In this case the premises have been put together already and then form the conclusion. If i have to follow my math (1+1=2) example this would be the correct form: (premises + premises) = conclusion according to your answer.

What we are doing now is writing down the process that happens in our brain if we put one and one together:

Premises #1 Ducks = Mammals (D --> M)
Premises #2 Mammals = Warm Blood (M --> W)
Conclusion Ducks are mammals and therefor (|) have warm blood.

After that you start about the Hypothetical Syllogism, which basically says that we can do the math and can skip B, because everyone knows Ducks are mammals (and therefor warmblooded).

I think i get it, it feels real simple now, and i feel like this logic is already the logic we (subconsciously) use in everyday situations. I guess this kind of logic is only the beginning to an wider set of Logics, which are more impressive.

When you say:
I am asking the question, what use has this logic withing philosophy?

I think I'm going to finish the rest of the chapter on this Logic, and then decide whether i find it interesting enough to go further with it. Thanks for your explanation.

"In this case the premises have been put together already and then form the conclusion. If i have to follow my math (1+1=2) example this would be the correct form: (premises + premises) = conclusion according to your answer." (vasska)

Yes. But when you say premises + premises = conclusion, you take two separate lines of logical inquiry and relate them to the final conclusion. Its better to think of it this way. Antecedent + Antecedent = Conclusion. Premises means Antecedent +Antecedent.

I JUST ADDED TO WHERE MORE ELABORATION IS NEEDED
What we are doing now is writing down the process that happens in our brain if we put one and one together:

Premises #1 Ducks = Mammals (D --> M)
Premises #2 Mammals = Warm Blood (M --> W)
Conclusion [BECAUSE] Ducks are mammals, [THEY MUST THEREFORE BE]warm blooded.

After that you start about the Hypothetical Syllogism, which basically says that we can do the math and can skip B, because everyone knows Ducks are mammals (and therefor warmblooded).[BECAUSE THE INFERENCE RULES STATE THAT WE CAN TAKE THAT KIND OF A SHORT CUT BECAUSE THE OUTCOME IN THIS SYSTEM WILL BE LOGICAL]



"I think i get it, it feels real simple now, and i feel like this logic is already the logic we (subconsciously) use in everyday situations. I guess this kind of logic is only the beginning to an wider set of Logics, which are more impressive."

Exactly!!!! Well said.

Great, guess i will continue with the rest of the chapter next weekend after my Cisco Exams on Friday =)

Logic is based on ID and non-contradiction; both are Aristotle's discoveries:
A is A
A cannot be both A and not A at the same time.
e. g. a failure to ID produced 9/11

The syllogism, the other part of Aristotle's philosophy was dominant during the Middle Ages and for the greater part of 2,000 years. It was always suspected; it could not deal with certain statements e. g. "all men are created equal" and it was finally debunked at the beginning of the XXth century. For one thing, Aristotle did not know the meaning of zero; this came later with the Arabs; and so he treated every proposition as if it dealt with some one thing. Modern logic does not make such an assumption and deals with empty sets. So thanks to the Hindus and its transmission by the Arabs, we know the meaning of zero. However, the Western World did contribute a discovery about zero which was not known in the Orient. Does anyone care to tell me what it is?

"Logic is based on ID and non-contradiction; both are Aristotle's discoveries:
A is A
A cannot be both A and not A at the same time.
e. g. a failure to ID produced 9/11"

Logic is indeed based on Identification and non-contradiction? that's propositional logic!! But did A, A v ~A = ~9/11???? I don't quite follow that. That seems like conjecture to me.

"The syllogism, the other part of Aristotle's philosophy was dominant during the Middle Ages and for the greater part of 2,000 years."

Too true! The scholastics did uphold the ancients work for centuries? even before, like Cicero etc.

"It was always suspected"

Was it???? There had to have been a few skeptics around that doubted the veracity of logic.

" it could not deal with certain statements e. g. "all men are created equal" and it was finally debunked at the beginning of the XXth century."

If that statement was within the realm of logic, which is inherently a closed system, all men are created equal could, given a well founded premises, in fact be true.

"For one thing, Aristotle did not know the meaning of zero; this came later with the Arabs; and so he treated every proposition as if it dealt with some one thing. Modern logic does not make such an assumption and deals with empty sets. So thanks to the Hindus and its transmission by the Arabs, we know the meaning of zero"

That's true too. Are you familiar with Indian numerical metaphysics???


"Modern logic does not make such an assumption and deals with empty sets. So thanks to the Hindus and its transmission by the Arabs, we know the meaning of zero. However, the Western World did contribute a discovery about zero which was not known in the Orient. Does anyone care to tell me what it is?"

WOW!!! That a great question! I never thought about that. John Neumann rings a bell, but that's too modern. Some would say it's Plato and the early conception of percipi quanta ex-nihilo. But really, it can't even begin with Plato, can it. I'd wager that it is around the Atomists and the conception of the void, like Democritus. But as to a conception of zero not known to the orient but in fact to the western mind, I'm curious. Please do tell.

Its all very interesting, but to be fair to Vasska, I'm not quite how the historical value and context of zero fits in to Vasska's original question though.

Also, JDPHD, of which I'm guessing by you're namesake, are you familiar with legal penumbra theory?

No, I don't know what the 'legal penumbra theory" is. Will you let me guess, I love to make wild guesses. Suppose you commit a crime and leave everybody in the dark; you know for sure others do not know but you yourself are not sure if others will ever find out. Instead of facing a clear future, you stand in a penumbra between now and then.

O.K. back to zero. The zero that we got from the East was locational. In other words, if people ever wanted to show a zero, they would use the abacus and an empty column in it would represent a zero which on paper the Hindus wrote as a period. The Arabs took it up and brought it West. You remember the Romans did not use a zero; neither did the Greeks. The locational zero came West long after the Greeks and Romans (the Iliad, the Oddisey, the Aenid and all that and much more like the Renaissance but by then we knew about the zero). Well, something happened in the West that revolutionized Mathematics. If by next posting, you figure it out, I'll give you the reference: it came out once in Scientific American. Why the East did not figure it out, well my wild guess is they believe the external world is an illusion.
O yes, one thing more: I'm really sorry the connections are not apparent but that is the way with logic. In logic, it is easier to ID than to connect. See Holmes is always IDing and Dr. Watson connecting. In what subject do you think connections are easiest? If you know, please, let me know.

Ducks aren't mammals, they're birds... but all birds are warm blooded.

No reason to get your back up JDPhD, it was a question of simple interest. I was hoping you were an actual JDPhd student. However, names can be deceiving. "Legal penumbra theory" is at the "hart" (misspell intended) of legal academia, so to speak. So I apologize? I shouldn't have made such assumptions about people, especially on the internet.


"O.K. back to zero. The zero that we got from the East was locational. In other words, if people ever wanted to show a zero, they would use the abacus and an empty column in it would represent a zero which on paper the Hindus wrote as a period. The Arabs took it up and brought it West. You remember the Romans did not use a zero; neither did the Greeks. The locational zero came West long after the Greeks and Romans (the Iliad, the Oddisey, the Aenid and all that and much more like the Renaissance but by then we knew about the zero). Well, something happened in the West that revolutionized Mathematics. If by next posting, you figure it out, I'll give you the reference: it came out once in Scientific American. Why the East did not figure it out, well my wild guess is they believe the external world is an illusion."(JDPhD)

That's actually pretty interesting. That would make for an interesting discussion in a different post. And while I disagree on your generalization of the eastern conceptions of extension being illusory, that's still a valid point.

O[h] yes, one thing more: I'm really sorry the connections are not apparent, but that is the way with logic. In logic, it is easier to ID than to connect. See Holmes is always IDing and Dr. Watson connecting. In what subject do you think connections are easiest? If you know, please, let me know.

From post # 7?


"A is A
A cannot be both A and not A at the same time.
e. g. a failure to ID produced 9/11"

-----------------------------------------------
Logical structure based off of translation
-----------------------------------------------
1.A (same as bi-conditional)
2.~(A & ~A) |-
3.9/11

-----------------------------------------------
Truth value (single variable)
-----------------------------------------------

___A(T value)___|___A | ~(A & ~A)__|-__9/11___
T......................|.....T.| .T..T F FT .......|..... T
F..................... |..... F.| .T. F F TF .......|..... F


Note: T-value rule on conjunction = T if both conjuncts true, F in any other case

-----------------------------------------------
Proof
-----------------------------------------------

1.A
2.~(A &~A) |-
3. ~A v ~A Demorgan 2
4. ~A ADD 3
5. A & ~A Conjunction 1, 4
6. A??????


I don't get it. I think the problem lies with the assumption A is A. If you rescind that, you have an Aristotelean tautology and it is logical, but assumption A is problematic.

-----------------------------------------------

As to which subjects I find connections easiest, A --> B in virtue of a non contradicted conditional based on universally accepted inference and derivatives rules, of course. Thats the way with logic I suppose.


Also Aedes, by George your right. Ducks aren't mammals, but as I have come to find out Duckbilled platypuses are. My bad.

"So take for example.

All ducks are mammals. All mammals are warm-blooded. Thus all ducks warm blooded.

Put yourself in the position of a lawyer.

All ducks are mammals and all mammals are warm blooded are the evidence you need to convince the judge that the only logical outcome of these statements is could be is that all ducks are warmblooded.

So you are right? 1 +1 =2, but it is premises = conclusion, not premises+premises = conclusion"


A Duck of Truth

If I was a lawyer I would point out, that the conclusion is untrue.
"All" ducks would include dead ducks, stuffed ducks, toy ducks, Daffy Duck, etc., wouldn't it? Surely all ducks are not warm blooded.
I would conclude from your example of logic that neither premise is true.
That not all ducks are mammals, that not all mammals are warm blooded, and then also your conclusion is untrue too.

So it would be better to say: Not all ducks are mammals and not all mammals are warm blooded thus not all ducks are warm blooded too.

As far as using subjective mathematical equations to define the objectivity of nature, logically the above mentioned flaws apply.
How can one objectively measure nature and insert those measures or premises into a subjective equation, in the effort to find a truthful conclusion when nature is truly and immeasurably inconclusive?
So much for the certainty of an objective conclusion!
And for that logical reasoning alone, science or measure invented probable uncertain quantum mechanics, and now are heading down a dark dead-end road, going totally the wrong way.

Not all ducks are the same and measure truly the flaw.

=
MJA

The example was meant to elaborate the point of a syllogistic chain. But I like your approach to the issue.

First, if we were lawyers, would we be arguing whether or not a duck is a duck? Probably! LOL!

In this particular example, we are following the fundamental concept of deductive reasoning. We are following the syllogistic chain from the first premise that a duck is a mammal, etc.

That "all" ducks would include dead ducks, stuffed ducks is true. Primarily... I think this would be an inductive conclusion. However, this does not negate the fact that a duck is a duck, regardless of the additional attribute it may have. A wooden duck would not be warm blooded, but it is not a duck, but a duck which is wooden. Call it a facsimile of duck, a copy of a duck, a type of duck? doesn't matter. A duck is, by definition, a warm blooded bird.

The premise is true? I guess it is just a matter of interpretation and accepted definition of a duck.

If we use mathematical equations the way I did? there would be some serious problems down the line. That is why we use predicate and propositional logic. As to the certainty of an objective conclusion? ironically, that is the basis for logic which is a closed system.

I am puzzled when you say;


Please elaborate because it sounds like a very good thought.

Also on a hilarious note as pointed out by Aedes? ducks are not mammals.

Thanks VCS, it takes a good thought to know one.

Einstein was right after all, God does't play with dice.
There is a better path to understanding nature than the current uncertainty of scientific measure, and that my fellow lovers of truth is simply truth itself.
Descartes and Einstein came so close until they went the wrong way too.
A revolution, a natural evolution of human thought powered by the simplicity of truth Mr. VCP, is about to set the universe free. I see it.
It was only the flawed uncertainties of knowledge, of ourselves, of what we've been taught and the giants we stand on, that stand in the way.
But our untrue thoughts weren't really stopping our progression, it only felt that way. That way is The Way!
Thales claimed he new the stars, yet failed to see the truth in front of his own feet.
Socrates couldn't question his way to the truth either.
Plato got lost in his own cave.
But they tried better than most.
The truth is much more simple than thought!
Bla ba Bla, you'll One day see it too !

=
MJA

Yea, Vid is spot-on here. I saw this, chuckled, and left off since I wasn't sure how much that particular logic supported where you were going. Nice clarification

O. K. The deduction is valid only if the premises are true.

You mean I'm not Yuri's doctor? Poor Yuri, he'll need a priest; you can call me!

The Supreme Court decision of Griswold v. Connecticut, 381 U.S. 479, 85 S. Ct. 1678, 14 L. Ed. 2d 510 (1965): Justice William O. Douglas used it: it ...

In Spanish, there is a saying that goes something like this: "Sophie's hips have a great deal of philosophy".

A basic principle in philosophy is NAME and FORM.

Name the form and inform the named.

Wait... what??? Determinacy in constitutional rights to privacy apply how here? And why would we need the legal journal citation? This must be a post for a different thread.

Sorry but you brought up the question of 'penumbra' to question my ID.:detective:

There is truth in Aristolean logic but it cannot be found in premises, propositions and conclusions,
nor in the man made complexities and uncertain measure's of science.
Truth IS much more simple than that, more simple than thought.
Nature's truth is simply equal, and the Lion my friends is One.
Why grasp only the tail when One can grasp it all?

=
MJA