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Common Misconceptions about Logic

the_croftmeister
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6/12/2013 6:31:55 PM
Posted: 3 years ago
There are a couple of pet peeves of mine when it comes to logic and reason. More specifically about what it can and can't do, and what it does and does not attempt to do. So I was wondering if anybody else has some. Or if they disagree with mine and think I'm promoting misconceptions of my own.

1. Logic is about facts.
Logic is principally concerned with deduction and contradiction. What can be deduced from what? What contradicts what? Many logics have tautologies which have the semblance of fact or at least truth but the traditional approach is that these are true by virtue of having no useful meaning and therefore do not provide any insight. That a particular logical system proves a particular tautology is a fact, but this is achieved through reason about the axioms of the metalogic, not the logic itself.

2. Logic is indisputable
This makes sense to some degree, if I have followed the rules of the logic that I am using then you can't tell me I'm wrong, but seeing has how nobody has come up with any good reasons to presume that any particular logic is the one true logic then this does not mean that my logic is beyond reproach. I can always challenge your logic on the grounds of its usefulness or its applicability to the problem at hand. Even in mathematics, one of the most precise and thus least ambiguous studies of man, there is still disagreement over the utility of different logics.

Logic is a tool, use it right and it strengthens your argument considerably since we have a reasonable understanding of the consequences of its use.
Thoughts anyone?
llamainmypocket
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6/15/2013 4:05:25 PM
Posted: 3 years ago
I'd really like to see this conversation go somewhere with academic logicians but it's not so I'll chime in.

Logic is an axiomatic system by which principles are injected to obtain a conclusion based solely upon the principles which are called axioms. It is a linear line of thought which can be deductive or inductive in nature. like mathematics, it does not matter which order you start from. just that A=B or B=A are true and that the one side equally reflects the other.

The limitations of the axiomatic system is that the conclusion of the linear problem only has the integrity of the axioms used. Axioms integrity=conclusion integrity. Naturally, axioms are considered proper when they are irrefutable facts; as irrefutable axiom = irrefutable conclusion. Because axiomatic systems are linear they are therefore finite. In order to achieve maximum integrity you need maximum information. If maximum information is all information then (All Information = maximum integrity) or (All Information=Truth)

The mission has then become a pursuit to craft a loop within the axiomatic system that covers all reasonable ground and therefore offers a reasonable foundation for a reasonable conclusion. This is still an assumption! It is as reasonable as we can make it though.

The result is 2+2=4 can be inferred to mean that you have four oranges. That A+B= it is reasonable to believe you have no other oranges. Therefore a loop is created between finite lines of logic. This is very good but ultimately it is still not maximum integrity. you still need all of the information it achieve maximum integrity and therefore have truth.

So I disagree. It's only prefect in its own context. We do not know that 1=1 because we do not fully understand the universe. We can only say that 1=1 is reasonable. At any point we may find information that invalidates the foundation. Perhaps 1=1 isn't the same one but distinct and therefore 1=1=false.

I realize that sounds strange but here is something simple. 1=1 but if 1Apple=1Apple and an apples mass varies then 1=1 is false by the introduction of new language.
Poetaster
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6/15/2013 4:41:06 PM
Posted: 3 years ago
I would agree with your critique, croftmeister, of those particular vulgar conceptions which float around. I myself am inclined to quarrel with the even more egregious misuse of the term "logic" to mean: "any line of thinking whatsoever".

General reasoning (usually a mixture of induction, evidential abduction, argument by example, personal anecdote, rhetoric, deduction, and the occasional fallacy, with no explicit transition between these) is obviously not the same as logic (that is, formal logic), but in common non-technical discourse people will often mix and match these tactics into a kind of "folk method" of argumentation, and then call it "logic".

I just find myself personally annoyed at this usage. Of course, general reasoning seems to be the preferred platform from which to debate most topics of public interest; I would just prefer that the transitions between different approaches be acknowledged as they are undertaken so that the type of argument being presented is properly recognized.
"The book you are looking for hasn't been written yet. What you are looking for you are going to have to find yourself, it's not going to be in a book..." -Sidewalker
Poetaster
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6/15/2013 4:51:12 PM
Posted: 3 years ago
llamainmypocket,

When you talk about the "integrity" of certain axioms, you seem to hinge this qualification on the factual or empirical accuracy of those axioms. Why do this? How can a set of axioms have an "integrity" by any other measure than their mutual consistency and, possibly, how rich or aesthetically pleasing their consequent structure is?

The axioms of Euclidean geometry are not empirically "true", but that is beside the point. They are still a perfectly acceptable and robust mathematical system whose theorems are not "endangered" by the fact that they fail to capture the nature of the physical universe.
"The book you are looking for hasn't been written yet. What you are looking for you are going to have to find yourself, it's not going to be in a book..." -Sidewalker
the_croftmeister
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6/15/2013 9:01:53 PM
Posted: 3 years ago
At 6/15/2013 4:41:06 PM, Poetaster wrote:
I would agree with your critique, croftmeister, of those particular vulgar conceptions which float around. I myself am inclined to quarrel with the even more egregious misuse of the term "logic" to mean: "any line of thinking whatsoever".

General reasoning (usually a mixture of induction, evidential abduction, argument by example, personal anecdote, rhetoric, deduction, and the occasional fallacy, with no explicit transition between these) is obviously not the same as logic (that is, formal logic), but in common non-technical discourse people will often mix and match these tactics into a kind of "folk method" of argumentation, and then call it "logic".

I just find myself personally annoyed at this usage. Of course, general reasoning seems to be the preferred platform from which to debate most topics of public interest; I would just prefer that the transitions between different approaches be acknowledged as they are undertaken so that the type of argument being presented is properly recognized.

Agreed, I've often wondered whether a separate philosophically constructed language (like Lojban or something) would be useful to indicate the transition between reason and appeal (this is how I like to characterise the two persuasive techniques). I don't like Lojban much myself but its the closest to the objective I've seen. This would make for interesting discussions. Also, I've come to the conclusion that such a language would have to be taught later in life (high school at least) or it would lose the precision it once had through all the standard processes of language drift.

Its a pity that not more people are interested in this topic, but never mind, I guess most people don't care too much, their normal reasoning does the job for them.
the_croftmeister
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6/15/2013 9:42:28 PM
Posted: 3 years ago
At 6/15/2013 4:05:25 PM, llamainmypocket wrote:
I'd really like to see this conversation go somewhere with academic logicians but it's not so I'll chime in.

Interestingly enough I study logic academically and have been working towards a research proposal on a formal logic system similar to Giorgi Japaridze's Computability logic so if there are any formal logicians in the community I would be very interested in their thoughts.


Logic is an axiomatic system by which principles are injected to obtain a conclusion based solely upon the principles which are called axioms. It is a linear line of thought which can be deductive or inductive in nature. like mathematics, it does not matter which order you start from. just that A=B or B=A are true and that the one side equally reflects the other.

I think you are artificially imposing this linearity, most logical calculi are at least branching trees in nature and some allow for limited graph-like behaviour. Of course, when humans study them they tend to order them absolutely (linearly) anyway but computer programs have been designed which can reason in parallel.

The limitations of the axiomatic system is that the conclusion of the linear problem only has the integrity of the axioms used. Axioms integrity=conclusion integrity. Naturally, axioms are considered proper when they are irrefutable facts; as irrefutable axiom = irrefutable conclusion.
Actually in most cases I would say that the integrity of a set of axioms is in whether or not they generate nonsensical conclusions. Axioms are not irrefutable facts, they are facts that we assume 'without proof' You can still reject them, we just see what happens when you don't.
Also, logic is not just about axioms, but also the proof rules that you use to combine them. All logical systems have both rules of inference and axioms (which are just rules with no antecedents).

Because axiomatic systems are linear they are therefore finite.
Linearity has nothing to do with finiteness, there are many examples of finite non-linear structures (partial orders, graphs, finite groups), and many examples of linear non-finite structures (ordinals 'omega' and above).

In order to achieve maximum integrity you need maximum information. If maximum information is all information then (All Information = maximum integrity) or (All Information=Truth)
What do you mean by maximum integrity? Integrity usually means not generating a contradictory conclusion, in which case you don't need any information. In fact in some cases the stronger your axioms and rules (equivalent to more information), the less integrity you have (G"del's incompleteness Theorem). Of course this is not always the case. If you mean some measure of correctness in the axioms (perhaps how accurately they model the system in question) then there might be some merit to what you are saying and this might be worth discussing further.

The mission has then become a pursuit to craft a loop within the axiomatic system that covers all reasonable ground and therefore offers a reasonable foundation for a reasonable conclusion. This is still an assumption! It is as reasonable as we can make it though.
I'm not entirely sure what you mean here. Computer science has demonstrated that self-interpreting systems are possible (otherwise self-hosting compilers would not be possible). Not only are these systems able to interpret themselves, but also every other sufficiently well defined system that we have ever built. I can write a program. And then write another program which can simulate the other program from its source code and check that it has the same conclusion. There is nothing magical about it and I can check the assumption that they are the same (by running the two programs and seeing them do the same things).

The result is 2+2=4 can be inferred to mean that you have four oranges. That A+B= it is reasonable to believe you have no other oranges. Therefore a loop is created between finite lines of logic. This is very good but ultimately it is still not maximum integrity. you still need all of the information it achieve maximum integrity and therefore have truth.
You are doing arithmetic here, not logic. Though a lot of the principles are the same. I think once I understand what you mean by maximum integrity then I might be able to see where you are trying to go with this.

So I disagree. It's only prefect in its own context.
That's basically what I said, logic is not beyond reproach, I can always challenge how useful it is to the problem is at hand.

We do not know that 1=1 because we do not fully understand the universe. We can only say that 1=1 is reasonable. At any point we may find information that invalidates the foundation. Perhaps 1=1 isn't the same one but distinct and therefore 1=1=false.
Now you are talking about semantics, is the 1 that we are referring to on the left the same as the 1 we are referring to on the right. They might not be. This comes down to the semantic interpretation or valuation function that we choose. If we allow the interpretation function to be non-deterministic (can output different values on the same input) then you are correct and 1 does not equal 1. However, this is just a language. You can always make any particular language wrong by changing what the terms mean. Perhaps you are making the mistake of assuming that logic is somehow relevant to how the universe actually works? It is not, it's only relevant to how we describe how the universe works in which case, you can tell me 1 is not equal to 1 all you want but until you can point to an example interpretation on the universe that makes it false (or at least doesn't make it true) I don't have to believe you.


I realize that sounds strange but here is something simple. 1=1 but if 1Apple=1Apple and an apples mass varies then 1=1 is false by the introduction of new language.
Indeed, it is a new language. That doesn't mean 1 != 1, just that your new language predicts that 1 != 1. My logic still says 1 = 1 and you can't change that. You have to instead convince me that using your logic would help me in some way so that I change my definitions to match yours and then we agree. There isn't a 1 true logic, it's just one way of looking at the world. I can invent a logic that predicts whatever theorems I like, just as I can write a program that outputs whatever I like. The tricky part is working out which one to use. This is still an ongoing process and it may never end.
Poetaster
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6/15/2013 10:11:53 PM
Posted: 3 years ago
At 6/15/2013 9:01:53 PM, the_croftmeister wrote:
At 6/15/2013 4:41:06 PM, Poetaster wrote:
I would agree with your critique, croftmeister, of those particular vulgar conceptions which float around. I myself am inclined to quarrel with the even more egregious misuse of the term "logic" to mean: "any line of thinking whatsoever".

General reasoning (usually a mixture of induction, evidential abduction, argument by example, personal anecdote, rhetoric, deduction, and the occasional fallacy, with no explicit transition between these) is obviously not the same as logic (that is, formal logic), but in common non-technical discourse people will often mix and match these tactics into a kind of "folk method" of argumentation, and then call it "logic".

I just find myself personally annoyed at this usage. Of course, general reasoning seems to be the preferred platform from which to debate most topics of public interest; I would just prefer that the transitions between different approaches be acknowledged as they are undertaken so that the type of argument being presented is properly recognized.

Agreed, I've often wondered whether a separate philosophically constructed language (like Lojban or something) would be useful to indicate the transition between reason and appeal (this is how I like to characterise the two persuasive techniques). I don't like Lojban much myself but its the closest to the objective I've seen. This would make for interesting discussions. Also, I've come to the conclusion that such a language would have to be taught later in life (high school at least) or it would lose the precision it once had through all the standard processes of language drift.

Its a pity that not more people are interested in this topic, but never mind, I guess most people don't care too much, their normal reasoning does the job for them.

Might I ask, then, whether you take issue with the classical categories of persuasion (i.e. ethos, pathos, and logos)? All of these persuasive methods are, of course, means of appeal, with logos being that which employs reason. Would you reject the designation of an "appeal to reason" as some kind of category error?

It's interesting that you should mention Lobjan (the logician's Esperanto), but I agree that its technical ambitions may be a bit presumptuous. Or, maybe I should ask: Why don't you like it?

Perhaps as a transcension of all this talk of verbal persuasion, have you ever seen a purely pictorial mathematical proof before? The exercise is essentially to prove a theorem using mute, wordless pictures. Here's one: http://upload.wikimedia.org... . It proves the pythagorean theorem graphically (it's annotated with some notation, but this isn't strictly necessary). This may call into question whether language is technically necessary for persuasion to occur, even if it is the most practical and efficient medium in which to do so. Imagine having a moral argument using only pictures!

More relevant to your thread's topic, I had the most frustrating experience of informally debating someone who kept asking, "What's your point?" after I had drawn a conclusion from my premises. For some reason this seemingly obtuse maneuver grew on me in its significance, and I later realized that it was a version of Lewis Carroll's famous paradox expounded in "What the Tortoise said to Achilles": http://en.wikipedia.org...

It basically points out that the act or process of a syllogistic inference is not encoded in the syllogism itself, but is externally supplied by the reasoner.

Anyway, this struck me as a certain "misconception" about logic that I noticed in an everyday conversation.
"The book you are looking for hasn't been written yet. What you are looking for you are going to have to find yourself, it's not going to be in a book..." -Sidewalker
the_croftmeister
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6/16/2013 8:08:28 AM
Posted: 3 years ago
At 6/15/2013 10:13:35 PM, xXCryptoXx wrote:
Logic has no facts and is based off nothing but emotion.

Care to back this up with some evidence?
the_croftmeister
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6/16/2013 8:36:02 AM
Posted: 3 years ago
At 6/15/2013 10:11:53 PM, Poetaster wrote:
Might I ask, then, whether you take issue with the classical categories of persuasion (i.e. ethos, pathos, and logos)? All of these persuasive methods are, of course, means of appeal, with logos being that which employs reason. Would you reject the designation of an "appeal to reason" as some kind of category error?
Take issue with them? In the sense that they are a useful categorisation of persuasive techniques no, I have no issue. I think perhaps I erred when I said persuasion. I rather meant that appeals are a means of persuasion and reason is something that persuades. To me, reason is employed purely to expose the consequences of statements. An appeal to reason is a persuasive technique but is not reason itself since the act of reasoning in no way presumes that reason should be believed.
For example, say I wanted you to believe in the Pythagorean theorem. I can use reason to provide a proof and then allow you to draw your own conclusion. Or I can point to the proof and say, I proved it therefore you should believe it. The former is reason, the latter is appeal. Persuasion is how you go about changing another person's view and in this sense an appeal to reason is part of it. Reason itself is just an action.

It's interesting that you should mention Lobjan (the logician's Esperanto), but I agree that its technical ambitions may be a bit presumptuous. Or, maybe I should ask: Why don't you like it?
I read a little about it and didn't find it aesthetically pleasing. I like pretty languages. I rather think we need a better logic before we start building a logical language like this (neither classical nor intuitionistic quite cut it for me). I also see Lojban as driven primarily by syntactical considerations (efficient and unambiguous parsing) rather than semantical ones. If you have read any of Japaridze's work, I hold a similar view that logic should be primarily driven by semantics. I don't want unambiguous grammar, I want unambiguous meaning.

Perhaps as a transcension of all this talk of verbal persuasion, have you ever seen a purely pictorial mathematical proof before? The exercise is essentially to prove a theorem using mute, wordless pictures. Here's one: http://upload.wikimedia.org... . It proves the pythagorean theorem graphically (it's annotated with some notation, but this isn't strictly necessary). This may call into question whether language is technically necessary for persuasion to occur, even if it is the most practical and efficient medium in which to do so. Imagine having a moral argument using only pictures!
I have seen a couple, though I would love to do a survey of the ones around, they are very cool. Though I wouldn't exactly call it a proof. Not really, but then I have quite a non-traditional view of what a proof is. It's a graphical demonstration of the concept certainly, and it makes it very accessible. But a proof has to have a derivation of some description. Also, I would say that this is language (again I have quite a broad conception) I definitely agree that alphabetic, linear language is not necessary for communication. Pictorial languages actually existed in history, I have a book on writing systems which includes a few examples (I'm not just talking about hieroglyphs but languages that communicated concepts in a single drawing). Now having a moral argument with such, that would be something.

More relevant to your thread's topic, I had the most frustrating experience of informally debating someone who kept asking, "What's your point?" after I had drawn a conclusion from my premises. For some reason this seemingly obtuse maneuver grew on me in its significance, and I later realized that it was a version of Lewis Carroll's famous paradox expounded in "What the Tortoise said to Achilles": http://en.wikipedia.org...
You'll have to explain this in more detail, I see some similarity but can't quite pose it in the same terms.

It basically points out that the act or process of a syllogistic inference is not encoded in the syllogism itself, but is externally supplied by the reasoner.

Anyway, this struck me as a certain "misconception" about logic that I noticed in an everyday conversation.
That is a good one, people often forget that we impose additional meaning on the mechanisms of logic beyond their simple manipulation of terms.

Glad to see this thread is generating some thoughts
wrichcirw
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6/16/2013 11:44:17 AM
Posted: 3 years ago
At 6/12/2013 6:31:55 PM, the_croftmeister wrote:
There are a couple of pet peeves of mine when it comes to logic and reason. More specifically about what it can and can't do, and what it does and does not attempt to do. So I was wondering if anybody else has some. Or if they disagree with mine and think I'm promoting misconceptions of my own.

1. Logic is about facts.
Logic is principally concerned with deduction and contradiction. What can be deduced from what? What contradicts what? Many logics have tautologies which have the semblance of fact or at least truth but the traditional approach is that these are true by virtue of having no useful meaning and therefore do not provide any insight. That a particular logical system proves a particular tautology is a fact, but this is achieved through reason about the axioms of the metalogic, not the logic itself.

The bolded belief stems from the soundness of the logic, whereas what you are discussing is the validity of the logic. Most people focus on soundness, although I agree that validity is quite important. Most people's logic is unsound because they are unable to properly link premises to conclusions, which is an issue with validity, a subset of soundness.

2. Logic is indisputable
This makes sense to some degree, if I have followed the rules of the logic that I am using then you can't tell me I'm wrong, but seeing has how nobody has come up with any good reasons to presume that any particular logic is the one true logic then this does not mean that my logic is beyond reproach. I can always challenge your logic on the grounds of its usefulness or its applicability to the problem at hand. Even in mathematics, one of the most precise and thus least ambiguous studies of man, there is still disagreement over the utility of different logics.

Again, this deals with soundness vs validity.

Logic is a tool, use it right and it strengthens your argument considerably since we have a reasonable understanding of the consequences of its use.
Thoughts anyone?

lol, it only strengthens an argument if the other side and the audience recognize valid and sound logic. From my experience on DDO this is simply not the case.
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
wrichcirw
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6/16/2013 11:58:01 AM
Posted: 3 years ago
I will also add here that the vast majority of debates here SHOULD deal with validity specifically. Overall soundness is not an issue, otherwise people would be able to question round #1 assumptions all the time. I've had people questioning round #1 assumptions in debates I've instigated where the opponent somehow won, which in my mind easily demonstrated how the opposition and the voting audience in those particular debates did not have a clue how to score a debate, or to respect operating assumptions for the debate.
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
AlbinoBunny
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6/16/2013 12:10:53 PM
Posted: 3 years ago
The fact that a lot of logic can't even be conceived as wrong in any imagined "world" makes it a very powerful tool. It can't be claimed to be absolute with complete certainty though, but what can?
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the_croftmeister
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6/16/2013 5:27:20 PM
Posted: 3 years ago
At 6/16/2013 11:44:17 AM, wrichcirw wrote:
At 6/12/2013 6:31:55 PM, the_croftmeister wrote:
There are a couple of pet peeves of mine when it comes to logic and reason. More specifically about what it can and can't do, and what it does and does not attempt to do. So I was wondering if anybody else has some. Or if they disagree with mine and think I'm promoting misconceptions of my own.

1. Logic is about facts.
Logic is principally concerned with deduction and contradiction. What can be deduced from what? What contradicts what? Many logics have tautologies which have the semblance of fact or at least truth but the traditional approach is that these are true by virtue of having no useful meaning and therefore do not provide any insight. That a particular logical system proves a particular tautology is a fact, but this is achieved through reason about the axioms of the metalogic, not the logic itself.

The bolded belief stems from the soundness of the logic, whereas what you are discussing is the validity of the logic. Most people focus on soundness, although I agree that validity is quite important. Most people's logic is unsound because they are unable to properly link premises to conclusions, which is an issue with validity, a subset of soundness.
My point is that soundness is not really a part of the operation of logic, it is only ever investigated with respect to some arbitrary semantic model. If we take the naive definition of soundness all we require additionally is that the premises are true. In order to justify the truth of the premises we have to use another argument, in which case we get one of two outcomes. Either we have new premises (which then also must be justified) or we have a tautology (which is a validity concern)
So soundness can never be proven with logic alone unless it is the same as validity (sometimes of a different logic). We always end up with another soundness criterion, or an arbitrary semantic model that we have to justify.
I agree that soundness is an interesting property, it just requires an appeal to something outside logic.

2. Logic is indisputable
This makes sense to some degree, if I have followed the rules of the logic that I am using then you can't tell me I'm wrong, but seeing has how nobody has come up with any good reasons to presume that any particular logic is the one true logic then this does not mean that my logic is beyond reproach. I can always challenge your logic on the grounds of its usefulness or its applicability to the problem at hand. Even in mathematics, one of the most precise and thus least ambiguous studies of man, there is still disagreement over the utility of different logics.

Again, this deals with soundness vs validity.
I'm not sure what you mean by that. Soundness has nothing to do with utility. Utility is about how useful the results are, not whether they are correct.

Logic is a tool, use it right and it strengthens your argument considerably since we have a reasonable understanding of the consequences of its use.
Thoughts anyone?

lol, it only strengthens an argument if the other side and the audience recognize valid and sound logic. From my experience on DDO this is simply not the case.
Fair call, I was assuming that in the case where they don't we can't really do much about it and so shouldn't let it bother us too much.

As an aside, I would say that in most cases the strength of an argument is (as we have been discussing) a validity concern, and thus not relative to who is observing the argument. As I commented to Poetaster above, the persuasion may not be strengthened (observer does not understand or rejects logic for any number of reasons or no reason at all), but arguments by and large stand on their own.
the_croftmeister
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6/16/2013 5:32:18 PM
Posted: 3 years ago
At 6/16/2013 12:10:53 PM, AlbinoBunny wrote:
The fact that a lot of logic can't even be conceived as wrong in any imagined "world" makes it a very powerful tool. It can't be claimed to be absolute with complete certainty though, but what can?

This is a pretty common conception of logic (though it only technically applies to logics with a modal semantics, not that we can't adopt a modal semantics for any logic we choose). But I'd say that not being able to imagine a world in which logic is wrong is a lack of imagination, not any particular feature of logic itself. You would have to put criteria on what these imagined worlds look like, which to support your conclusion would eventually wind up amounting to 'be logical'. And 'logic is right in all logical worlds', is somewhat of a tautological statement.
the_croftmeister
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6/16/2013 5:34:39 PM
Posted: 3 years ago
At 6/16/2013 11:58:01 AM, wrichcirw wrote:
I will also add here that the vast majority of debates here SHOULD deal with validity specifically. Overall soundness is not an issue, otherwise people would be able to question round #1 assumptions all the time. I've had people questioning round #1 assumptions in debates I've instigated where the opponent somehow won, which in my mind easily demonstrated how the opposition and the voting audience in those particular debates did not have a clue how to score a debate, or to respect operating assumptions for the debate.

Agreed, and not just for debates. You have to accept premises at some point, in which case you are arguing only validity no matter how much you want to deal with soundness.
wrichcirw
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6/16/2013 7:34:35 PM
Posted: 3 years ago
At 6/16/2013 5:27:20 PM, the_croftmeister wrote:
At 6/16/2013 11:44:17 AM, wrichcirw wrote:
At 6/12/2013 6:31:55 PM, the_croftmeister wrote:
There are a couple of pet peeves of mine when it comes to logic and reason. More specifically about what it can and can't do, and what it does and does not attempt to do. So I was wondering if anybody else has some. Or if they disagree with mine and think I'm promoting misconceptions of my own.

1. Logic is about facts.
Logic is principally concerned with deduction and contradiction. What can be deduced from what? What contradicts what? Many logics have tautologies which have the semblance of fact or at least truth but the traditional approach is that these are true by virtue of having no useful meaning and therefore do not provide any insight. That a particular logical system proves a particular tautology is a fact, but this is achieved through reason about the axioms of the metalogic, not the logic itself.

The bolded belief stems from the soundness of the logic, whereas what you are discussing is the validity of the logic. Most people focus on soundness, although I agree that validity is quite important. Most people's logic is unsound because they are unable to properly link premises to conclusions, which is an issue with validity, a subset of soundness.
My point is that soundness is not really a part of the operation of logic, it is only ever investigated with respect to some arbitrary semantic model. If we take the naive definition of soundness all we require additionally is that the premises are true. In order to justify the truth of the premises we have to use another argument, in which case we get one of two outcomes. Either we have new premises (which then also must be justified) or we have a tautology (which is a validity concern)
So soundness can never be proven with logic alone unless it is the same as validity (sometimes of a different logic). We always end up with another soundness criterion, or an arbitrary semantic model that we have to justify.
I agree that soundness is an interesting property, it just requires an appeal to something outside logic.

Well, soundness can be debated. A debate ostensibly should only be dealing with the validity of an assertion, given certain assumptions. Another debate can then revolve around the assumptions themselves, until like you say you reach a tautology. But then, even tautologies have givens, right? Given A, A=A.

At this point, you'd have to question if there's a better method. The only problem is that any and all methods we deem reasonable are also logical.

2. Logic is indisputable
This makes sense to some degree, if I have followed the rules of the logic that I am using then you can't tell me I'm wrong, but seeing has how nobody has come up with any good reasons to presume that any particular logic is the one true logic then this does not mean that my logic is beyond reproach. I can always challenge your logic on the grounds of its usefulness or its applicability to the problem at hand. Even in mathematics, one of the most precise and thus least ambiguous studies of man, there is still disagreement over the utility of different logics.

Again, this deals with soundness vs validity.
I'm not sure what you mean by that. Soundness has nothing to do with utility. Utility is about how useful the results are, not whether they are correct.

Basically, when people challenge the usefulness or applicability of a certain conclusion, that's something that screams "valid", but not "sound" - if it was invalid, people would just say "that's wrong". For example, you can say that "given that eating chocolate causes cancer, cancer is undesirable, and people should not do anything undesirable, people should then stop eating chocolate". That's certainly valid, but a lot of people would question the usefulness or applicability of such a conclusion.

I have a lot of difficulty thinking of something that is logically sound and yet somehow questionable in applicability to real life.

Logic is a tool, use it right and it strengthens your argument considerably since we have a reasonable understanding of the consequences of its use.
Thoughts anyone?

lol, it only strengthens an argument if the other side and the audience recognize valid and sound logic. From my experience on DDO this is simply not the case.
Fair call, I was assuming that in the case where they don't we can't really do much about it and so shouldn't let it bother us too much.

It bothers me because a lot of debating revolves around addressing fallacious arguments. All of these fallacies stem directly from applying formal logic to language. If we are to assume that debating does not involve logic, then we pretty much dismiss debating as have anything to do with reasonable discussion.

As an aside, I would say that in most cases the strength of an argument is (as we have been discussing) a validity concern, and thus not relative to who is observing the argument. As I commented to Poetaster above, the persuasion may not be strengthened (observer does not understand or rejects logic for any number of reasons or no reason at all), but arguments by and large stand on their own.
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
wrichcirw
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6/16/2013 7:40:00 PM
Posted: 3 years ago
Oh, a sound argument would run something like "given that there are people who like eating chocolate, that chocolate in moderate quantities does not pose a health risk, and people should do what they like, then people who like chocolate should not feel guilty about eating moderate quantities of it."

That's logically sound from what I can tell, and easily applicable to real life.
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
xXCryptoXx
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6/16/2013 8:26:27 PM
Posted: 3 years ago
At 6/16/2013 8:08:28 AM, the_croftmeister wrote:
At 6/15/2013 10:13:35 PM, xXCryptoXx wrote:
Logic has no facts and is based off nothing but emotion.

Care to back this up with some evidence?

Logic has no evidence. I am using my feelings to know what I say is true. In the same way, we know God exists.
Nolite Timere
wrichcirw
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6/16/2013 8:41:58 PM
Posted: 3 years ago
At 6/16/2013 8:26:27 PM, xXCryptoXx wrote:
At 6/16/2013 8:08:28 AM, the_croftmeister wrote:
At 6/15/2013 10:13:35 PM, xXCryptoXx wrote:
Logic has no facts and is based off nothing but emotion.

Care to back this up with some evidence?

Logic has no evidence. I am using my feelings to know what I say is true. In the same way, we know God exists.

What if someone felt that God does not exist? Would that person be right because they were using their feelings to know what they said is true?
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
xXCryptoXx
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6/16/2013 8:46:52 PM
Posted: 3 years ago
At 6/16/2013 8:41:58 PM, wrichcirw wrote:
At 6/16/2013 8:26:27 PM, xXCryptoXx wrote:
At 6/16/2013 8:08:28 AM, the_croftmeister wrote:
At 6/15/2013 10:13:35 PM, xXCryptoXx wrote:
Logic has no facts and is based off nothing but emotion.

Care to back this up with some evidence?

Logic has no evidence. I am using my feelings to know what I say is true. In the same way, we know God exists.

What if someone felt that God does not exist? Would that person be right because they were using their feelings to know what they said is true?

If someone feels that God doesn't exist then their feeling are wrong therefore they aren't using logic. But my feelings are right because I feel they are right.
Nolite Timere
the_croftmeister
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6/16/2013 9:53:39 PM
Posted: 3 years ago
At 6/16/2013 8:46:52 PM, xXCryptoXx wrote:
At 6/16/2013 8:41:58 PM, wrichcirw wrote:
At 6/16/2013 8:26:27 PM, xXCryptoXx wrote:
At 6/16/2013 8:08:28 AM, the_croftmeister wrote:
At 6/15/2013 10:13:35 PM, xXCryptoXx wrote:
Logic has no facts and is based off nothing but emotion.

Care to back this up with some evidence?

Logic has no evidence. I am using my feelings to know what I say is true. In the same way, we know God exists.

What if someone felt that God does not exist? Would that person be right because they were using their feelings to know what they said is true?

If someone feels that God doesn't exist then their feeling are wrong therefore they aren't using logic. But my feelings are right because I feel they are right.

True, their feelings might be wrong, but they aren't likely to change their opinions based on your feelings. If you just like telling people they are wrong then fair enough. Not sure what God would have to say about that though.
xXCryptoXx
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6/16/2013 9:57:32 PM
Posted: 3 years ago
At 6/16/2013 9:53:39 PM, the_croftmeister wrote:
At 6/16/2013 8:46:52 PM, xXCryptoXx wrote:
At 6/16/2013 8:41:58 PM, wrichcirw wrote:
At 6/16/2013 8:26:27 PM, xXCryptoXx wrote:
At 6/16/2013 8:08:28 AM, the_croftmeister wrote:
At 6/15/2013 10:13:35 PM, xXCryptoXx wrote:
Logic has no facts and is based off nothing but emotion.

Care to back this up with some evidence?

Logic has no evidence. I am using my feelings to know what I say is true. In the same way, we know God exists.

What if someone felt that God does not exist? Would that person be right because they were using their feelings to know what they said is true?

If someone feels that God doesn't exist then their feeling are wrong therefore they aren't using logic. But my feelings are right because I feel they are right.

True, their feelings might be wrong, but they aren't likely to change their opinions based on your feelings. If you just like telling people they are wrong then fair enough. Not sure what God would have to say about that though.

Then they aren't using their logic. I am right because I feel that I am right. Logic is based on feelings. Logically I know I am right, therefore I am right.
1. I feel that God exists.
2. Logic is based on feelings.
3. Therefore Logically, God exists.
Nolite Timere
the_croftmeister
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6/16/2013 10:21:52 PM
Posted: 3 years ago
At 6/16/2013 7:40:00 PM, wrichcirw wrote:
Oh, a sound argument would run something like "given that there are people who like eating chocolate, that chocolate in moderate quantities does not pose a health risk, and people should do what they like, then people who like chocolate should not feel guilty about eating moderate quantities of it."

That's logically sound from what I can tell, and easily applicable to real life.

It's only sound because it has no premises (and therefore equivalent to validity). If I was to state the tautology prefixation for example (A->B)->(C->A)->(C->B), then I am stating a tautology which is valid with no premises. However, if I were talk about the semantic rule A->B |= (C->A)->(C->B) then I am asserting that semantically, every model of my logic in which A->B is true would also have (C->A)->(C->B) is true. This is soundness. I still have to limit the models that I am considering in order for this claim to make sense.

Soundness often appears when we move all our assumptions into the argument with 'given that' statements. This isn't really the point. It all comes down to where you draw the line between your logic and your meta-logic and your logic and it's semantics.

If you had instead dealt with the argument
1. There are people who like eating chocolate.
2. Chocolate in moderate quantities does not pose a health risk
3. People should do what they like.
Therefore:
People who like chocolate should not feel guilty about eating moderate quantities of it.

You do not strictly need premise 1 since it is contained in the conclusion. If we go along with this argument being valid, then I would say you still have to demonstrate the truth of those premises in order to demonstrate its soundness.
Yes in the debate format we often ignore the demonstration of the assumptions in round #1 only requiring demonstration of subsequent assumptions, that doesn't mean we have demonstrated soundness. In fact as I mentioned above, the only time you can ever demonstrate soundness is by making it equivalent to validity (finding a tautology).

You ask about tautologies having givens with the example Given A, A=A. This is not the same thing. You are using A as a parameter, not a statement. Thus the correct formalisation of this statement would be 'for all A, A=A'. This is a tautology in all serious attempts at the formalisation of equality that I have seen. However this is not (A->(A=A)) since this requires that in the case that A is true, A=A. In the former conception A is not really an assumption since we do not use the fact that it is true in order to obtain A=A. If the latter is actually what you meant then we start getting into second order concerns which are significantly more complicated. Not to say that I am not willing to discuss them, I just don't think it was what you were after.

It bothers me because a lot of debating revolves around addressing fallacious arguments. All of these fallacies stem directly from applying formal logic to language. If we are to assume that debating does not involve logic, then we pretty much dismiss debating as have anything to do with reasonable discussion.
I do dismiss debating as having much to do with reasonable discussion. I find other expository methods like socratic dialogues and panel discussions to much more useful in obtaining results to disputes. See my opinion question "Does the debate format really contribute to the development of strong arguments and rational discourse?"
Of course I wouldn't go as far as to say it has nothing to do with rational discourse, just that rational discourse is not about debating, and certainly not about 'winning' or 'persuading'.
the_croftmeister
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6/16/2013 10:23:43 PM
Posted: 3 years ago
At 6/16/2013 9:57:32 PM, xXCryptoXx wrote:
At 6/16/2013 9:53:39 PM, the_croftmeister wrote:
At 6/16/2013 8:46:52 PM, xXCryptoXx wrote:
At 6/16/2013 8:41:58 PM, wrichcirw wrote:
At 6/16/2013 8:26:27 PM, xXCryptoXx wrote:
At 6/16/2013 8:08:28 AM, the_croftmeister wrote:
At 6/15/2013 10:13:35 PM, xXCryptoXx wrote:
Logic has no facts and is based off nothing but emotion.

Care to back this up with some evidence?

Logic has no evidence. I am using my feelings to know what I say is true. In the same way, we know God exists.

What if someone felt that God does not exist? Would that person be right because they were using their feelings to know what they said is true?

If someone feels that God doesn't exist then their feeling are wrong therefore they aren't using logic. But my feelings are right because I feel they are right.

True, their feelings might be wrong, but they aren't likely to change their opinions based on your feelings. If you just like telling people they are wrong then fair enough. Not sure what God would have to say about that though.

Then they aren't using their logic. I am right because I feel that I am right. Logic is based on feelings. Logically I know I am right, therefore I am right.
1. I feel that God exists.
2. Logic is based on feelings.
3. Therefore Logically, God exists.

1. I feel that God does not exist
2. Logic is based on feelings
3. Therefore logically, God does not exist

Unless you are saying either that I am lying or that every person feels the same about everything
the_croftmeister
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6/16/2013 10:25:59 PM
Posted: 3 years ago
Or even better,

1. I feel that your feelings are wrong
2. Logic is based on feelings
C. Therefore your feelings are wrong.
wrichcirw
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6/16/2013 10:27:53 PM
Posted: 3 years ago
At 6/16/2013 9:57:32 PM, xXCryptoXx wrote:
At 6/16/2013 9:53:39 PM, the_croftmeister wrote:
At 6/16/2013 8:46:52 PM, xXCryptoXx wrote:
At 6/16/2013 8:41:58 PM, wrichcirw wrote:
At 6/16/2013 8:26:27 PM, xXCryptoXx wrote:
At 6/16/2013 8:08:28 AM, the_croftmeister wrote:
At 6/15/2013 10:13:35 PM, xXCryptoXx wrote:
Logic has no facts and is based off nothing but emotion.

Care to back this up with some evidence?

Logic has no evidence. I am using my feelings to know what I say is true. In the same way, we know God exists.

What if someone felt that God does not exist? Would that person be right because they were using their feelings to know what they said is true?

If someone feels that God doesn't exist then their feeling are wrong therefore they aren't using logic. But my feelings are right because I feel they are right.

True, their feelings might be wrong, but they aren't likely to change their opinions based on your feelings. If you just like telling people they are wrong then fair enough. Not sure what God would have to say about that though.

Then they aren't using their logic. I am right because I feel that I am right. Logic is based on feelings. Logically I know I am right, therefore I am right.
1. I feel that God exists.
2. Logic is based on feelings.
3. Therefore Logically, God exists.

lol, this is a perfect example of a valid argument that is completely and utterly unsound. =)
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?
Poetaster
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6/16/2013 10:50:12 PM
Posted: 3 years ago
At 6/16/2013 8:36:02 AM, the_croftmeister wrote:
At 6/15/2013 10:11:53 PM, Poetaster wrote:
Might I ask, then, whether you take issue with the classical categories of persuasion (i.e. ethos, pathos, and logos)? All of these persuasive methods are, of course, means of appeal, with logos being that which employs reason. Would you reject the designation of an "appeal to reason" as some kind of category error?

Take issue with them? In the sense that they are a useful categorisation of persuasive techniques no, I have no issue. I think perhaps I erred when I said persuasion. I rather meant that appeals are a means of persuasion and reason is something that persuades. To me, reason is employed purely to expose the consequences of statements. An appeal to reason is a persuasive technique but is not reason itself since the act of reasoning in no way presumes that reason should be believed.

Yes, I would say very much the same thing. Methodologies and systems of reasoning are procedurally inaugurated by an implicit set of values external to them. Reason is persuasive insofar as the parties of discourse value it as such.

For example, say I wanted you to believe in the Pythagorean theorem. I can use reason to provide a proof and then allow you to draw your own conclusion. Or I can point to the proof and say, I proved it therefore you should believe it. The former is reason, the latter is appeal. Persuasion is how you go about changing another person's view and in this sense an appeal to reason is part of it. Reason itself is just an action.

Agreed. I'd also point out that you are perhaps grazing the perimeter of Carroll's paradox with this explanation. (More below).

It's interesting that you should mention Lobjan (the logician's Esperanto), but I agree that its technical ambitions may be a bit presumptuous. Or, maybe I should ask: Why don't you like it?
I read a little about it and didn't find it aesthetically pleasing. I like pretty languages. I rather think we need a better logic before we start building a logical language like this (neither classical nor intuitionistic quite cut it for me). I also see Lojban as driven primarily by syntactical considerations (efficient and unambiguous parsing) rather than semantical ones. If you have read any of Japaridze's work, I hold a similar view that logic should be primarily driven by semantics. I don't want unambiguous grammar, I want unambiguous meaning.

Got it.


Perhaps as a transcension of all this talk of verbal persuasion, have you ever seen a purely pictorial mathematical proof before? The exercise is essentially to prove a theorem using mute, wordless pictures. Here's one: http://upload.wikimedia.org... . It proves the pythagorean theorem graphically (it's annotated with some notation, but this isn't strictly necessary). This may call into question whether language is technically necessary for persuasion to occur, even if it is the most practical and efficient medium in which to do so. Imagine having a moral argument using only pictures!

I have seen a couple, though I would love to do a survey of the ones around, they are very cool. Though I wouldn't exactly call it a proof. Not really, but then I have quite a non-traditional view of what a proof is. It's a graphical demonstration of the concept certainly, and it makes it very accessible. But a proof has to have a derivation of some description. Also, I would say that this is language (again I have quite a broad conception) I definitely agree that alphabetic, linear language is not necessary for communication. Pictorial languages actually existed in history, I have a book on writing systems which includes a few examples (I'm not just talking about hieroglyphs but languages that communicated concepts in a single drawing). Now having a moral argument with such, that would be something.

If there is an analogical relation between the geometrical parts which comprise a purely pictorial proof of a theorem, and the logical symbols which may express and derive the same theorem through axiomatized deduction procedures, may I ask what discrepancy of legitimacy could exist between these two means of demonstration?

Do mind me also asking how you would describe your concept of a proof?


More relevant to your thread's topic, I had the most frustrating experience of informally debating someone who kept asking, "What's your point?" after I had drawn a conclusion from my premises. For some reason this seemingly obtuse maneuver grew on me in its significance, and I later realized that it was a version of Lewis Carroll's famous paradox expounded in "What the Tortoise said to Achilles": http://en.wikipedia.org...
You'll have to explain this in more detail, I see some similarity but can't quite pose it in the same terms.

Ok, so this conversational version of the paradox is much less formal than the problem as posed by the Tortoise to Achilles. Carroll's paradox, in that original form, considers some deductive argument:

A
B
Therefore, X.

It then notices that an implicit hypothetical C: "If A and B, then X" lurks beneath this argument. In some ways, this statement C appears to be necessary to complete the deduction if we are to spell out all of its machinery. But we can always formulate some hypothetical of the same form as C for any given set of premises in a deductive argument, creating a problem of infinite regress.

I suppose the version of this which I encountered in conversation amounted to a suggestion that my argument for a conclusion was somehow ineffective in deriving that conclusion because I had not said something like, "if my argument is good, then you should be compelled to accept the conclusion", which is comparable to the "invisible hypothetical" which supposedly problematizes deductive arguments in Carroll's paradox above. So my realization was that such a response (i.e. the "What's your point?" reply) obliquely exploits a discursive analog to Carroll's paradox.


It basically points out that the act or process of a syllogistic inference is not encoded in the syllogism itself, but is externally supplied by the reasoner.

Anyway, this struck me as a certain "misconception" about logic that I noticed in an everyday conversation.
That is a good one, people often forget that we impose additional meaning on the mechanisms of logic beyond their simple manipulation of terms.

Glad to see this thread is generating some thoughts.

Ah! I've remembered another misconception. I saw this one committed by a very intelligent person in conversation:

"If your argument contains a logical error, then your conclusion is false."

This, of course, is itself an error.
"The book you are looking for hasn't been written yet. What you are looking for you are going to have to find yourself, it's not going to be in a book..." -Sidewalker
the_croftmeister
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6/16/2013 11:18:22 PM
Posted: 3 years ago
At 6/16/2013 10:50:12 PM, Poetaster wrote:
Yes, I would say very much the same thing. Methodologies and systems of reasoning are procedurally inaugurated by an implicit set of values external to them. Reason is persuasive insofar as the parties of discourse value it as such.

Agreed. I'd also point out that you are perhaps grazing the perimeter of Carroll's paradox with this explanation. (More below).
Of course, I was thinking of the wrong Achilles and Tortoise story. Yes, I do understand, this is why I don't see logic as ever being persuasive. Also, why I find it so frustrating when people talk in these forums with reason and then get exasperated when other people don't change their opinions. The best you can do is ask why they don't believe. If they don't put stock in reason then there is no point in jumping up and down about it, that just makes you look petty. (I have been guilty of this, I know, I just try really hard to avoid it, I do understand why it is so annoying).

If there is an analogical relation between the geometrical parts which comprise a purely pictorial proof of a theorem, and the logical symbols which may express and derive the same theorem through axiomatized deduction procedures, may I ask what discrepancy of legitimacy could exist between these two means of demonstration?
Given your first statement there is no discrepancy. However, what I doubt is whether all common examples of 'graphical proofs' have this kind of analogical relationship. The ability to extract geometric intuitions from diagrams is a very powerful tool of the human brain and in many cases I would think that too much of the work is done here. The second reason is that geometric proofs like this often bear too much similarity to the phenomena that they are trying to prove to be useful in their understanding, i.e. once you understand the proof you start seeing proofs everywhere. The second is not a rejection of its proof nature, just its utility.

Do mind me also asking how you would describe your concept of a proof?
I don't mind you asking, it just might take a bit to get through it all. I'd first ask if you are familiar with the lambda calculus, the Church-Turing thesis and the Curry-Howard Correspondence? That will give me a good idea where to start.

Ah! I've remembered another misconception. I saw this one committed by a very intelligent person in conversation:

"If your argument contains a logical error, then your conclusion is false."

This, of course, is itself an error.
Ahaha, I think we've all been guilty of this one at some point or another, good call.

On a side note, have you taken a look at my response in the thread on consciousness? I notice you have a stated interest in the hard problem, and I'd be very interested in your thoughts.
wrichcirw
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6/16/2013 11:20:34 PM
Posted: 3 years ago
At 6/16/2013 10:21:52 PM, the_croftmeister wrote:
At 6/16/2013 7:40:00 PM, wrichcirw wrote:
Oh, a sound argument would run something like "given that there are people who like eating chocolate, that chocolate in moderate quantities does not pose a health risk, and people should do what they like, then people who like chocolate should not feel guilty about eating moderate quantities of it."

That's logically sound from what I can tell, and easily applicable to real life.

1) It's only sound because it has no premises (and therefore equivalent to validity). 2) If I was to state the tautology prefixation for example (A->B)->(C->A)->(C->B), then I am stating a tautology which is valid with no premises. 3) However, if I were talk about the semantic rule A->B |= (C->A)->(C->B) then I am asserting that semantically, every model of my logic in which A->B is true would also have (C->A)->(C->B) is true. This is soundness. I still have to limit the models that I am considering in order for this claim to make sense.

1) Wait, what? The premises are the givens:
a) there are people who like chocolate
b) chocolate in moderate quantities does not pose a health risk, and
c) people should do what they like

Is there anything wrong with the premises? Largely no, so I would say that largely, this argument is sound.

It's not possible to get a wholly sound argument in English, but stuff like this comes close.

2) Untrue. The givens are A, B, and C, as well as the symbolism of formal logic.

3) Not familiar with |= notation.

Soundness often appears when we move all our assumptions into the argument with 'given that' statements. This isn't really the point. It all comes down to where you draw the line between your logic and your meta-logic and your logic and it's semantics.

If you had instead dealt with the argument
1. There are people who like eating chocolate.
2. Chocolate in moderate quantities does not pose a health risk
3. People should do what they like.
Therefore:
People who like chocolate should not feel guilty about eating moderate quantities of it.

A) You do not strictly need premise 1 since it is contained in the conclusion. B) If we go along with this argument being valid, then I would say you still have to demonstrate the truth of those premises in order to demonstrate its soundness.
Yes in the debate format we often ignore the demonstration of the assumptions in round #1 only requiring demonstration of subsequent assumptions, that doesn't mean we have demonstrated soundness. C) In fact as I mentioned above, the only time you can ever demonstrate soundness is by making it equivalent to validity (finding a tautology).

A) I disagree. You need this premise because without it, there's no reason to think there are people who like chocolate. Without this premise, if there are no people who like chocolate, then the conclusion is false.
B) I agree. However, I think they are relatively easy to prove.
C) Even tautologies have givens.

You ask about tautologies having givens with the example Given A, A=A. This is not the same thing. You are using A as a parameter, not a statement. 1) Thus the correct formalisation of this statement would be 'for all A, A=A'. This is a tautology in all serious attempts at the formalisation of equality that I have seen. However this is not (A->(A=A)) since this requires that in the case that A is true, A=A. In the former conception A is not really an assumption since we do not use the fact that it is true in order to obtain A=A. If the latter is actually what you meant then we start getting into second order concerns which are significantly more complicated. Not to say that I am not willing to discuss them, I just don't think it was what you were after.

1) "For all A" still requires "A" as a given. It requires something to exist in the first place. I could be mistaken here, it's been a while since I took formal logic.

It bothers me because a lot of debating revolves around addressing fallacious arguments. All of these fallacies stem directly from applying formal logic to language. If we are to assume that debating does not involve logic, then we pretty much dismiss debating as have anything to do with reasonable discussion.
I do dismiss debating as having much to do with reasonable discussion. I find other expository methods like socratic dialogues and panel discussions to much more useful in obtaining results to disputes. See my opinion question "Does the debate format really contribute to the development of strong arguments and rational discourse?"

I read your opinion piece and disagree. I agree with all of the issues you cite, but the debate isn't necessarily about convincing the opposing side, but rather to have at the end of a debate a resulting synthesis that may be more useful than what was present before the debate. It also forces both sides to use what they consider to be the best arguments for their case, which has an effect of putting their positions in a crucible, thus "burning" away imperfections in a lengthy and untested assertion.

Of course I wouldn't go as far as to say it has nothing to do with rational discourse, just that rational discourse is not about debating, and certainly not about 'winning' or 'persuading'.

Well, of course I agree here, but this isn't really what I stated, which is that debating is about rational discourse, or that rational discourse is inherent in debating.
At 8/9/2013 9:41:24 AM, wrichcirw wrote:
If you are civil with me, I will be civil to you. If you decide to bring unreasonable animosity to bear in a reasonable discussion, then what would you expect other than to get flustered?