I have to ask,what is the propositional logic system you are using? SD logic has many different versions of the same thing, so you may want to state the system that you are using. For instance, past members have mentioned what system they do under the author of the book they studied from. So for example, I know Herrick, Bergmann, etc, and as a result you know the particular inference, replacements, symbols, etc. What exactly is the make and edition of your SD/propositional logic?

I have seen a few of your posts which no one really answers, so it may help to explain which framework you are working under so that we become acquainted with your system. Logic is much like different dialects of the same language.

Hello. I don't know. I can find out though.
Which parts of the question could mean something different if it was a different system I am using?
I don't even know where to start with these two questions...

What text are you using?

why is logic so complicated? isnt it just supposed to be the way the healthy brain works? are there actually different kinds of logic or is it that there are different kinds of logical proofs to show that we are being logical? the only thing i ever saw in the way of a book on logic was something called wff and pruf or something like that, and i didnt get it at all.

I'm on a campaign to reduce the use of the word "folks".



Check the rules for your tree proof system. Many such systems allow insertion of a LEM branch (such as A v ~A) anywhere.



Well, there are four binary connectives. Try each one in place of "#" until you find a connective that allows all of the above to be true and consistent.



Well there you go. I've asked several times for the author/source of the material you're studying, and you've always ignored the question. At least this time you say you don't know the source of the material you're studying...??

Ok i may sound stupid here but what is this all about could somebody put it in lamens terms so we're all on the same page???? :~

To a point it is. Having a healthy brain is a problematic assumption though and the issues arises, however, in what defines a healthy brain? I think that if you narrow the criteria down, it is reasoning that contributes to the most complicated aspects of (at least our) form of life. Look at the fundamental aspects of the law for example. Primary questions that deal with logic are such questions as what defines a reasonable man? Law assumes what a reasonable man would be able and not be able to do. Based on this criteria of reasonability, a person can fit within the framework or not (insanity defense, etc.). That being said? some people reason badly. With logic (and why it is so complicated), we can describe our reasoning and identify at least some of the ways we go wrong by examining fallacies and so on. We also devise systems for better reasoning, hence propositional logic, predicate logic, etc. But as you asked why logic is so complicated, when you really start to get to an in-depth point with logical systems, a myriad of contradictions or some hilarious and nauseating conclusion ends up turning a proof into a pyrrhic victory no matter how you look at it.

I think that many people at least on the forum are interested in the paradoxes that arise from the study of logic. Ironically, I think these people are more interested in the paradoxes themselves than the logical systems which necessitate them. I remember a long time ago, there was this one guy who could not grasp the fundamental message behind Zeno's paradox. He kept on saying how absurd it was that, as the paradox implies, an arrow travelling from A to B would be in continuous flight because logically the distance halved over and over again for every part of the path of the trajectory of the arrow making its flight indefinite. Simply, he assumed common sense rather than the premises behind the paradox. But where does that common sense come from? Reasoning? and logic.

As to types of logic, there are many. You primarily see SD/Propositional logic and the occasional bit of Predicate logic on the forum. Personally, propositional logic is my Sudoku, so I enjoy it vastly more than the other methods. Predicate/Quantificational logic is the next step up from Propositional logic. It is a bit more abstract than propositional using for example universal and existential quantifiers, etc. It's a very good system and useful at times, although I do not care for it as much as propositional logic? but that is just personal preference. But there are many other forms of logic as well, like modal and inductive logic. So many forms of the same thing? reasoning.

Wff and Proofs are essential components in the predicate logic (as well as the others) system. A Wff (said like "woof," but short for "well formed formula") define the standard "grammatical" structure of propositional logic. Basically what's allowed and what's not allowed. So say you have this sentence; Alan is home and Bob is home. This is a well formed formula (wff) because it adheres to standard grammatical structure of prop logic. But say you had this sentence; Alan Bob fly a kite. Reasonably, this does not make any sense. Is Alan with Bob? Is it Alan or Bob flying the Kite? Not a well formed formula. The proof on the other hand is the composition used to put a logical statement into form so that we can use inferences and replacement rules to derive the conclusion. This is an example of a logical proof;

That's sort of my problem too "Imnotrussion." I don't really know what to do

Anyways one of our texts is Hodges' Intro to Elementary Logic and Critical Thinking.

As for the binary connectives, would I be correst in supposing that the 4 are "and" "or" "if/then" and "if and only if"

how do i go about finding whether they are true and consistent?
start making a table? see if there is no occasion wherein the premises are all true and the conclusion false?

This is a tutorial on the basic connectives, your binary connectives;
http://www.philosophyforum.com/forum/philosophy-forums/branches-philosophy/logic/1454-propositional-logic-symposia-3-disjunction-conditional-biconditional-negation.html
However, I would point out the when use the term "binary connective," you are referring to a more mathematical form of the same thing.



Again, here is a tutorial on the primary connectives as well as the truth values you are attempting to find;
http://www.philosophyforum.com/forum/philosophy-forums/branches-philosophy/logic/1454-propositional-logic-symposia-3-disjunction-conditional-biconditional-negation.html

Also, here is a tutorial on making a truth tables which addresses most of your concerns;
http://www.philosophyforum.com/forum/philosophy-forums/branches-philosophy/logic/1514-propositional-logic-symposia-6-complex-partial-truth-tables.html

I apprecaite the help.
I am familiar with that material but my problem is not that but rather how my questions apply to those principles...

---------- Post added 07-12-2009 at 01:54 PM ----------

Regarding the first question, I think I am looking at [A V -A] -> R but I dont know how to prove R is a logical consequence which is what they are asking...

Well, the consequence of R is implied in the whole formula because the whole statement is a conditional.

First a few short reminders. In a conditional, you have three distinct things; an antecedent, a consequent, and a conditional connective. These are pretty much the universal definitions for the components of a conditional. So take a look at how this all translated; A-->B is equivalent to [Antecedent (A)] --> [Consequent (B)]. Also, it is important to understand the factors of a well-formed formula (wff). One of the main things to keep in mind with a wff is the fact that (A v ~A) --> R is exactly the same in form and function as A --> R. (A v ~A) is a sub-component sentence in the conditional... so in so many words, you must regard that particular statement as the antecedent in itself. Another thing to point out is that you may not use a bracket alone unless it is an isolated statement in a bigger one. It should be (A v ~A) and not [Av~A]. The rules go parentheses (), then brackets [], then etc. {}.

Now on to your question. You ask how to prove that R is a logical consequence. I am saying that the consequent R is implied in the conditional. It is already implied because you have (in the nature of the definition of the conditional outlined above) set up the conditional like that. You have a consequent (A v ~A) and as it was stated in the short summation of a part of a wff, it counts as a whole part of the antecedent. Anything that follows an antecedent which then follows the conditional connective is the consequent. You don't really prove anything as far as a basic conditional is concerned. When you introduce other statements and a solution, then you have something to work with.

That is why I believe that what is confusing you may be the fact that you think the conditional connective in (A v ~A) -->R is substituted for a turnstile or solution symbol. If you were asked to find the logical consequence of (A v ~A) -->R, the problem would have looked something like this; (A v ~A) -->R |- R where R is the subject for solution.

Problem is you are attempting to decipher a given logical statement by itself? so basically, you would be staring at that problem on paper for hours without really doing anything because nothing can be done at this point other than make a truth table.

Is he supposed to show that a tautology follows from any set of premises by natural deduction, or by truth-table. Natural deduction is a bit hard, but it is easy to that any argument which has a tautology as a conclusion is a valid argument.
Of course, such an argument must be valid, since it is impossible for it to have true premises and a false conclusion. Vacuously impossible.

Well the table would look something like this I think...

A v -A

T T F T
F T T F

And since R is a logical consequence, we have true premises makes a true conclusion, but supposing R were not true, were would have true premises making a false conclusion which wouldn't work.

But I don't see what the point of putting this on a tree would be...

Regarding the other question, I have knocked off the possibilities of "and" or "or" being the connectives, and I know that "if P then P" is a tautology, but I haven't figured how to relate that to the rest of the question...

---------- Post added 07-12-2009 at 03:38 PM ----------

Well, the way I did my truth tables for the second question neitehr "if/then" nor "If and only if" seem to be working...

I had already determined that neither "and" nor "or" would work because p#P had to be a tautology (# being my mysterious connective...)...

P#P has to be a tautology, while Q#P is not a tautological consequence of the sentences P#Q and P...

In a truth table for

([P->Q] ^ P] -> [Q -> P]

I got all T's, as I did when I replaced the "if/then" with "if and only if" which makes them both tautological consequences...

Horace,

To be honest, the thread and the logic involved are so jumbled that it's a miracle that any sense is coming out of this to being with, so at some point one has to hang up ones hat at some time. And it's ironic because this is supposed to be on some form of logic which is essentially utilized by streamlining these processes. To some point, clarity is essential in logic.

Your post #14, where on earth are you getting R from in your truth table. I refuse to believe that you are using unstated assumptions in a formal propositional truth table because that is a careless mistake. I still think you are confusing the consequent of the conditional with the actual statement for solution. If anything, were the R included in your assessment, the truth probability matrix would be 4 lines deep for two variables? not two which is for one sole variable. Something is amiss.

Horace, I underestimated the question and may have misled you. For that you have my deep, sincere, heartfelt apology. Sorry.

I incorrectly assumed that the mystery connective ("#") stood in place for one of the commonly used connectives of propositional logic. Propositional logic commonly uses four binary connectives (and, or, if/then, iff) and one unary connective (not).

But there are technically a total of four unary connectives and sixteen binary connectives, as in boolean algebra.

So it appears that your assignment is to find the meaning of the mystery connective ("#") from all the possible binary connectives, not just the four commonly used in propositional logic.

It seems that your mystery connective is that of converse implication, which has the form:

"P ← Q", which is equivalent to P v ~Q

or in the case of

"P ← P", it is equivalent to P v ~P



I will leave it to you to work out the truth table for the other part of the problem, but it does check out.


Your first post says that 'A v ~A' is a logical consequence of R, not that R is a logical consequence of 'A v ~A'.



The law of the excluded middle is foundational in bivalent classical propositional logic. The point of the question is probably to show that the "P v ~P" form follows from any sentence in propositional logic, and that the sentence tableau method has a specific rule just to allow this in a truth tree, to show that any sentence of the form "P v ~P" follows from any other sentence in propositional logic

You deserve marks for your patience VideCorSpoon...How does this look?

A/B | [A v -A] --> R

T/T | T T FT T T
T/F | T T TF F F
F/T | F T TF T T
F/F | F T TF F F

---------- Post added 07-12-2009 at 07:02 PM ----------

I've been doing it backwards...
As goapy pointed out, it's supposed to be [A v -A] as a logical consequence of any sentence R...

So w

---------- Post added 07-12-2009 at 07:03 PM ----------

I've been doing it backwards...
As goapy pointed out, it's supposed to be [A v -A] as a logical consequence of any sentence R...

So we are looking at R -> [A v -A]

---------- Post added 07-12-2009 at 07:06 PM ----------

This is getting a little confusing.
I am going to open a new post to simplify matters...