Propostional Logic Symposia - [1] - Introduction and Basics

@Arjen,

@VideCorSpoon,

*places two more cents on the table*

You should check out Gottlob Frege. He is the one who devised the first form of formal logics and its notations. There is a topic on him and the forming of thought-objects here. I think you also replied in it once or twice.

Anyway, Try to realise wht logic is instead of looking for its links with "reality". Logic is not a way to determine "reality". It is a way to determine thought-objects.

@Arjen,

@VideCorSpoon,

1) I think what you call abstract reasonings I call thought-objects.
2) I know logic has moved on since Frege. I say so in my opening post on Frege. The reason I point to him is because foundations are very important. When one understands the foundations one can understand the limits of the system. The foundations of logic are thought objects and I was of the impression that you are trying to make for a "loophole" so that logic can be applied as a system to deduce truth in "reality". I am beginning to think I am wrong...am I?

@Arjen,

Foundations are very important. The foundations I'm trying to convey are the foundations of formal logic, much like trying to speak a different language. I hate to burst your bubble, but logic is like that. I wish it were a little more poetic and open to creative license, but its not really like that. Its like math...

Reality is a relative term in logic. We are displacing our reality in the extended world for the closed system on paper within the proof. I really don't know how else to convey this point.

It's not that you are wrong... actually far from it. You have a valid point. But the symposia is meant to show readers the way to do formal logic, not get tangled up in the bureaucracy of the definition of logic and its relation to the world according to personal opinion or preference.

@VideCorSpoon,

VideCorSpoon, honestly in every post you write on this you are stating things in which I think that you have completely missed the point and completely understood the point.

What I am asserting to is that indeed from your posts people might get the idea that logic is related directly to reality. If that would be the case it would be very easy for people to confuse the workings in their mind with the workings in reality. This is the definition of psychoses and I think very important to keep an eye on. Apart from that it is one of the basic rules in logic. Logic is a tool, nothing more, nothing less. Be carefull with the usage of the tool is all I guess.

@Arjen,

Ok... that sounds fine.

But keep this in mind from the very beginning of the symposium...

@VideCorSpoon,

Ok, I can take a hint. I just think it is really important to realise what the logical system can and cannot do. But I'll get out of the topic in the way I have been in it.

@de budding,

de_budding wrote:

If man made global warming is really happening, then the polar ice caps will be melting.
The polar ice caps are melting,
Therefore man made global warming is really happening.

Quick question on this one. Why is it a false conclusion?
Is the reason that "the polar ice caps are melting" and "the polar ice caps will be melting" is not the same thing?
I would have answered: Wrong premises but correct conclusion. :confused:

@VideCorSpoon,

Technically you are right. The way the sentence "the polar icecaps will be melting" is phrased in such a way and put in the general context of the rest of the proof that you could look at it like that. However, the implication of sentence by itself implies that the polar icecaps will be melting. In any case, that polar ice cap will melt. The way I see it, this satisfies both the necessary and sufficient conditions required to make the sentence a statement rather than a conditional.

@EmperorNero,

Quote:

If man made global warming is really happening, then the polar ice caps will be melting.
The polar ice caps are melting,
Therefore man made global warming is really happening.

NoEmperorNero wrote:

Quick question on this one. Why is it a false conclusion?
Is the reason that "the polar ice caps are melting" and "the polar ice caps will be melting" is not the same thing?
I would have answered: Wrong premises but correct conclusion. :confused:

The conclusion may be true (it just depends on whether or not man-made global warming really IS happening, now that probably is true, but still arguable).

The premises also, are probably true. So, let's say that this argument consists of true premises and a true conclusion. It is still an invalid argument.

When evaluating an argument, we first need to see if it logically follows; the actual truth of the premises and conclusion does not matter in this regard, because the form of the argument is either valid or invalid, regardless of the truth value of the statements. With a valid deductive argument, if the premises are true, then the conclusion is necessarily true.

The premises here do not necessarily lead to the conclusion. With this argument, the premises and conclusion could all be true (to our knowledge), but the actual argument does not logically follow, and so it is invalid.

We can represent this in the following manner (had to adjust a couple words for the tense, but the meaning remains the same):

P: Man made global warming is really happening
Q: The polar ice caps are melting

This type of argument is called "affirming the consequent", and is a formal fallacy that is always invalid for a deductive argument.

You could come up with other varieties of this argument, in english, to see clearly how it is invalid, such as:

If I am looking into a mirror, I see my reflection.
I see my reflection.
Thus, I am looking into a mirror.

Now, all of these things could in fact be true at once, but we all know that simply seeing our reflection does not necessarily mean we are looking into a mirror; we could be staring out at a pond, looking into a glass, etc.

@Pangloss,

Quote:

If man made global warming is really happening, then the polar ice caps will be melting.
The polar ice caps are melting,
Therefore man made global warming is really happening.

VideCorSpoon;58444 wrote:

Technically you are right. The way the sentence "the polar icecaps will be melting" is phrased in such a way and put in the general context of the rest of the proof that you could look at it like that. However, the implication of sentence by itself implies that the polar icecaps will be melting. In any case, that polar ice cap will melt. The way I see it, this satisfies both the necessary and sufficient conditions required to make the sentence a statement rather than a conditional.

Pangloss;58472 wrote:

This type of argument is called "affirming the consequent", and is a formal fallacy that is always invalid for a deductive argument.

You could come up with other varieties of this argument, in english, to see clearly how it is invalid, such as:

If I am looking into a mirror, I see my reflection.
I see my reflection.
Thus, I am looking into a mirror.

Now, all of these things could in fact be true at once, but we all know that simply seeing our reflection does not necessarily mean we are looking into a mirror; we could be staring out at a pond, looking into a glass, etc.

So, that the polar ice caps are melting is not a sufficient condition for the conclusion that global warming is really happening?
They might be melting because we installed giant hair dryers on the ice caps.
(Don't mind the specific wording in my example.)
We can conclude:
Global warming is real => The polar ice caps melt
We can not conclude:
The polar ice caps melt => Global warming is real

Corrections?

PS. I don't understood the difference between a statement and a conditional.

@VideCorSpoon,

The main thing I would say is that the format of the statements would be more precise if they were reversed. In the case of "Global warming is real => The polar ice caps melt," there needs to be a viable premise or two to support the conclusion. The conclusion as I see it is "global warming is real." This is what we should generally conclude, right? So the fact that polar icecaps melt could for all intensive purposes actually be the result of giant hairdryers. This hints at induction rather than deduction to reach the overall conclusion. If we say in the first place that global warming is real, all we are doing is providing an axiom and deriving anything from that assumed fact. Spinoza is a famous example fo someone who assumes a framework first before proving the fundamental elements of that framework. His method is a synthetic approach.

But logic is more truth functional than that. We need proof of global warming. This would be a good proof for global warming; "If the polar icecaps melt, then global warming is real. The polar icecaps are melting. Therefore, global warming is real." This is an example of the modus ponens argument in propositional logic (i.e. P-->Q, P, |- Q ) In the analysis of the statement, it has both necessary and sufficient conditions and is a viable contingent statement, meaning that the truth or falsity of the statement depends entirely on circumstance. We set the circumstance in such a way where the evidence proves beyond logical doubt that the overall statement is correct.

On the differences between a statement and a conditional. A conditional (in logical terms) contains a two parts. An antecedent and a conclusion. An antecedent is the premises that we need to get the conclusion. In logic, the conditional is represented as P -->Q. So take the example; If Paul goes running, then Quincy goes rung as well. The tell-tale sign of a conditional in English is the "If, then" which we would associate with any conditional statement. If P occurs (namely Paul running) then it follows that Q (Quincy will run) will as well.

A statement basically makes a logical inference composed of essentially a cluster of conditionals, disjunctions, and other logical inferences. The global warming statement stated earlier is a prime example of a statement. We provided premises which supported our conclusion.

@VideCorSpoon,

VideCorSpoon;59373 wrote:

The main thing I would say is that the format of the statements would be more precise if they were reversed. In the case of "Global warming is real => The polar ice caps melt," there needs to be a viable premise or two to support the conclusion. The conclusion as I see it is "global warming is real." This is what we should generally conclude, right? So the fact that polar icecaps melt could for all intensive purposes actually be the result of giant hairdryers. This hints at induction rather than deduction to reach the overall conclusion. If we say in the first place that global warming is real, all we are doing is providing an axiom and deriving anything from that assumed fact. Spinoza is a famous example fo someone who assumes a framework first before proving the fundamental elements of that framework. His method is a synthetic approach.

I like to state for the record, that I don't believe in global warming. Not judging the truthfulness of the premises, a logical conclusion is fine if we declare an axiom and deriving from it, right?
That argument could easily be attacked by questioning the axiom. Or the other premises.

VideCorSpoon;59373 wrote:

But logic is more truth functional than that. We need proof of global warming. This would be a good proof for global warming; "If the polar icecaps melt, then global warming is real. The polar icecaps are melting. Therefore, global warming is real." This is an example of the modus ponens argument in propositional logic (i.e. P-->Q, P, |- Q ) In the analysis of the statement, it has both necessary and sufficient conditions and is a viable contingent statement, meaning that the truth or falsity of the statement depends entirely on circumstance. We set the circumstance in such a way where the evidence proves beyond logical doubt that the overall statement is correct.

I see. The argument in its original form is basically only words. There is no value behind them.

@EmperorNero,

I'm not really a firm believer in global warming either. Global warming is not a new phenomena but has in fact been occurring in 400 year increments for at least a last three or four millennia ranging from hot to cold depending on climate and magnetic pole shifts. Check out Discontinuity of Greek Civilization by Rhys Carpenter. He essentially argues that periodic climate change affected the way in which civilization all over the world evolved. I started a thread on it a while back, it would be cool to restart the topic.

http://www.philosophyforum.com/forum/lounge/general-discussion/2267-low-point-civilization.html

But anyway, back on topic.

But logic is essentially made up of axioms. Logic is a closed system where the sky could be green and unicorns could roam the earth devouring small kittens. So in a sense, axioms are used in logic. But the logic of a proof demands that ample evidence be provided so we can derive a deductive conclusion. Axioms, which are inherently inductive in most cases, are a tricky business.

@VideCorSpoon,

I'll put that book on my list. I find that topic very interesting.

VideCorSpoon;59403 wrote:

But logic is essentially made up of axioms. Logic is a closed system where the sky could be green and unicorns could roam the earth devouring small kittens. So in a sense, axioms are used in logic. But the logic of a proof demands that ample evidence be provided so we can derive a deductive conclusion. Axioms, which are inherently inductive in most cases, are a tricky business.

Yes, agree. And that it is tricky business, I can see that from it taking me a page of posting to grasp.

I can see you had a debate earlier in the thread whether logic a closed system.
Like math, I believe it is a rationalistic tool, that only makes statements based on former assumptions. The assumptions can to come from somewhere else.
I admit that it looks like this to me at the moment, as I'm not very far in my studies, and only judge by the tip of the iceberg.

If done correctly, our deductions will correspond with reality. But there is always this dualism, where our closed system formed by rationalism "floats" above reality; and it's only connected by thin strings. The better job we do as philosophers, the closer the two will be.

@VideCorSpoon,

oh wait..cause in my logic class all is dificult...
but..ok specially the part about so many maths...
for instances the euclides theorem

@Arjen,

I have a question. Does a valid argument necessarily become logical as well?

@mister kitten,

mister kitten;124948 wrote:

I have a question. Does a valid argument necessarily become logical as well?

What do you mean by "logical argument"? I know what "valid argument" means, but not the term, "logical argument". I suppose someone might mean by "logical argument", "valid argument", but the term, "logical argument" has no fixed meaning in logic.

@VideCorSpoon,

Hahaha, that's funny. What is a "valid argument"?

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