[Why is it that when I click 'save' it destroys my post? Grrrrr.] Quick version: @gotlucky Our disagreement sounds like symantics. While logic isn't a "purpose" in itself, it does have a purpose, and that purpose is to produce accurate conclusions if the premises are accurate and complete. Since we can not know if the premises are accurate and complete, we can not trust logic to produce an accurate conclusion. This is precisely why we perform experiments.
Seraiah: While logic isn't a "purpose" in itself, it does have a purpose, and that purpose is to produce accurate conclusions if the premises are accurate and complete.
While logic isn't a "purpose" in itself, it does have a purpose, and that purpose is to produce accurate conclusions if the premises are accurate and complete.
The definition of logic, first from wikipedia:
Logic (from the Greek λογική logikē) is the study of valid reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science. It examines general forms that arguments may take, which forms are valid, and which are fallacies. In philosophy, the study of logic is applied in most major areas: metaphysics, law, ontology,epistemology, and ethics. In mathematics, it is the study of valid inferences within some formal language. Logic is also studied inargumentation theory. Logic was studied in several ancient civilizations, including India, China, and Greece. In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric. Logic is often divided into three parts, inductive reasoning, abductive reasoning, and deductive reasoning.
Logic (from the Greek λογική logikē) is the study of valid reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science. It examines general forms that arguments may take, which forms are valid, and which are fallacies. In philosophy, the study of logic is applied in most major areas: metaphysics, law, ontology,epistemology, and ethics. In mathematics, it is the study of valid inferences within some formal language. Logic is also studied inargumentation theory.
Logic was studied in several ancient civilizations, including India, China, and Greece. In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric.
Logic is often divided into three parts, inductive reasoning, abductive reasoning, and deductive reasoning.
The definition of logic, from wiktionary:
Noun Wikipedia has an article on: Logic logic (countable and uncountable; plural logics) (uncountable) A method of human thought that involves thinking in a linear, step-by-step manner about how a problem can be solved. Logic is the basis of many principles including the scientific method. (philosophy, logic) The study of the principles and criteria of valid inference and demonstration. [quotations ▼] (uncountable) (mathematics) The mathematical study of relationships between rigorously defined concepts and of proof of statements. (countable) (mathematics) A formal or informal language together with a deductive system or a model-theoretic semantics. (uncountable) Any system of thought, whether rigorous and productive or not, especially one associated with a particular person. It's hard to work out his system of logic. (uncountable) The part of an electronic system that performs the boolean logic operations, short for logic gates or logic circuit. Fred is designing the logic for the new controller.
Noun
logic (countable and uncountable; plural logics)
What you will notice is that logic is not a purpose, it is a tool. Logic is either the study of reasoning or it is method, a tool.
Seraiah: Since we can not know if the premises are accurate and complete, we can not trust logic to produce an accurate conclusion.
Since we can not know if the premises are accurate and complete, we can not trust logic to produce an accurate conclusion.
I hope you get around to reading that essay I linked for you, as it really is very interesting. Two great sections from Asimov's essay:
My answer to him was, "John, when people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together." The basic trouble, you see, is that people think that "right" and "wrong" are absolute; that everything that isn't perfectly and completely right is totally and equally wrong. However, I don't think that's so. It seems to me that right and wrong are fuzzy concepts, and I will devote this essay to an explanation of why I think so.
My answer to him was, "John, when people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together."
The basic trouble, you see, is that people think that "right" and "wrong" are absolute; that everything that isn't perfectly and completely right is totally and equally wrong.
However, I don't think that's so. It seems to me that right and wrong are fuzzy concepts, and I will devote this essay to an explanation of why I think so.
Naturally, the theories we now have might be considered wrong in the simplistic sense of my English Lit correspondent, but in a much truer and subtler sense, they need only be considered incomplete.
@ Luminar
You still haven't adequately addressed the issues I pointed out in my last post. Attempting to undermind logic is a very big task, requiring extensive thought on epistemology, which I am fairly certain you haven't studied enough. The argument you presented in your last post still didn't explain why Occam's Razor is essential to logic, or rather it wasn't a valid explanation.
Seraiah:A is B C is B Therefore A is C This is only true because it has always been true in testable, repeatable, observations.
faber est suae quisque fortunae
You both are wrong. That is an invalid argument:
Men are humans.
Women are humans.
Therefore, men are women.
It is an invalid argument.
"U trollin bro? I'm obviously not referring to the concepts or definitions."
No I am being flippant.
'Men do not change, they unmask themselves' - Germaine de Stael
@Torsten I'm going to quote myself again: gotlucky: A false inference is a false conclusion, which can only result from a set of premises that has at least one false premise or is an incomplete set of premises, or the argument is invalid. Now let's look at what you said: Torsten: No, one can make false conclusions, while all stated premises are correct. People are just more difficult to convince that something is wrong, when they check the premises and find them to be correct. Take ad hominem fallacies for instance. Person A is stupid, Person A makes statement B, Hence statement B is false. Premis A and B maybe correct after testing. It doesn't however follow that said statement is false by the virtue of those fallacies. This falls under the part of my quote where I said "or the argument is invalid". Even if Person A is stupid and makes B statement, ad hominem is a logically fallacy. In other words, it is a non sequitur. The conclusion does not follow from the premises. Logical fallacy = invalid argument
@Torsten
I'm going to quote myself again:
gotlucky: A false inference is a false conclusion, which can only result from a set of premises that has at least one false premise or is an incomplete set of premises, or the argument is invalid.
A false inference is a false conclusion, which can only result from a set of premises that has at least one false premise or is an incomplete set of premises, or the argument is invalid.
Now let's look at what you said:
Torsten: No, one can make false conclusions, while all stated premises are correct. People are just more difficult to convince that something is wrong, when they check the premises and find them to be correct. Take ad hominem fallacies for instance. Person A is stupid, Person A makes statement B, Hence statement B is false. Premis A and B maybe correct after testing. It doesn't however follow that said statement is false by the virtue of those fallacies.
No, one can make false conclusions, while all stated premises are correct. People are just more difficult to convince that something is wrong, when they check the premises and find them to be correct. Take ad hominem fallacies for instance.
Person A is stupid, Person A makes statement B, Hence statement B is false.
Premis A and B maybe correct after testing. It doesn't however follow that said statement is false by the virtue of those fallacies.
This falls under the part of my quote where I said "or the argument is invalid". Even if Person A is stupid and makes B statement, ad hominem is a logically fallacy. In other words, it is a non sequitur. The conclusion does not follow from the premises.
Logical fallacy = invalid argument
QFT
This (below).
I can't believe the astonishing stupidity of some of the posters here. I mean
"A is C
B is C
Therefore A is B"
sounds like a valid argument to some of you dimwits? Jesus Christ.
sounds like a valid argument to some of you dimwits?
See my post, Seraiah. What you have is an invalid argument.
If it makes you feel better it's hereby ammended with what I obviously meant: if A = B And C = B Then A=C You leave out a damn comma around here and suddenly everyone becomes irrational hyperventilating monkeys.
JackCuyler: Actually, you have that exactly backwards. It's been true in testable, repeatable, observations because it's true.
It is still invalid. As I said before:
If Men are Humans.
And
If Women are Humans.
Then
Men are Women.
men =/= humans woman =/= humans men =/= woman men is not synonomous with humans.
Seriah, what I posted is the exact same, false argument you posted earlier. Look at it carefully.
Oh and the fuck am I supposed to know what you "meant" when you put forth a logically invalid argument?
Friedmanite,
Actually, upon rereading Seraiah's latest argument, it appears that he has actually switched his argument. Before he stated:
A is B
C is B
Therefore A is C.
But now he uses the "=" sign, which is "if and only if".
So it appears that he has changed his argument, though I don't think he realized it (neither did I, as I didn't look closely when he restated it.) And Seraiah, I don't know if you already knew this, but your original argument was, in fact, invalid.
Consider: Socrates is a man.
Consider:
Socrates is a man.
We are not saying that Man = Socrates. We are saying that Socrates is in the category "men". If this is not the way you intended to use the word "is", then you should realize that your use is not how logicians treat that argument form.
Gotlucky, an equals sign is most definitely not "if and only if". The latter is a logical connective used with propositions. "Is" means equal, and to say that "A is B" or "A is equal to B" means that A and B are objects, not propositions.
It is still invalid. As I said before: If Men are Humans. And If Women are Humans. Then Men are Women.
That's a category mistake. I think it's only egalitarians that think as silly as that.
Friedmanite: Gotlucky, an equals sign is most definitely not "if and only if". The latter is a logical connective used with propositions. "Is" means equal, and to say that "A is B" or "A is equal to B" means that A and B are objects, not propositions.
I was taught to use <--> for iff, but I was made aware that some people use = to mean that, not that we should. Anyway, it sounds like Seraiah is trying to say iff, even if he isn't demonstrating it properly. His argument as he first stated it was certainly invalid, and I suppose you might be right about "=", but I've heard that some people have used it to mean iff.
Torsten: That's a category mistake. I think it's only egalitarians that think as silly as that.
It is not a category mistake. One can talk about men and women belonging to the category "human". The point is that Seraiah's argument is invalid. You can substitute anything:
Apples are fruit. Oranges are fruit. Therefore, apples are oranges.
Apples are fruit.
Oranges are fruit.
Therefore, apples are oranges.
Or, even better:
This is something. That is something. Therefore, this is that.
This is something.
That is something.
Therefore, this is that.
A more in depth explanation of categories can be found here. If you search for category mistake, you can read up on their explanation, though the wiki explanation is sufficient.
GotLucky is correct, Seraiah's argument is still invalid, it violates the law of identity.
\It is not a category mistake. One can talk about men and women belonging to the category "human".
It is a catagory mistake in the sense of conceptual levels. They aren't equal, just that one is included into one another.
I was thinking some more about this, and I think Seraiah's statements show that he does intend to use iff even if "=" is not standard for "iff".
Seraiah: men =/= humans woman =/= humans men =/= woman men is not synonomous with humans.
It seems that Seraiah is under the impression that "is" means synonymous. As in, a bachelor is synonymous with an unmarried man. But this would not be the standard use of "is", as we could also say a bachelor is a man. I think what he is trying to say is:
Something is a bachelor if and only if it is an unmarried man.
Also, so that Seraiah can see why what he said is not how to express it logically:
We are not saying that Socrates is synonymous with man. We are saying that Socrates belongs to the category "man".
Torsten: It is a catagory mistake in the sense of conceptual levels. They aren't equal, just that one is included into one another.
I still maintain that it is not a category mistake. Men and women both belong to the category human. Men and women are not the same. That is the point. The argument is invalid because it can lead to conclusions such as "men are women". A valid argument can never do that.
If you create an argument using the form Seraiah provided, and you had true premises and a true conclusion, it would only be by coincidence.
I still maintain that it is not a category mistake. Men and women both belong to the category human.
I know that and also can follow why you said that. Carefully read what one of your own sources did say.
Most famously, Ryle (1949) introduced the idea of the category mistake as a way of dispelling the confusions he thought to be rampant in the Cartesian theory of the mind, and thus of dissolving many apparent problems in philosophy of mind. According to Ryle, one makes a category mistake when one mistakes the logical type or category of a certain expression (1949, 16–17). Thus, e.g., a foreigner would make a category mistake if he observed the various colleges, libraries, and administrative offices of Oxford, and then asked to be shown the university. The foreigner mistakes the university for another institution like those he has seen, when in fact it is something of another category altogether: “the way in which all that he has already seen is organized” (1949, 16). The category mistake behind the Cartesian theory of mind, on Ryle's view, is based in representing mental concepts such as believing, knowing, aspiring, or detesting as acts or processes (and concluding they must be covert, unobservable acts or processes), when the concepts of believing, knowing, and the like are actually dispositional (1949, 33). Properly noting category distinctions may help alleviate a variety of philosophical problems and perplexities, and the idea of the category mistake was widely wielded (by Ryle and others) with this aim. http://plato.stanford.edu/entries/categories/
http://plato.stanford.edu/entries/categories/
Double posted.
It is essential to probability. Or rather, probability is essential to it. It is just the condensed form of saying that the more assumptions one makes, the more likely one is to be wrong. I have never studied logic, but I'm certain you would be above ad hominems. Anyway, I'm fairly certain there's a very simple refutation to all of this.
I also note that while many people have used the old "your argument is circular because it uses logic itself" argument, I preemptively responded to that in the opening post and nobody has refuted or even acknowledged those arguments. I claim victory.
I read that section already. He is saying:
Colleges belong to the category "learning institution". Universities belong to the category "learning insitution". However, colleges do not belong to the category university, and universities do not belong to the category colleges. Do not mistake colleges and universities as the same category.
Colleges belong to the category "learning institution".
Universities belong to the category "learning insitution".
However, colleges do not belong to the category university, and universities do not belong to the category colleges.
Do not mistake colleges and universities as the same category.
Likewise:
Men belong to the category human. Women belong to the category human. However, men do not belong to the category women, and women do not belong to the category men.
Men belong to the category human.
Women belong to the category human.
However, men do not belong to the category women, and women do not belong to the category men.
Torsten,
Upon reading your original response to me, I'm wondering if I might have misunderstood what you were getting at. Were you saying that the argument was invalid because it leads to category mistakes? Or were you saying that the argument was valid and I was the one making the mistake?
I assumed you meant the former, but after rereading maybe I misread you.
It seems that Seraiah is under the impression that "is" means synonymous.
@gotlucky,
I was just looking at the statement (man=human, woman=human, hence man=woman). I didn't mean that this is a vertical category mistake, but rather a horizontal one. Actually there is already a hidden mistake in the premises I think a man doesn't equal a human, but man is part of the humans as umbrella term for a group of subdivisions(man, woman). None of this disproves logic of course.
Seraiah,
Your original argument wasn't blatantly obvious. It had nothing to do with grammar; it was completely false according to the rules of logic. Posters have pointed numerous examples why it isn't true. If you still don't understand why, go back reread what you posted. I'm under the impression that you still don't understand where your mistake is.
Again, this is exactly what you wrote:
Take this example:
A is B C is B Therefore A is C
This is completely 100% false.
Don't confuse things here.
Mathematically,
if a = b and b = c, then a = c.
That's called transitivity. It's valid because the equal sign is an equivalence relation.
You cannot confuse this in propositional logic. The equal sign makes no sense.
This is precisely what I said earlier. Suppose A, B, and C are statements, or in logic terms, atomic sentences
=> means only if
<= means if
<=> means if and only if
((A => B) and (B => C)) => (A => C) is always true in all possible combinations of truth values of A, B, and C. We call such propositions tautologies. Tautologies are true precisely due to the meanings of the truth functional connectives. In the preceding example, the connectives are => and "and". Note that there is a difference between tautological truth and logical truth. Logical truths depend on the meanings of the atomic sentences themselves, and hence may not be tautologies.
Torsten: Actually there is already a hidden mistake in the premises I think a man doesn't equal a human, but man is part of the humans as umbrella term for a group of subdivisions(man, woman).
Actually there is already a hidden mistake in the premises I think a man doesn't equal a human, but man is part of the humans as umbrella term for a group of subdivisions(man, woman).
Right, man is not synonymous with human. I was criticizing Seraiah's original argument which he did not state correctly.
Seraiah: It is blatantly obvious what I meant by "is" in the context, even if it was not 100% true to the term. I have since then ammended, and clarified, the statements so I fail to see what you're still discussing.
It is blatantly obvious what I meant by "is" in the context, even if it was not 100% true to the term. I have since then ammended, and clarified, the statements so I fail to see what you're still discussing.
No, it was not blatantly obvious what you meant. You are in a thread on logic, and you used logical terms incorrectly. Forgive me for thinking that you knew how to use logical terms correctly.
Seraiah: My "original argument" wasn't any less valid, as I have simply clarified what I meant the entire time. (Which again, was blatantly obvious to anyone less than a grammar Nazi.)
My "original argument" wasn't any less valid, as I have simply clarified what I meant the entire time. (Which again, was blatantly obvious to anyone less than a grammar Nazi.)
I was giving you the benefit of the doubt in that post, that while your original argument was invalid, it was not the argument you meant to state. I suppose I shouldn't extend that anymore.
gotlucky: No, it was not blatantly obvious...
@ Luminar The problem is you haven't made a argument explaining how Occam's Razor is needed for probability. There are people who reject Occam's Razor and still have no problem with probability. As I pointed out in my first post in this thread, you also need to make a argument that Foundationalism is the only valid epistemological position for circularity to be a serious problem with logic or Occam's Razor, the reason being that some epistemological positions (such as Coherentism) don't see circularity as deadly to validity. I recommend you read a book on critical thinking, it will help you better understand what is necessary when creating a argument, reading up on epistemology is also a good idea. ( "Asking the Right Questions: A Guide to Critical Thinking" ) One last thing, I didn't commit the ad hominem fallacy in my last post. It was mentioned that you hadn't studied epistemology, that was all, for it to be a ad hominem I would have needed to claim that since you haven't studied epistemology you are wrong. I never said that.
The problem with your original argument is not grammar or ambiguity. It's just flat out false - end of story. You can admit that you made a mistake, or continue to insist that "it was obvious", and make yourself look even more foolish.