Urgent Help Required (2 Problems)

[Horace]

Folks, I have no idea how to solve these two matters.

1. I need to show by the sentence tablueau method that the sentence [A V -A] is a logical consequence of any sentence "R."
And

2. I need to figure out what this binary truth-functional sentential connective (#) actually is in light of
P#P being a tautology, and Q#P not being a tautological consequence of the sentences P#Q and P.

This is homework, and I don't want people to think I'm just hunting for answers. I really don't know how to go about solving these.
Any tips for the process? Very grateful for any help...

[VideCorSpoon]

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.

[Horace]

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...

[kennethamy]

Originally Posted by Horace

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?

[salima]

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.

[goapy]

Originally Posted by Horace

Folks

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

Originally Posted by Horace

1. I need to show by the sentence tablueau method that the sentence [A V -A] is a logical consequence of any sentence "R."

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

Originally Posted by Horace

2. I need to figure out what this binary truth-functional sentential connective (#) actually is in light of
P#P being a tautology, and Q#P not being a tautological consequence of the sentences P#Q and P.

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.

Originally Posted by Horace

This is homework, and I don't want people to think I'm just hunting for answers. I really don't know how to go about solving these.

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...??

[Imnotrussian]

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???? :~

[VideCorSpoon]

Originally Posted by salima

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.

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;

http://i31.tinypic.com/24mhu2v.jpg

[Horace]

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?

[VideCorSpoon]

Originally Posted by Horace

As for the binary connectives, would I be corre[c]t in supposing that the 4 are "and" "or" "if/then" and "if and only if"

This is a tutorial on the basic connectives, your binary connectives;
http://www.philosophyforum.com/forum...-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.

Originally Posted by Horace

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?

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...-negation.html

Also, here is a tutorial on making a truth tables which addresses most of your concerns;
http://www.philosophyforum.com/forum...th-tables.html