About logic

@Fido,

Fido wrote:

In your original post in reference to snakes as reptiles, each is an identity. If you are talking about snakes, you are not talking about mice. An identity is just that. Saying Mark Twain is identical with Samual Clemens tells us little about either, but it does say something about one person's identity. Certainly there is a relationship between one thing and another. Within that realtionship things, people, ideas, and etc. do not change their identity. Things do not change apart from forces acting upon them. Still; what is the identity of a thing? What is its genus and species? What does it have in common with other things, and in what sense is it different. If you say all pit vipers are snakes, but all snakes are not pit vipers you have refined a relationship, but also defined an identity, which is, in a sense unique. Now, I know Aristotle covered some of this. Are you going to make me quote from some dusty book that will only make me sneeze so you can sit and deny?

Do you perhaps mean that snakes are one kind of thing and reptiles another kind of thing? (I don't know what it means to call some kind of thing an identity). If I say that all pit vipers are snakes, I am saying that the class of pit vipers are included within the class of snakes. That is not a statement of identity like, the class of creatures with kidneys is identical with the class of creatures with hearts, which is a biological truth, meaning that every creature with a kidney is a creature with a heart, and, every creature with a heart is a creature with a kidney. But although (in your sentence) the class of pit vipers are included in the class of snakes, so that every pit viper is a snake: it is not true that the class of snakes is included in the class of pit vipers, so that some snakes are not pit vipers. So there is no identity between the two classes. All entities are self-identical, of course. So that the class of snakes is identical with itself, and the class of pit vipers is identical with itself. So that all pit vipers are pit vipers is, of course, true, and so is, all snakes are snakes, true. But the statement, all pit vipers are snakes is true, but it is not a statement of identity. You should distinguish among:

1. All pit vipers are pit vipers.
2. All snakes are snakes.

and, 3. All pit vipers are snakes.

1, and 2, and 3, are all true, of course. But only 1 and 2 are statements of identity. 3 is not a statement of identity. It is a statement of partial class inclusion.

No dusty books. Just a little clear thinking. I hope this helps.

But computers are not so dusty. Wikipedia has a nice article on the identity relation. It is:

Identity (philosophy) - Wikipedia, the free encyclopedia

@Fido,

Fido wrote:

Logic is always and only true within its contexts. We forever reason beyond our ability to prove. We live in a world we cannot prove. We presume a certain logical course of events, of cause and effect, without any firm grasp on a first cause or last effect. Logic is good for disproving what is thought wrong, but proving a theory wrong does not prove another theory right. And we can only push it so far into the future without error. If reason tells us that there is a fifty/fifty chance that a flipped coin will land heads up it tells us nothing about which way the coin will land the next time it is flipped. It has a one hundred percent chance of landing heads or tails up, because the natural force of gravity acts as an immutable law, which is a formulation of behavior. Will gravity always act in this fashion? No one can say with certainty, only that it is logical to expect it to based upon our experience.

Faith is at both ends of logic, and this is okay. As long as people are alive enough to feel, and can check the effects of logic on human beings with their emotions there will be no danger from the tyranny of logic. And, recall; that it is logical people who are most responsible for the curses this humanity endures, and has suffered. It was logical for the Nazis to gas Jews within the context of their ideology. It was logical for Dominicans to burn heritics within the context of their dogma. And it was logical to develop nuclear weapons within the context of physical inquiry. Outside of the paradigms that make particular thoughts logical, and particular actions rational, neither actions nor thoughts may be logical. Humanity knows nothing, so instead of being logical should be careful.

The term, "logical" is used in different ways. I think you are using it to mean, "reasonable" when you say that it is "logical" (reasonable) to expect gravity to continue to act as it has in the past. And I think that is true. But "logic" is often used to mean the study of argument, and what are the rules for good arguments as opposed to bad arguments. In philosophy that is how "logic" is generally used. In a more narrow sense, when we say that a statement or proposition is logical, we often mean that the statement follows correctly from other statements. Thus, from the statements, all cats are mammals, and all mammals are animals, it follows (logically) that, all cats are animals.

@Fido,

Fido wrote:

Logic is always and only true within its contexts. We forever reason beyond our ability to prove. We live in a world we cannot prove. We presume a certain logical course of events, of cause and effect, without any firm grasp on a first cause or last effect. Logic is good for disproving what is thought wrong, but proving a theory wrong does not prove another theory right. And we can only push it so far into the future without error. If reason tells us that there is a fifty/fifty chance that a flipped coin will land heads up it tells us nothing about which way the coin will land the next time it is flipped. It has a one hundred percent chance of landing heads or tails up, because the natural force of gravity acts as an immutable law, which is a formulation of behavior. Will gravity always act in this fashion? No one can say with certainty, only that it is logical to expect it to based upon our experience.

Faith is at both ends of logic, and this is okay. As long as people are alive enough to feel, and can check the effects of logic on human beings with their emotions there will be no danger from the tyranny of logic. And, recall; that it is logical people who are most responsible for the curses this humanity endures, and has suffered. It was logical for the Nazis to gas Jews within the context of their ideology. It was logical for Dominicans to burn heritics within the context of their dogma. And it was logical to develop nuclear weapons within the context of physical inquiry. Outside of the paradigms that make particular thoughts logical, and particular actions rational, neither actions nor thoughts may be logical. Humanity knows nothing, so instead of being logical should be careful.

The term, "logical" is used in different ways. I think you are using it to mean, "reasonable" when you say that it is "logical" (reasonable) to expect gravity to continue to act as it has in the past. And I think that is true. But "logic" is often used to mean the study of argument, and what are the rules for good arguments as opposed to bad arguments. In philosophy that is how "logic" is generally used. In a more narrow sense, when we say that a statement or proposition is logical, we often mean that the statement follows correctly from other statements. Thus, from the statements, all cats are mammals, and all mammals are animals, it follows (logically) that, all cats are animals. Aristotle put his work on logic in a book called, Organon. "Organon" means in ancient Greek, "tool". And that, of course, is what logic is. A tool to be used for clear thinking, and, more specifically, a tool to be used for determining what it is you can know supposing you know something else. For instance, it is by the tool of logic that I know that some fruit are apples because I already know that all apples are fruit.

@kennethamy,

kennethamy wrote:

Do you perhaps mean that snakes are one kind of thing and reptiles another kind of thing? (I don't know what it means to call some kind of thing an identity). If I say that all pit vipers are snakes, I am saying that the class of pit vipers are included within the class of snakes. That is not a statement of identity like, the class of creatures with kidneys is identical with the class of creatures with hearts, which is a biological truth, meaning that every creature with a kidney is a creature with a heart, and, every creature with a heart is a creature with a kidney. But although (in your sentence) the class of pit vipers are included in the class of snakes, so that every pit viper is a snake: it is not true that the class of snakes is included in the class of pit vipers, so that some snakes are not pit vipers. So there is no identity between the two classes. All entities are self-identical, of course. So that the class of snakes is identical with itself, and the class of pit vipers is identical with itself. So that all pit vipers are pit vipers is, of course, true, and so is, all snakes are snakes, true. But the statement, all pit vipers are snakes is true, but it is not a statement of identity. You should distinguish among:

1. All pit vipers are pit vipers.
2. All snakes are snakes.

and, 3. All pit vipers are snakes.

1, and 2, and 3, are all true, of course. But only 1 and 2 are statements of identity. 3 is not a statement of identity. It is a statement of partial class inclusion.

No dusty books. Just a little clear thinking. I hope this helps.

But computers are not so dusty. Wikipedia has a nice article on the identity relation. It is:

Identity (philosophy) - Wikipedia, the free encyclopedia

All pit vipers who are not politicians are snakes. It is clearly a refence to identity. All pit vipers are reptiles as well, so you can say that all pit vipers are snakes, and all snakes are reptiles so all pit vipers are reptiles even if all reptiles are not pit vipers. Reptiles is like a conceptual manifold. Like all concepts, it is one thing, this one thing is its identity, but within that one thing are many different kinds of things. Even pit viper is a class containing many kinds of pit viper, and yet it is one thing as a concept. As a matter of identity it is correct to say every pit viper is a snake and a reptile. It is equally true that sylogism helps to refine a definition, and what a thing is and what all things like it are, is an identity.

@Di Wu,

Di Wu wrote:

I think there is some truth in the quote.

Yes Logic can be fallible, but in most cases it is correct.
Hence within Logic one can find the security at least of being able to be right with confidence as much as being wrong with confidence.

Logic can provide the sense of security (emphasis on 'sense') of being surely right or surely wrong.

As I pointed out, logic is neither fallible, nor is it not fallible. People, who use logic are fallible. Logic is always correct, the way arithmetic is always correct. But it is people who use logic, like people who use arithmetic, who sometimes make mistakes.

@kennethamy,

kennethamy wrote:

The term, "logical" is used in different ways. I think you are using it to mean, "reasonable" when you say that it is "logical" (reasonable) to expect gravity to continue to act as it has in the past. And I think that is true. But "logic" is often used to mean the study of argument, and what are the rules for good arguments as opposed to bad arguments. In philosophy that is how "logic" is generally used. In a more narrow sense, when we say that a statement or proposition is logical, we often mean that the statement follows correctly from other statements. Thus, from the statements, all cats are mammals, and all mammals are animals, it follows (logically) that, all cats are animals.

It says above, that logic is the study of reasoning. I would bet that rhetoric is the study of argument. Yes, reasonable and logical are easily interchanged. I expect ratio, as opposed to religio, in Latin, from where we get our word rational is also eqivalent. You might remember that signs such as numbers are only good because they point to realities. If it were not possible to count simple things like apples using numbers it would not be possible to do complex things like calculate the distance to the stars. Res means thing, from which we get our word reality. I trust without proof that it has some relation to the word, reason. Logic comes from the Greek, Logos which does not mean word as John has it; but sentence. And number logic makes sense because the numbers stand for words in a sentence. Since most of our sentences are some form of equivilent statement, which tends to establish an identity as equasions do they are very similer. If, for example, I say, you are wrong; it is like saying you equal wrong. Now, I would not say that since it would hardly identify you among all of us who are wrong. But, you get my drift? The first step in reason is to establish an identity. This is what your sylogism does.

@Fido,

Fido wrote:

It says above, that logic is the study of reasoning. I would bet that rhetoric is the study of argument. Yes, reasonable and logical are easily interchanged. I expect ratio, as opposed to religio, in Latin, from where we get our word rational is also eqivalent. You might remember that signs such as numbers are only good because they point to realities. If it were not possible to count simple things like apples using numbers it would not be possible to do complex things like calculate the distance to the stars. Res means thing, from which we get our word reality. I trust without proof that it has some relation to the word, reason. Logic comes from the Greek, Logos which does not mean word as John has it; but sentence. And number logic makes sense because the numbers stand for words in a sentence. Since most of our sentences are some form of equivilent statement, which tends to establish an identity as equasions do they are very similer. If, for example, I say, you are wrong; it is like saying you equal wrong. Now, I would not say that since it would hardly identify you among all of us who are wrong. But, you get my drift? The first step in reason is to establish an identity. This is what your sylogism does.

Rhetoric is the study of persuasion.

But whose (or what's ) identity is being established? That's what I don't get.

A syllogism is a kind of argument. And the function of an argument is to establish a conclusion. It may be, sometimes, that the conclusion is a statement of identity of the form, A=A. But not necessarily. And that the conclusion of a particular argument is a statement of identity is just an accident of that particular argument. Most arguments do not have as conclusions, statements of identity. I don't know what you mean by an "equivalent statement". but if you happen to mean an identity statement, as I pointed out, neither your syllogism nor my syllogism contain any identity statements, so I don't understand what evidence you would have for saying that most statements are identity statements. I would think that is obviously false. The trouble is, I don't know what you mean by "identity" or, "identity" statement, since what you call identity statements are clearly not identity statements. Perhaps you are confused by the term "is" in the sentence, "Butter is yellow". That is not an identity statement. That doesn't mean that butter and yellow are one and the same thing. (Obviously, many other kinds of things are also yellow). The "is" in that sentence, is what is called, the "is" of predication. "Yellow" in that sentence is predicated of butter. Not identified with butter. There is also the "is" of existence, as in, "George W. Bush" is. (George W. Bush exists). And then, there is the "is" of identity. For instance, "Quito is the capital of Ecuador", meaning that the city of Quito and the capital of Ecuador are one and the same. But that is but one of the meanings of the term, "is". Clearly, when you say, "You are wrong" that doesn't mean (in any way) that I am the same thing as wrong. In fact, that doesn't make any sense. What you are doing is predicating wrongness of me. How could I be the same thing as wrong if there are many other people who also are wrong? Just as in my previous example, "butter is yellow: certainly does not mean that butter and yellow are the same thing. Butter is a substance of some kind. Yellow is a color. And, many other things are yellow aside from butter. And only some butter is yellow, in any case. I really recommend that you read that link on Identity that I gave you in my last post. It might clear some things up for you.

@Fido,

Fido wrote:

I don't which to offend anyone, but identity is essential to logic and syllogism is only an attempt at establishing an identity. Certainly, it has weaknesses, and is easily manipulated; but because it is so easy, it is practiced by every child to a greater or lesser extent, and so the accumulation of identities, definitions, really can begin and continue without any formal training in logic, which is more the processes by which identities are handled to add to knowledge. It is easy to see that children learn through a variety of methods to tell the difference between things, and I think it is easy to to see that syllogism and identity, like information accepted on faith plays a part. What part in ratio I cannot say. I can say that people reach a level of inductive and deductive reasoning with a great deal of formed knowledge.

I don't want to seem as ignorant as this statement may make me seem; but until a few years ago I had no concept of identity or conservation, as two sides of the same fuzz ball, until working it out in public on one of these forums. That does not mean I did not have the concept of identity conservation; I just did not have all the details formally. Children work out identity of objects in reality through syllogism every time they learn to distinguish between cats and dogs, even while each has more in common than not. Once one is presented with a formal idea, whether it is correct or not is unimportant, because then one can prove or disprove it, as one cannot ever do with an unformed concept. Does that make sense?

no offense taken fido
yeah i believe you are correct with this statement
basically its impossible not to use syllogism because without it you could not arrive at a logic
this is how we form our languages and i see what your saying
it seems there are a few different definitions
maybe i should have elaborated on mine as much as you did
assuming the environment is separated is what i think you refer to.. it is the foundation
and we all must do this and i agree with that
but can i mention that you must assume separation in order to conceive the idea of non-separation
and in that sense you are still very correct
it seems to be quite impossible to not make assumptions of your reality

@l0ck,

l0ck wrote:

no offense taken fido
yeah i believe you are correct with this statement
basically its impossible not to use syllogism because without it you could not arrive at a logic
this is how we form our languages and i see what your saying
it seems there are a few different definitions
maybe i should have elaborated on mine as much as you did
assuming the environment is separated is what i think you refer to.. it is the foundation
and we all must do this and i agree with that
but can i mention that you must assume separation in order to conceive the idea of non-separation
and in that sense you are still very correct
it seems to be quite impossible to not make assumptions of your reality

How does the syllogism make use of identity?

@kennethamy,

Logic is about being able to determine whether or not an argument is valid. If the argument is not valid, then the argument does not support/prove the conclusion. This does not necessarily mean that the conclusion is not true; nor does it necessarily mean that points made in the argument are not true.

eg. all mammals are animals
all cats are animals
therefore, all cats are mammals

Even though each point and the conclusion are true statements, the argument is not a valid argument. Which you can easily see when you use true statements, but the conclusion is obviously not true:

all insects are animals,
all cats are animals,
therefore, all cats are insects.

Logic is also a way of exposing pure rhetoric. Because rhetoric does not need to be true, nor does it need to be valid, it only needs to be persuasive (sales and politics are fraught with pure rhetoric).

@kennethamy,

kennethamy wrote:

How does the syllogism make use of identity?

Consider if you only had a pile of objects or animals with names on them, and you desired to know if a cat were the same as a feline, or if a lion was a cat in order to evaluate and catagorize what to you is recieved knowledge. These names, as they are identities, are what childen have to work with, and syllogism is their first logical approach to classification. What is what. Cheese is food, and food can be cheese, but not all food can be classified as cheese. Some identities contain other identities and some are contained; much as we say genus and species. Every identity is a definition, and every definition is a concept because it includes and excludes, classifies, and so relates this identity to this or that identity. As Kant might say: Knowledge is judgement. Until we can make an objective judgement upon any subject (as concepts are) we can honestly say nothing is known.

@Isa,

Isa wrote:

Logic is about being able to determine whether or not an argument is valid. If the argument is not valid, then the argument does not support/prove the conclusion. This does not necessarily mean that the conclusion is not true; nor does it necessarily mean that points made in the argument are not true.

eg. all mammals are animals
all cats are animals
therefore, all cats are mammals

Even though each point and the conclusion are true statements, the argument is not a valid argument. Which you can easily see when you use true statements, but the conclusion is obviously not true:

all insects are animals,
all cats are animals,
therefore, all cats are insects.

Logic is also a way of exposing pure rhetoric. Because rhetoric does not need to be true, nor does it need to be valid, it only needs to be persuasive (sales and politics are fraught with pure rhetoric).

If I may borrow freely from The Story of Philosophy, from a scholar I have read much of: Will Durant, then let me begin with a quotation of his, from Voltaire: "If you wish to converse with me, define your terms."

The Doctrine of the syllogism is Aristotle's contribution to philosophy. A syllogism is a trio of propositions of which the third (the conclusion) follows from the conceded truth of the other two, (the major and the minor premises). As the mathematically inclined will notice, this is a statement such as If A is B, and C is A, then B is C. As in the mathematical case, the conclusion is reached by canceling from both premises their common terms, A.

The problem lies in this: That the major premise that the syllogism takes for granted precisely the point to be proved.

Now, syllogism must be useless as logic if it can prove nothing, so what purpose does it serve but as a hypothetical ordering of nature?

And, quoting: " How shall we proceed to define an object or a term? Aristotle answers that every good definition has two parts, stands on two good feet... First it assigns the object in question to a group or class whose general charactoristics are its own, and secondly, it indicates wherein the object differs from all other members of its class."

Syllogism is only the first leg of the logical animal.

To define anything you must be able to say both what it is, and what it is not.... Fido

@Fido,

Fido wrote:

It says above, that logic is the study of reasoning. I would bet that rhetoric is the study of argument. Yes, reasonable and logical are easily interchanged. I expect ratio, as opposed to religio, in Latin, from where we get our word rational is also eqivalent. You might remember that signs such as numbers are only good because they point to realities. If it were not possible to count simple things like apples using numbers it would not be possible to do complex things like calculate the distance to the stars. Res means thing, from which we get our word reality. I trust without proof that it has some relation to the word, reason. Logic comes from the Greek, Logos which does not mean word as John has it; but sentence. And number logic makes sense because the numbers stand for words in a sentence. Since most of our sentences are some form of equivilent statement, which tends to establish an identity as equasions do they are very similer. If, for example, I say, you are wrong; it is like saying you equal wrong. Now, I would not say that since it would hardly identify you among all of us who are wrong. But, you get my drift? The first step in reason is to establish an identity. This is what your sylogism does.

What is the identity established by my syllogism. An identity is expressed by a statement of the form, A is A. (Cats are Cats) or Mark Twin is Samuel L. Clemens.
The conclusion of my syllogism is not a statement of that form? Therefore, my syllogism does not establish an identity.

But,

Here is a syllogism that does, indeed, establish an identity:

1. Mark Twain is Samuel L. Clemens.
2. Samuel L. Clemens is the author of Tom Sawyer.

Therefore, 3. Mark Twain is the author of Tom Sawyer.

You see the difference between my former syllogism which does not establish an identity, and this second syllogism which does establish an identity?

@kennethamy,

kennethamy wrote:

Here is a syllogism that does, indeed, establish an identity:

1. Mark Twain is Samuel L. Clemens.
2. Samuel L. Clemens is the author of Tom Sawyer.

Therefore, 3. Mark Twain is the author of Tom Sawyer.

You see the difference between my former syllogism which does not establish an identity, and this second syllogism which does establish an identity?

The suposed identity is established by the unstated premise, that there is but one Samuel L. Clemens, not by the actual argument.

:p

@perplexity,

perplexity wrote:

The suposed identity is established by the unstated premise, that there is but one Samuel L. Clemens, not by the actual argument.

:p

What is the identity?

Identity is a two-term relation. That there is but one anything is not an identity statement. Something has to be identical with something, even if it is with itself.

@Neshama,

If Mark Twain is one Samuel L Clements while a another Samuel L Clements wrote the book, it follows that Mark Twain did not write the book.

A logical statement is never more true than a premise it relies upon.

Smile

@perplexity,

perplexity wrote:

If Mark Twain is one Samuel L Clements while a another Samuel L Clements wrote the book, it follows that Mark Twain did not write the book.

A logical statement is never more true than a premise it relies upon.

I am talking about the Sam Clemens who was Mark Twain. Didn't you know?

And that is the first premise.
1. Mark Twain = Sam Clemens
2. Mark Twain wrote, Tom Sawyer.

Therefore, 3. Sam Clemens wrote Tom Sawyer.

So, given: 1, and 2 are true, so must 3 be true.

@kennethamy,

kennethamy wrote:

I am talking about the Sam Clemens who was Mark Twain. Didn't you know?

The point is that what I know is the premise without which the argument fails to work, the crucial premise being that Sam L Clemens is but one person.

@kennethamy,

kennethamy wrote:

I am talking about the Sam Clemens who was Mark Twain. Didn't you know?

And that is the first premise.
1. Mark Twain = Sam Clemens
2. Mark Twain wrote, Tom Sawyer.

Therefore, 3. Sam Clemens wrote Tom Sawyer.

So, given: 1, and 2 are true, so must 3 be true.

And all about establishing identity. Now can it be phrased in such a way as to exclude all others? Let the logic begin.

@Fido,

Fido wrote:

And all about establishing identity. Now can it be phrased in such a way as to exclude all others? Let the logic begin.

Peruse the archive of any online philosophy forum.

If there was ever a question not so inclined to beg the question of what exactly the question is, do let us know.

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