Propostional Logic Symposia - [1] - Introduction and Basics

@mister kitten,

mister kitten;124981 wrote:

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

A valid argument is when the conclusion follows logically from the premises.

A sound argument, though, is both valid and has true premises. So if I said to you; "All horses are apes. All apes are animals. Therefore, all horses are animals." Looking at this, you can tell that it is certainly not sound but it is valid.

A valid argument cannot take you from true premises to a false conclusion. The conclusion must be true (at least as far as a sound argument is concerned). You could have a valid argument with at least one false premises and a false conclusion. But like in the example I gave earlier, the argument could have a false premises in there somewhere and a true conclusion. To take that even further, you can have an argument with all false premises and a true conclusion. Actually, what may help you out is this truth table from symposia 3;

So take this example;

Bob ran 1000 miles in 1 hour. Anyone who runs 1000 miles in 1 hour is superhuman. Bob is superhuman.

The premises follow from the conclusion, thus it is a valid argument. However, it is far from sound. Now does a valid argument become logical? By most accounts, yes.

If you have any other questions let me know.

@mister kitten,

mister kitten;124981 wrote:

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

Ignorance is not funny, it is sad.

Validity - Wikipedia, the free encyclopedia

@kennethamy,

kennethamy;125008 wrote:

Ignorance is not funny, it is sad.

What is this supposed to mean in regards to mister kittens post? In fact, mister kitten had to restate the question twice due to you. This quote above sounds like a personal attack directed against someone who was just asking a simple question. Something like this not conducive to a learning environment such as philosophy forum, and certainly not in this thread series. Please try to be courteous to other members, both in terms of how you interact with them and the effort you put into your response.

Keep the responses (and questions) relevant to logic, not your personality.

@VideCorSpoon,

VideCorSpoon;125079 wrote:

What is this supposed to mean in regards to mister kittens post? In fact, mister kitten had to restate the question twice due to you. This quote above sounds like a personal attack directed against someone who was just asking a simple question. Something like this not conducive to a learning environment such as philosophy forum, and certainly not in this thread series. Please try to be courteous to other members, both in terms of how you interact with them and the effort you put into your response.

Keep the responses (and questions) relevant to logic, not your personality.

That was a very uncharitable interpretation, V. How about this one: Ignorance in humans is sad in that it causes lots of bad things to happen (nationalism and other political problems, religions, pseudoscience, etc.)

@VideCorSpoon,

VideCorSpoon;125079 wrote:

What is this supposed to mean in regards to mister kittens post? In fact, mister kitten had to restate the question twice due to you. This quote above sounds like a personal attack directed against someone who was just asking a simple question. Something like this not conducive to a learning environment such as philosophy forum, and certainly not in this thread series. Please try to be courteous to other members, both in terms of how you interact with them and the effort you put into your response.

Keep the responses (and questions) relevant to logic, not your personality.

Goodness, gracious, me! I didn't mean to make anyone cry.

@kennethamy,

Emil;125088 wrote:

That was a very uncharitable interpretation, V. How about this one: Ignorance in humans is sad in that it causes lots of bad things to happen (nationalism and other political problems, religions, pseudoscience, etc.)

Fresh out of charity at the moment. How about this one though: it is wise to admit oneself ignorant (within the context of Indian philosophy) because one does not know everything. So in some cases, ignorance in humans is not sad, but rather wise. Also, it sounds like you are connecting relative issues of nationalism, religion, etc. to ignorance?

kennethamy;125100 wrote:

Goodness, gracious, me! I didn't mean to make anyone cry.

Good golly oh mighty! Again, do not attempt to make members feel unwelcome to post their genuine questions. There is a limit to trolling.

Also, this nonsense ends here. Anything not pertaining to the topic at hand (logic, etc) will be removed. Have a nice day!

@kennethamy,

If I am writing this post and it is posted, then it can be observed.

I am writing this. It (hopefully) is posted.
Therefore, it can be observed.

Are these arguments the same?

@VideCorSpoon,

"Does a valid argument necessarily become logical as well?"

An argument is said to be valid when the premisses follow from the conclusion according to certain rules and procedures about the form, but not the content, of the assertions. This is seen when you substitute, for example, letters for more explicit content:
All A is B
All B is C
Therefore all A is C
This is a valid deductive argument.

Now whether the argument is "true" or in more common language, "logical" (meaning "sound" "deserving of assent")---and I think this accounts for the misunderstanding--- depends not just on the form but on the content. The argument: all fish are purple things, all purple things are happy things, therefore all fish things are happy things might be logically valid, but at least the two premises are questionable as matters of fact.

What causes us to assent to an argument is not just its proper logical form that obeys certain rules (e.g.,middle terms must be distributed at least once), but whether there are sufficient warrants for accepting the truth of the premises.

I hope my comments help clarify the problem, which seems to be a linguistic one. Considering an argument as logically invalid or valid is one of the tests for accepting it, since additionally one must also determine if the components (premises) are true or false.

---------- Post added 02-05-2010 at 02:44 PM ----------

mister kitten;125170 wrote:

If I am writing this post and it is posted, then it can be observed.

I am writing this. It (hopefully) is posted.
Therefore, it can be observed.

Are these arguments the same?

In both there are two antecedent conditions. First,you must have written the text (the post must have understandable content), and second the text is posted (and consequently viewable by Others) in fact. Another unstated condition is there must be viewers to view the post.

In the first argument, you have made the if/then structure obvious; in the second it is only implied. Either seems able to be translated into the other.

@jgweed,

jgweed;125173 wrote:

"Does a valid argument necessarily become logical as well?"

An argument is said to be valid when the premisses follow from the conclusion according to certain rules and procedures about the form, but not the content, of the assertions. This is seen when you substitute, for example, letters for more explicit content:
All A is B
All B is C
Therefore all A is C
This is a valid deductive argument.

This is incorrect. An argument may be valid without having a valid form. It is the content of the propositions that determine whether it is valid or not. This is a common mistake to make, even for logic textbooks. The key to realizing the error is to acknowledge that there are many forms an argument has. Some forms are valid and others are not. The form you mentioned above is valid (hypothetical syllogism, predicate logic version) but one could also analyze a valid argument that has the above form to have this form:
[INDENT]P
Q
Thus, S
[/INDENT]Which is invalid. The argument is still valid.

@mister kitten,

mister kitten;125170 wrote:

If I am writing this post and it is posted, then it can be observed.

I am writing this. It (hopefully) is posted.
Therefore, it can be observed.

Are these arguments the same?

No, because there are not two arguments there.

The first sentence is not an argument at all. It is a conditional statement.

The second two sentences do constitute an argument. But it is clearly invalid. A different argument, similar to it, could be valid if another premise is added. That premise would be: "If I am writing this post, and it is posted, then it can be observed" Then, you can add the premises, "I am writing this". and "it is posted", and then, the conclusion, "It can be observed", and you will have something that is not only an argument, but also a valid argument.

@kennethamy,

kennethamy;125408 wrote:

No, because there are not two arguments there.

The first sentence is not an argument at all. It is a conditional statement.

The second two sentences do constitute an argument. But it is clearly invalid. A different argument, similar to it, could be valid if another premise is added. That premise would be: "If I am writing this post, and it is posted, then it can be observed" Then, you can add the premises, "I am writing this". and "it is posted", and then, the conclusion, "It can be observed", and you will have something that is not only an argument, but also a valid argument.

It is always possible to add a single premise to make any argument valid. That is worth reflecting on.

@VideCorSpoon,

Is a true argument necessarily valid? All true arguments are necessarily valid?

@mister kitten,

mister kitten;129729 wrote:

Is a true argument necessarily valid? All true arguments are necessarily valid?

There is no such thing as a true argument. So, I do not know what you mean. Can you say what you mean by a "true argument"? Maybe you mean an argument with truth premises. Or maybe you mean an argument with a true conclusion. Or maybe you mean an argument with true premises and a true conclusion. The answer in all of those case is, no.

@kennethamy,

kennethamy;129730 wrote:

There is no such thing as a true argument. So, I do not know what you mean. Can you say what you mean by a "true argument"? Maybe you mean an argument with truth premises. Or maybe you mean an argument with a true conclusion. Or maybe you mean an argument with true premises and a true conclusion. The answer in all of those case is, no.

Perhaps he means sound argument, but there is no way to know what it is that people mean when they utter "true argument". I always take it as a sign that they should pick up a logic textbook.

@VideCorSpoon,

Let us say, Mister Kitten, that a true argument is one in which the conclusion is consonant with matters of fact (leaving aside whether these are REALLY TRUE, and what we precisely mean by matters of fact). Think of two possible cases:

It is quite conceivable that the conclusion was true despite it being argued from untrue premises or premises which had no logical bearing or connexion with the conclusion. For if each step in the argument is judged true or false, including the conclusion, then validity has nothing to contribute except perhaps a (often useful) guarantee that the conclusion either does or does not follow from the premises.

On the other hand, take an example in which each of the premises is judged to be true, and we also know that no rule of logic has been violated in reaching the conclusion. We must then, it seems to me, say that the conclusion "must" be true, and if we think it false, we need to reconsider our holding it to be so.

@jgweed,

jgweed;129738 wrote:

Let us say, Mister Kitten, that a true argument is one in which the conclusion is consonant with matters of fact (leaving aside whether these are REALLY TRUE, and what we precisely mean by matters of fact). Think of two possible cases:

It is quite conceivable that the conclusion was true despite it being argued from untrue premises or premises which had no logical bearing or connexion with the conclusion. For if each step in the argument is judged true or false, including the conclusion, then validity has nothing to contribute except perhaps a (often useful) guarantee that the conclusion either does or does not follow from the premises.

On the other hand, take an example in which each of the premises is judged to be true, and we also know that no rule of logic has been violated in reaching the conclusion. We must then, it seems to me, say that the conclusion "must" be true, and if we think it false, we need to reconsider our holding it to be so.

What is a "true step" in the argument?

What he means, Mr. Kitten, is that if the premises of a valid argument are true, then so will the conclusion be true. And, if the conclusion of a valid argument is false, then one or more of the premises will be false. But, if the premises of an argument, valid or invalid, are false, then the conclusion can be either true or false.

So we have this schema:

Argument valid:
Premises are true, then conclusion is true.
Premises are false: unknown whether conclusion is true or false

Argument invalid:

Premises true, unknown whether argument is true or false.
Premises false, unknown whether argument is true or false.

So, we know that the conclusion of a valid argument is true only when we know that the premises are true, and in no other case. In all other cases of the combination of true or false premises, and validity of argument, we cannot know whether the conclusion is true or whether it is false. So the crucial case is: premises true, argument valid, therefore, conclusion true.

@VideCorSpoon,

Okay, assuming there could be a true argument would the argument necessarily be valid?

I meant true as in the premise and conclusion are true.

@mister kitten,

mister kitten;129754 wrote:

Okay, assuming there could be a true argument would the argument necessarily be valid?

I meant true as in the premise and conclusion are true.

As I have pointed out many times, the answer to that is definitely, no. Here is an example of an argument with true premises, but a false conclusion, which is not valid.

All dogs are mammals
All cats are mammals

Therefore, all humans are mammals.

True premises
True conclusion
Invalid Argument

Therefore, since the above is an argument with true premises and a true conclusion, but is not valid, it follows that some arguments with true premises, and a true conclusion, are not valid.

Picking up a logic book would not be a bad idea. Not many posters on this forum are versed in elementary logic.

@VideCorSpoon,

As always, my offer to send a logic textbook stands. Just pm me your email. The textbook is Tomassi, Paul - Logic.

@Emil,

Emil;129780 wrote:

As always, my offer to send a logic textbook stands. Just pm me your email. The textbook is Tomassi, Paul - Logic.

I wonder how many people who ask logic questions will take you up on your offer? Maybe you could keep count.

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