The essence of logic is to find out what argumentative structures

[Mentat]

Originally posted by Tom
No, and I've never heard of that. Can you explain?

Sure, but you'll probably recognize it, before I'm through.

The paradox of Deductive Logic
Let's take, for example, Euclid's rule: "If two sides of a triangle are equal to the same, they are equal to each other" (I think that's how it goes).

For the purpose of this example, let's say that there is a triangle, where it can be shown that the two sides are equal to the same, but I refuse to believe that they are equal to each other.

Now, you would wish to use deductive logic to show me that it must be so, but...

Proposition 1 is "The two sides are equal to the same"
Proposition 2 is "If two sides are equal to the same, they are equal to each other"

Now, I'll accept those two, but it is another proposition altogether (Proposition [oo]) to say that "Therefore, the two sides are equal to each other". I refuse to accept Proposition [oo], and have no reason to yet. So, you say, "if you accept Propositions 1 and 2, then you must accept Proposition [oo]", which we'll call Proposition 3.

Well, now I'll agree to Propositions 1, 2, and 3, but I still disagree with Proposition [oo], and I don't have to agree with it, because you have yet to say that "if you accept 1, 2, and 3, you must accept Proposition [oo]".

And so it goes on. This is an Inductive approach, in that I am telling you that, no matter how many new propositions you produce, you will still never resolve this paradox.


The paradox of Inductive Logic
This is much more simple. Basically, deductive logic tells us...

1) Inductive Logic is based on learning from observed patterns.
2) What we think is a "pattern" is not necessarily a pattern (it could be a coincidence every time) unless you have tried it as many times as possible (which is infinite, obviously).
3) Therefore, Inductive Logic is based on trying something an infinite amount of times, and is thus not "proof" of anything.

It's called Logic, by David Baum. Just a first textbook on the subject.

So far, we slowly crawled through the introduction, and we are about half way through the first of two chapters on syllogistic logic. I'll post some more by the end of the week.

Thanks. It's very interesting to me.

I really want to get to symbolic logic, because that's where the power of deductive reasoning gets a huge boost.

Yeah, I've had some dealings with symbolic logic before (mostly in Raymond Smullyan's books, which I highly recommend, btw), and I think it's probably one of the most interesting things I've studied.

 

[quantumdude]

Originally posted by Mentat
And so it goes on. This is an Inductive approach, in that I am telling you that, no matter how many new propositions you produce, you will still never resolve this paradox.

It seems that all this does is highlight incompleteness: that the formal system has axioms that cannot be proved within the system. That's not a paradox.

I don't want to get into Goedel here at all in this topic. Indeed, I have another dormant topic in the Math forum that is moving towards that (I think it's time to revive that one, too). This thread is about using logic, whereas discussions such as this are more along the lines of proving things about logic, which is not what I'm after here. Basically, I started this thread for people like Lifegazer and Alexander so I could stop repeating the same explanations of their fallacies, and instead cut and paste sections from the Logic Notes.

Both of them are gone now, but I think it will still be a good idea to teach anyone here who wants to learn.

3) Therefore, Inductive Logic is based on trying something an infinite amount of times, and is thus not "proof" of anything.

Now this is mentioned in the Introduction, and I covered it in the Logic Notes. It is openly admitted that induction is not proof, and the book stresses the fact that terms such as "sound" are reserved strictly for deductive arguments, and that such absolute terms would be misplaced on an argument that gives only partial support for its conclusion.

 

[Mentat]

Originally posted by Tom
It seems that all this does is highlight incompleteness: that the formal system has axioms that cannot be proved within the system. That's not a paradox.

True. However, it does show that Inductive Reasoning is required to show the flaw in Deductive Logic, and vice versa.

I don't want to get into Goedel here at all in this topic. Indeed, I have another dormant topic in the Math forum that is moving towards that (I think it's time to revive that one, too). This thread is about using logic, whereas discussions such as this are more along the lines of proving things about logic, which is not what I'm after here. Basically, I started this thread for people like Lifegazer and Alexander so I could stop repeating the same explanations of their fallacies, and instead cut and paste sections from the Logic Notes.

Alright, I just wondered if the book mentioned it.

Now this is mentioned in the Introduction, and I covered it in the Logic Notes. It is openly admitted that induction is not proof, and the book stresses the fact that terms such as "sound" are reserved strictly for deductive arguments, and that such absolute terms would be misplaced on an argument that gives only partial support for its conclusion.

But you can only reach the conclusion of Inductive Logic's incompleteness through Deductive Logic, which is itself incomplete (by virtue of Inductive Logic). It's rather circular, and that's why I called it a paradox. However, we needn't discuss this at all, unless the book happens to bring it up.

Side Note: Science is based on the Inductive Method, so shouldn't it be viewed as giving only "partial support", as you put it? I covered this in "A Universe Without Logic" where I said that every case of "cause-and-effect" that we've ever observed could be coincidence. However, this is off-topic, so I'll leave it alone.

 

[quantumdude]

Originally posted by Mentat
True. However, it does show that Inductive Reasoning is required to show the flaw in Deductive Logic, and vice versa.

I haven't read the Goedel's entire proof yet, but I do know that he proved his theorem deductively, so it seems that induction is not required to show incompleteness.

Side Note: Science is based on the Inductive Method, so shouldn't it be viewed as giving only "partial support", as you put it?

Yes. We will get to the scientific method of falsificationism in Part III: Induction.

I'll try to post something more in the notes this weekend.

 

[Mentat]

And I'll try to solve some more of your exams, as soon as I get my glasses fixed.

 

[drnihili]

With regards to the paradox of deductive logic. The most famous presentation of this is from Lewis Carroll (aka C.L. Dodgson) in What the Tortoise said to Achilles. It's reprinted in one of Hofstadter's books, I forget which one though. THe problem has very little to do with incompleteness in the Goedelian sense. Instead it's primarily a problem with the philosophical notion of a rule.

Any logical system must use rules to allow the transition from one statement to another. But these rules can also be written explicitly as a statement of the logic, typically as an axiom. Systems using "natural deduction" have lots of rules and no axioms. Axiomatic systems have lots of axioms and very few rules. The problem comes when one insists that every rule be reduced to an axiom. It turns out that's just impossible to do and still have anything resembling a logical system.

One way of trying to resolve the problem is via metalogic. In metalogic you prove things about a logical system, for example that any inference made in it is valid. In a sense though this merely puts the problem off for a bit. Metalogic must of course make inferences, and those inferences are subject to the same sort of objection which can only be resolved by appeal to meta-metalogic. And the list goes on.

Interestingly, this issue receives very little attention and is generally considered to not really be a problem. It's just accepted that no reasonably powerful logic system can show it's own soundness in the relevant sense. Every starting point can be questioned, but we do have to start somewhere.

The problems with inductive logic are far more trenchant. Perhaps the best read on those is Goodman's The New Riddle of Induction

 

[Mentat]

Originally posted by drnihili
With regards to the paradox of deductive logic. The most famous presentation of this is from Lewis Carroll (aka C.L. Dodgson) in What the Tortoise said to Achilles. It's reprinted in one of Hofstadter's books, I forget which one though...

Godel, Escher, Bach: An Eternal Golden Braid. That's actually where I first read about it.

THe problem has very little to do with incompleteness in the Goedelian sense. Instead it's primarily a problem with the philosophical notion of a rule.

Any logical system must use rules to allow the transition from one statement to another. But these rules can also be written explicitly as a statement of the logic, typically as an axiom. Systems using "natural deduction" have lots of rules and no axioms. Axiomatic systems have lots of axioms and very few rules. The problem comes when one insists that every rule be reduced to an axiom. It turns out that's just impossible to do and still have anything resembling a logical system.

One way of trying to resolve the problem is via metalogic. In metalogic you prove things about a logical system, for example that any inference made in it is valid. In a sense though this merely puts the problem off for a bit. Metalogic must of course make inferences, and those inferences are subject to the same sort of objection which can only be resolved by appeal to meta-metalogic. And the list goes on.

Interestingly, this issue receives very little attention and is generally considered to not really be a problem. It's just accepted that no reasonably powerful logic system can show it's own soundness in the relevant sense. Every starting point can be questioned, but we do have to start somewhere.

This is a very good explanation of the problem of Deductive Logic, drnihili! If I might point out - though you probably already noticed - you did run into something similar to Godel's Incompleteness, when you said that "it's just accepted that no reasonably powerful logic system can show it's own soundness in the relevant sense". This is probably why Tom had associated the problem of Deductive Logic with Godel.

The problems with inductive logic are far more trenchant. Perhaps the best read on those is Goodman's The New Riddle of Induction

Really? I guess there's more to it than I had imagined (I had just assumed the obvious incompleteness of Inductive Logic: namely, you can't try anything an infinite number of times). I'll look that up that book as soon as I can. Thanks .

 

[Mentat]

Oh, and belated welcome to the PFs!

I guess I just hadn't seen you post before (or I would have extended this welcome earlier).

 

[quantumdude]

Now that Mentat's mom has let him come back, maybe we can pick this thread up again.

 

[Mentat]

Originally posted by Tom
Now that Mentat's mom has let him come back, maybe we can pick this thread up again.

I will start as soon as I can, but I have to get off-line in a couple of minutes, so it can't be today. I'll try for tomorrow.

 

[Dissident Dan]

Originally posted by Tom

Thanks Mentat for "keeping me company".

No, they are all correct.

Oh, contraire!

You caught this error when CJames made it, but you let it slip by this time:
---------------------------------------------------------------
quote:
-----------------
Argument 2:
Some Englishmen are Protestants.
Winston Churchill was a Protestant.
Therefore, Winston Churchill was an Englishman.
------------------

Some PF members are atheists.
Futurist was a PF member.
Therefore, Futurist was an atheist (this one is for those of you who have been here for a while).
--------------------------------------------------------------

The original example had an object-object link. The one that Mentat gave had a subject-object link. If the first sentence was "Some atheists are PF members.", then it would have been a correct counter-example.

 

[Mentat]

Originally posted by Dissident Dan
Oh, contraire!

You caught this error when CJames made it, but you let it slip by this time:
---------------------------------------------------------------
quote:
-----------------
Argument 2:
Some Englishmen are Protestants.
Winston Churchill was a Protestant.
Therefore, Winston Churchill was an Englishman.
------------------

Some PF members are atheists.
Futurist was a PF member.
Therefore, Futurist was an atheist (this one is for those of you who have been here for a while).
--------------------------------------------------------------

The original example had an object-object link. The one that Mentat gave had a subject-object link. If the first sentence was "Some atheists are PF members.", then it would have been a correct counter-example.

I know that I may be wrong, but I disagree with what I understand from your post. I don't see why "Some atheists are PF members" would have been better, since the first proposition of the book's example is "Some Englishmen are protestants". Is it just because the "atheist" part was supposed to correspond to the "Protestant" part?

In that case, I still disagree, since I didn't hold in the second proposition that Futurist was an atheist, but that he was a PF member. The fact that mine places the religion aspect at different parts of the issue didn't/doesn't seem relevant to me. IOW it didn't/doesn't seem relevant to me that what I took for granted was Futurists being a member of a certain group to deduce his being a member of a certain religion, while the book's example did it vice versa.

 

[Mentat]

Oh wait, your right, Dan. I was supposed to keep the scheme as:

some p are q
r is a q
therefore r is a p

Sorry about that.

Here's another possible counter:

Some PF members are very intelligent
Edward Witten is very intelligent
Therefore Edward Witten is a PF member.

Is that better?

 

[Dissident Dan]

The new example is correct.

 

[quantumdude]

Originally posted by Dissident Dan
Oh, contraire!

You caught this error when CJames made it, but you let it slip by
this time:

OK, good catch.

Argument 2:
Some Englishmen are Protestants.
Winston Churchill was a Protestant.
Therefore, Winston Churchill was an Englishman.
------------------

Some PF members are atheists.
Futurist was a PF member.
Therefore, Futurist was an atheist (this one is for those of you who have been here for a while).
--------------------------------------------------------------

The original example had an object-object link. The one that Mentat gave had a subject-object link. If the first sentence was "Some atheists are PF members.", then it would have been a correct counter-example.

I just want to note that that is not a counterexample of any argument because the conclusion is true.

Just to review, and to refresh my own memory, the easiest way to do a counterexample is start with a conclusion that is false, and construct true premises using their terms.

If I start with: Therefore, Greg Bernhardt is a woman.

Then I can build the argument around it using true premises.

Some women are PF members. True[/color]
Greg Bernhardt is a PF member. True[/color]
Therefore, Greg Bernhardt is a woman. False[/color]

In this argument, as well as in Argument 2 above and in Mentat's do-over, the middle term is in the predicate of both premises.

edit: fixed a typo

 

[Mentat]

Originally posted by Tom
Before I move on to the next part on immediate inferences, let me give some exercises on what has been presented so far.

Indicate whether each of the following sentences expresses an A, E, I, or O statement. When necessary translate the sentence into standard form. Indicate whether any meaning is lost in the translation. Write an abbreviation for each sentence, indicating which term each letter represents. Also give the schema for each statement.

1. Lassie is not a cocker spaniel.

I need a little help here, should this be represented as (having first indicated that "Lassie" = "L" and that "c" = "cocker spaniel"):

No L are c. That is an A statement. It's schema would just be: no p are q.

Is that the way we are supposed to do that, or did I miss something (or the whole point )?

If this is right, then I will attempt the rest of the statements.

 

[Mentat]

Uh...Tom? I need verification that I'm doing this right, or I can't continue.

 

[quantumdude]

Sorry Mentat, I've been busy but now I'm back.

Originally posted by Mentat
I need a little help here, should this be represented as (having first indicated that "Lassie" = "L" and that "c" = "cocker spaniel"):

No L are c. That is an A statement. It's schema would just be: no p are q.

Actually, that's not an A statement. "No p are q" is an E statement. An A statement is "All p are q". However, you got the correct schema.

Is that the way we are supposed to do that, or did I miss something (or the whole point )?

You got it, aside from the label (swap E for A and you have it). In this case, "Lassie" is singular subject, and it is to be understood as "All of the members of the class of which Lassie is the only member". That said, this is to be understood as a universal negative[/color] statement, aka an E statement.

Here it is completely worked out:

Original Sentence:
Lassie is not a cocker spaniel.

Standard Form:
No dogs that are Lassie are cocker spaniels.

Abbreviation:
No L are C.

Schema:
No S are P.
[/color]

edit: fixed bold font bracket

 

[Mentat]

Good to see you back, Tom.

I'll get started immediately.

Originally posted by Tom
Indicate whether each of the following sentences expresses an A, E, I, or O statement. When necessary translate the sentence into standard form. Indicate whether any meaning is lost in the translation. Write an abbreviation for each sentence, indicating which term each letter represents. Also give the schema for each statement.

Number 1 was covered so I will move on to...

2. Most records cost less than five dollars.

This is an I statement.

Standard Form:
Most records cost less than five dollars.

Abbreviated Form:
Some r are l.

Schema:
Some p are q.

3. Sixty percent of all college students work part-time to pay for their education.

This is an A statement. (I'm not really sure, but I think so )

Standard Form:
All students belonging to the class "sixty percent of college students", work part-time to pay for their education.

Abbreviated Form:
All S are W.

Schema:
All p are q.

4. Almost all professional basketball players are over six feet four inches tall.

This is definitely an I statement.

Standard Form:
Some pro. basketball players are over 6'4" tall.

Abbreviated Form:
Some p are o.

Schema:
Some p are q.

5. All politicians are not dishonest.

This is an O statement. Using the principle of charity here, since this could mean two different things.

Standard Form:
Some Politicians are not dishonest.

Abbreviated Form:
Some P are not d.

Schema:
Some p are not q.

6. War is not healthy for children and other living things.

This is an E statement.

Standard Form:
No War is healthy for children and other living things.

Abbreviated Form:
No W are h.

Schema:
No p are q.

7. Only those who bought tickets in advance were able to get seats.

This is an A statement.

Standard Form:
All buyers [trying not to use the same letter twice] who bought tickets in advance were able to get seats.

Abbreviated Form:
All b are a.

Schema:
All p are q.


That's it. I'm pretty sure I got some of those wrong (as I wasn't certain when answering some of them), but that was pretty fun.

 

[quantumdude]

It was tough, but I actually resisted the urge and did not log on once the entire long weekend.

2. Most records cost less than five dollars.

This is an I statement.

Right. This is an example of one of those cases in which meaning is lost in formalization ("some" does not mean the same as "most"). It highlights the tradeoff we make when going from informal language to standard form logic: We lose shades of meaning from the intended thought, but we gain the ability to unambiguously evaluate the logic of the translated sentence. It is unfortunate, but it would not be possible to test syllogisms for validity if we did not translate sentences, as we will see in Chapter 2.

3. Sixty percent of all college students work part-time to pay for their education.

This is an A statement. (I'm not really sure, but I think so )

It can't be an A statement, because that is the "Universal Affirmative" statement, and 60% of a whole is not universal. This is a tricky one, because it is a combination of two types, I and O. That is, it expresses the I statement...

Some college students work part-time to pay for their education.[/color]

...but not exactly. That is because the logical quantifier "some" includes the case of "all". But, we are told a very specific "some" (60 percent) that most definitely does not include "all". So, the above also expresses the O statement...

Some college students do not work part-time to pay for their education[/color]

This is called an "exceptive statement", and is discussed in the Logic Notes in the 12th post from the top (do a "control-F" for the word "exceptive" and you'll be taken right to it).

4. Almost all professional basketball players are over six feet four inches tall.

This is definitely an I statement.

Almost. It is another exceptive I + O statement. "Almost all" communicates the idea that it is "some but not all"

5. All politicians are not dishonest.

This is an O statement. Using the principle of charity here, since this could mean two different things.

Very good. You recognized that this could mean either "All politicians are honest" or "Some politicians are not dishonest". When there is ambiguity, it is always best to ascribe the weaker of the two positions to an opponent, and so avoid mistakenly increasing his burden of proof.

6. War is not healthy for children and other living things.

This is an E statement.

Right. I would even go so far as to say that it is two[/color] E statements:


War is not healthy for children.
War is not healthy for other living things.
[/color]

Since the predicate is compound, so is the statement. But, since we are not on Quantificational Logic yet the distinction is not yet important.

7. Only those who bought tickets in advance were able to get seats.

This is an A statement.

Right. This is an "exclusive statement" that actually expresses a "universal affirmative".

I'll get going on the next installment of the Notes ASAP.

Thanks for playing!

edit: fixed a bold font bracket

 

[Mentat]

Originally posted by Tom
It was tough, but I actually resisted the urge and did not log on once the entire long weekend.

I just can't believe it!

Anyway, I'm glad you're back, as I'd like to keep working on this thread.

It can't be an A statement, because that is the "Universal Affirmative" statement, and 60% of a whole is not universal. This is a tricky one, because it is a combination of two types, I and O. That is, it expresses the I statement...

Some college students work part-time to pay for their education.[/color]

...but not exactly. That is because the logical quantifier "some" includes the case of "all". But, we are told a very specific "some" (60 percent) that most definitely does not include "all". So, the above also expresses the O statement...

Some college students do not work part-time to pay for their education[/color]

This is called an "exceptive statement", and is discussed in the Logic Notes in the 12th post from the top (do a "control-F" for the word "exceptive" and you'll be taken right to it).

I see. I'll go look that up ASAP.

Almost. It is another exceptive I + O statement. "Almost all" communicates the idea that it is "some but not all"

Hmm. I was close though .

Right. I would even go so far as to say that it is two[/color] E statements:


War is not healthy for children.
War is not healthy for other living things.
[/color]

Since the predicate is compound, so is the statement. But, since we are not on Quantificational Logic yet the distinction is not yet important.

Interesting point.

 

[Mentat]

Tom,
I just looked up that part on exceptives, and I have a question:

Why must a statement be considered exceptive, merely because it can be both an I statement or an O statement? After all, it seems that any I statement has an inverse form that is in the form of an O statement.

What I mean is: Doesn't any statement of the form "some p are q" always imply that "some p are not q" (otherwise, it would not be "some p are q" but "all p are q" (an A statement)). Please help me out on this whenever you have time.

 

[drnihili]

Originally posted by Mentat
Tom,
I just looked up that part on exceptives, and I have a question:

Why must a statement be considered exceptive, merely because it can be both an I statement or an O statement? After all, it seems that any I statement has an inverse form that is in the form of an O statement.

What I mean is: Doesn't any statement of the form "some p are q" always imply that "some p are not q" (otherwise, it would not be "some p are q" but "all p are q" (an A statement)). Please help me out on this whenever you have time.

I statements do not generally imply O statemtents. To see this, consider making a statement about a group you only know a litte about. For example, I have a beard. On the basis of that, we can conclude that some contributors to this thread have beards. Notice that we don't first have to check to see whether other people have beards. And the I statement remains true even if we should later discover that all contributors have beards.

Now it's true that we don't typically make an I statement if we know that the A statement is also true. It would sound odd to say "Some whales are mammals". But this isn't because saying it would be false. Instead it's because there are rules of conversation that encourage us to give as much information as we reasonably can. THis sort of thing is generally taken care of in the field of pragmatics. Specifically, the requirement to not assert an I statement when you know the corresponding A statement to be true is part of the theory conversational implicature developed by Grice.

 

[Mentat]

Originally posted by drnihili
I statements do not generally imply O statemtents. To see this, consider making a statement about a group you only know a litte about. For example, I have a beard. On the basis of that, we can conclude that some contributors to this thread have beards. Notice that we don't first have to check to see whether other people have beards. And the I statement remains true even if we should later discover that all contributors have beards.

Now it's true that we don't typically make an I statement if we know that the A statement is also true. It would sound odd to say "Some whales are mammals". But this isn't because saying it would be false. Instead it's because there are rules of conversation that encourage us to give as much information as we reasonably can. THis sort of thing is generally taken care of in the field of pragmatics. Specifically, the requirement to not assert an I statement when you know the corresponding A statement to be true is part of the theory conversational implicature developed by Grice.

Thank you for that, drnihili. That makes perfect sense now.

 

[HeavensWarFire]

UUMMMMM


I couldn't help but to realize what looks to be an error in judgement:

I statements do not generally imply O statemtents. To see this, consider making a statement about a group you only know a litte about. For example, I have a beard. On the basis of that, we can conclude that some contributors to this thread have beards. Notice that we don't first have to check to see whether other people have beards. And the I statement remains true even if we should later discover that all contributors have beards.

I am not sure the admission a of a single contributor having a specific charactoristic is the same as the term "some." "Some" seems to imply more than one, to what degree exactly, no one knows, hence, the use of the word "some" for a generally unknown amount of something; but how can you infer that some have beards simply because you have found a case of a single person actually having a beard? Does a single person constitute a "some" in the strickest sense?

I understand the term "some" to be of an undefined amount of something, but the some is more generally than a single case.

Take for example the following analogies.

A person arrives to a party, and they are asked by someone else if they have gotten a portion of a cake, to which they reply, "Yes, i got some cake."

In the case above, we really don't know what is meant by "some." What is the some? A bite? An actual slice? Or a crumb?

In the example of "some Ps are Qs" the word "some" is not all exclusive, hence, it would follow then that "some Ps 'are not' Qs" since you did not use an all exclusive term.

An all exclusive term would be something like, "all" or "unexceptionally" since you are not really leaving room for any kinds of deviations, or alternatives.

A true law, a true rule, would be an axiom that you can not really find an exception for. Which brings us to the paradox of whether or not a rule is the exception, rather than the actual rule. Maybe some rules are the exceptions rather than the standard, no?

 

[HeavensWarFire]

Part 2



This doesn't sound correct either:

Now it's true that we don't typically make an I statement if we know that the A statement is also true. It would sound odd to say "Some whales are mammals". But this isn't because saying it would be false.

But it is a missuse of language, since, the very idea of a mammal is a pretty well defined term. Hence, if you say some mammals are whales, then by default you are allowing for the possibility for one to think that some whales 'are not mammals,' hence, it would in fact be false to make such a statement, if it is the case that all whales are mammals, unexceptionally.

Certain terms, exclude other ideas automatically. This is what gives language in some instances the power to establish resolution to a problem.

Take for example, the notion, that an "unstoppable truck can break, and be stopped by an unbreakable wall."

You are having a collisions of concepts that can not be logically sound due to the terms being used, and justapose.

If a truck is really "unstoppable," then it must either move a wall, or break a wall, but you can't break a wall that is "unbreakable." Hence, you are logically at a stand still, since you have ran into a contradiction that can not logically hold to be true when it juggles 2 highly oppositional ideas. One or the either of the main predicates of a sentence must be true, but you can't have 2 predicates of opposing meaning to be true.

This is why it gets hard to explain the whole idea of "an unmoved mover," or a big bang.

If there is nothing to cause the motion of an object, then why wouldn't it be the case that the object will remain stationary if there is nothing else to act on the object?

How could GOD be a self-sustained mover, if all things require a mover to set them into motion?

What caused GOD to be, if GOD is the cause of everything else?

Why would something that was once a huge blob of hydrogen, all of the sudden, after an immense amount of time of just being a big blob explode upon itself, and spring a Universe from its raw materials?

Doesnt make sense.


To think there was a time, when the blob was just a blob, not murmuring, not moving, not having any kind of activity, and then all of the sudden, it has activity, like a particular molecule moving from its stationary position until it bumped into another, and that in turn bumped into a third, until kaboom, you had this mass population of atoms bouncing off each other to the point where, kaboom, it all just exploded, then the main question becomes as to what caused the first domino to fall so that it would then knock over all the remaining dominos?

Dont make sense.

If all things are stationary, then how can any movement commence?

Something must have either been in motion by accidant always, and thus the cause all other motions. Or there must have been something that "had the will" to be the exception to the rule with regards to all things being still, and in a concentrated location.

Life is a grand Mystery. Kinda like GOD. Neither one of them make sense really. But then again, Immanual Kant was wrong, and David Human right. We do impose our ideas onto life. The idea of order is a human concept that has no real basis in reality.

 

[drnihili]

Those are good points about the use of language. The question is whether they are in the realm of logic or in the realm of pragmatics. The standard answer is that they are issues of pragmatics. The seminal piece on this issue is H. P. Grice's "Logic and Conversation". If the issue interests you and you're near a decent library, I recommend the anthology Pragmatics: A Reader edited by Steven Davis. It contains Grice's paper and many others.

I don't have time at the moment for a point by point response, but I'll try for that later today.

nihili

 

[Evo]

I confess that I have only just begun to read through the posts, but I notice that people seem to be overthinking things.

Logic is simple, it shouldn't be this hard to grasp.

Tom, great information on logical declarative sentences. Takes me back a few years.

In my experience, people either are capable of logical thinking, or they're not.

 

[logicalroy]

Sure, but you'll probably recognize it, before I'm through.

The paradox of Deductive Logic
Let's take, for example, Euclid's rule: "If two sides of a triangle are equal to the same, they are equal to each other" (I think that's how it goes).

For the purpose of this example, let's say that there is a triangle, where it can be shown that the two sides are equal to the same, but I refuse to believe that they are equal to each other.

Now, you would wish to use deductive logic to show me that it must be so, but...

Proposition 1 is "The two sides are equal to the same"
Proposition 2 is "If two sides are equal to the same, they are equal to each other"

Now, I'll accept those two, but it is another proposition altogether (Proposition [oo]) to say that "Therefore, the two sides are equal to each other". I refuse to accept Proposition [oo], and have no reason to yet. So, you say, "if you accept Propositions 1 and 2, then you must accept Proposition [oo]", which we'll call Proposition 3.

Well, now I'll agree to Propositions 1, 2, and 3, but I still disagree with Proposition [oo], and I don't have to agree with it, because you have yet to say that "if you accept 1, 2, and 3, you must accept Proposition [oo]".

And so it goes on. This is an Inductive approach, in that I am telling you that, no matter how many new propositions you produce, you will still never resolve this paradox.


The paradox of Inductive Logic
This is much more simple. Basically, deductive logic tells us...

1) Inductive Logic is based on learning from observed patterns.
2) What we think is a "pattern" is not necessarily a pattern (it could be a coincidence every time) unless you have tried it as many times as possible (which is infinite, obviously).
3) Therefore, Inductive Logic is based on trying something an infinite amount of times, and is thus not "proof" of anything.

Thanks. It's very interesting to me.

Yeah, I've had some dealings with symbolic logic before (mostly in Raymond Smullyan's books, which I highly recommend, btw), and I think it's probably one of the most interesting things I've studied.

You must be kidding! Dude, you have not proven there to be any paradoxes with DEDUCTION. You simply don't know enough. You are confused. You erroneously beieve you accepting the premises has something to do with OBJECTIVE truth. You wrote: "Now, you would wish to use deductive logic to show me that it must be so, but...
Proposition 1 is "The two sides are equal to the same"
Proposition 2 is "If two sides are equal to the same, they are equal to each other"
Now, I'll accept those two, but it is another proposition altogether (Proposition [oo]) to say that "Therefore, the two sides are equal to each other". I refuse to accept Proposition [oo], and have no reason to yet"
THAT'S because you are crazy! Your first premise isn't a complete sentence to begin with. The second makes more sense than the first, but what does "the same mean?" From what I gather in your example, proposition [oo] would be a conclusion in your example. If the premises are true then the conclusion MUST be true. That's like saying: "I don't agree that Roy has a sister; therefore Roy can't have a sister." Get over yourself! You not accepting the conclusion HAS NOTHING TO DO WITH LOGIC. You must see a psychologist for that. In this world there are OBJECTIVE FACTS and they will be true whether you agree with them or not. For example, it is an OBJECTIVE FACT that here on Earth ALL trees are a form of plantlife. Does that need your agreement to be true? No offense, but most people have the wrong ideas about LOGIC of which I am formally trained. I am not self taught. You are like most beginners who do not know the difference between PSYCHOLOGY and PHILOSOPHY. You am a majority of people who post here are confusing the two subjects. PHILOSOPHY is NOT a branch of PSYCHOLOGY where we can just sit around and express our emotions, thoughts and beliefs. That is what a psychology forum should be about. You are in a PHILOSOPHY forum correct? Learn something about REAL PHILOSOPHY. Philosophy is not just a belief or an opinion like most beginners believe. Here is a PROFESSIONAL LINK to where there are people who have PHD in PHILOSOPHY and answers questions like your for free:http://www.shef.ac.uk/uni/projects/ptpdlp/questions/feedback/feedback.html . Scroll down to "SUBMIT QUESTION" or you can read previous answers to questions like yours by going to the "ANSWERS" icon. Once you see what REAL PHILOSPHY is about you will see that sites like this (where anyone can vent their feelings )are a joke. This forum should be labeled "PSYCHOLOGY FORUM" not PHILOSOPY.

 

[Math Is Hard]

Calm down, Roy. Everything's going to be OK. Really.