Propostional Logic Symposia - [1] - Introduction and Basics

[VideCorSpoon]

Wait a tick Arjen! Sorry, I couldn't resist it.

Sucks to say but formal logic is a lot like math. Keep in mind this is an introduction. This is not all propositional logic has to offer. Oh, I trust you... but I think we have drastically different understandings in logic.

But please do start a thread on propositional logic, I'm sure it will be very informative.

[Arjen]

Originally Posted by VideCorSpoon

Wait a tick Arjen! Sorry, I couldn't resist it.

Sucks to say but formal logic is a lot like math. Keep in mind this is an introduction. This is not all propositional logic has to offer. Oh, I trust you... but I think we have drastically different understandings in logic.

But please do start a thread on propositional logic, I'm sure it will be very informative.

To tell you the truth I had not seen your proader intent with the topic. Especially after the second topic I am inclined to say just a little word on this matter:

Logic is used only to deduce correct reasoning. A correct logical statement has no bearing on what exists in reality. I may be abe to prove given the right logical assumptions that grass is black for instance, but it would no more be true than grass being green.

I hope this is clear to everybody.

[de_budding]

The difference between validity and truth; I think it is pretty apparent and most of us are familair with people using false logic day to day anyways.
Dan,

[Arjen]

The thing of it is that the logic can be completely accurate, but the outcome of the reasoning does not have to correspond with reality. This is something that "popular science" exploits with a detrimental effect on the worldview of many.

The distinction I am trying to make is beween the reasoning and the outcome of the reasoning. There is no relation between the two. That is why I can say accurate things, based on an inaccurate reasoning by luck or hearsay for instance.

Hope this helps.

[VideCorSpoon]

Arjen,

That logic is used only to deduce correct reasoning, I would agree with you as far as propositional logic is concerned. I think you, de_budding, and I agree that logic is a closed system. Within the closed system, the sky could be pink and elephants could have wings. But logic also has sub systems that help us determine reality. Right now I am going through propositional logic, where things look like a closed system, and in many cases they are. But in quantificational logic, a part of predicate logic, we look at quantifiers like existential (∃) and universal quantifiers (V…sorry, I don’t know how to do this symbol in word, but it looks like an upside down A), like the type of logic Austin Duggan was asking about in the post “Question about logic sentence.” However, in that logic problem, there is an issue that renders the problem unsolvable.

So you are right in a way when you say logic is can be accurate, but not necessarily in line with reality. But propositional logic is the tip of the iceberg. There are many subsystems of logic that are incorporated into logic and in a way help determine reality (i.e. truth functional quantification).

[Arjen]

Originally Posted by VideCorSpoon

Arjen,

That logic is used only to deduce correct reasoning, I would agree with you as far as propositional logic is concerned. I think you, de_budding, and I agree that logic is a closed system. Within the closed system, the sky could be pink and elephants could have wings. But logic also has sub systems that help us determine reality. Right now I am going through propositional logic, where things look like a closed system, and in many cases they are. But in quantificational logic, a part of predicate logic, we look at quantifiers like existential (∃) and universal quantifiers (V…sorry, I don’t know how to do this symbol in word, but it looks like an upside down A), like the type of logic Austin Duggan was asking about in the post “Question about logic sentence.” However, in that logic problem, there is an issue that renders the problem unsolvable.

The problem is not insolveable, even though it may seem to be. There is an ontological problem which can be formalised as falsum. It is, in reality quite easy. Free will presumes deni-all because deni-all allows for fantasies in stead of reality. That is a different topic though.

So you are right in a way when you say logic is can be accurate, but not necessarily in line with reality. But propositional logic is the tip of the iceberg. There are many subsystems of logic that are incorporated into logic and in a way help determine reality (i.e. truth functional quantification).

In predicate logic the same closed system exists. It is a formalisation of thought-objects and nothing more. We may think it is "real", but we must seperate what we think and what we think to percieve from the things in-the-selves. If we do not we start to believe in illusions. The only thing logic can do is simplefy our reasonings and make it easier to find fault with them.

[VideCorSpoon]

Originally Posted by Arjen

The problem is not insolveable, even though it may seem to be. There is an ontological problem which can be formalised as falsum. It is, in reality quite easy. Free will presumes deni-all because deni-all allows for fantasies in stead of reality. That is a different topic though.

In predicate logic the same closed system exists. It is a formalisation of thought-objects and nothing more. We may think it is "real", but we must seperate what we think and what we think to percieve from the things in-the-selves. If we do not we start to believe in illusions. The only thing logic can do is simplefy our reasonings and make it easier to find fault with them.

Within the realm of formal quantificational logic... its not. Arjen, I asume from your message that we are both familiar with predicate logic... you don't remember the golden rule about a single proof initially incorporating Existential and Universal quantifiers????

As to your second response. Ok.

[Arjen]

Originally Posted by VideCorSpoon

Within the realm of formal quantificational logic... its not. Arjen, I asume from your message that we are both familiar with predicate logic... you don't remember the golden rule about a single proof initially incorporating Existential and Universal quantifiers????

I wonder what you are getting at..

[VideCorSpoon]

That the proof is unsolvable because quantificational proof's cannot contain a contradictory and tautological existential and universal quantifier in a disaggregated way. I don't understand what else I could have been getting at?

[Arjen]

Originally Posted by VideCorSpoon

That the proof is unsolvable because quantificational proof's cannot contain a contradictory and tautological existential and universal quantifier in a disaggregated way. I don't understand what else I could have been getting at?

I think you are misunderstanding this "golden rule". It has no bearing whatsoever on the distinction I was making. The "golden rule" has bearing on incorrect formulations. I was noting that logic is about thought-objects and that correct formulations only correspond to those thought objects. If the formulation is correct it still says nothing about reality.

On top of that I would like to say that predication logic can (and is) used to formulate formula's, but that these still only refer to thought-objects. When anything we think corresponds to reality that is not because the formulation was correct or anything. When what we think corresponds to reality that is because our thoughts are "A" and reality is "A".

According to some leading philosophers a difference would still exist a priori because A(t) refers to a thought object and A(r) refers to reality.

My two cents..