Valid and Invalid Logic Arguments: Explained

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Discussion Overview

The discussion revolves around the validity of various logical arguments involving implications and truth tables. Participants explore the correctness of specific statements regarding arithmetic and logical reasoning, with a focus on understanding logical validity and the use of truth tables as a method of evaluation.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant presents four logical arguments and seeks help in determining their validity.
  • Another participant claims that arguments 2, 3, and 4 are correct, while argument 1 is incorrect, suggesting the use of truth tables for evaluation.
  • A different participant questions the necessity of truth tables and suggests that understanding the premises is sufficient to determine validity.
  • Some participants express confusion about truth tables and seek alternative methods for evaluating the arguments.
  • One participant argues that the validity of an argument is determined by whether the premises support the conclusion, asserting that argument 1 is valid.
  • Another participant counters that the relationship between premises and conclusions is not as straightforward as claimed, using an example involving wealth and purchasing power.
  • Several participants engage in a back-and-forth about the implications of conditional statements, with some clarifying that "if A then B" does not imply "if not A then not B."
  • There are multiple corrections and clarifications regarding the logical structure of arguments, with some participants expressing frustration over misunderstandings.

Areas of Agreement / Disagreement

Participants generally disagree on the validity of the arguments presented, with multiple competing views on how to evaluate them. The discussion remains unresolved, with differing opinions on the role of truth tables and the interpretation of logical statements.

Contextual Notes

Some participants express a lack of familiarity with formal logic concepts, which may affect their understanding of the arguments. There are also references to the historical context of logic before formal systems like truth tables were established.

Who May Find This Useful

This discussion may be useful for individuals interested in logic, mathematical reasoning, and the evaluation of arguments, particularly those who are new to formal logic and seek to understand the nuances of logical implications.

peos69
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Can anybody help me with the following arguments:

1) If 2+2=5 then 2+3=6 but,2+2=/=5 hence 2+3=/=6

2) If 2+2=4 then 2+3=6 but, 2+2=4 hence 2+3=6

3) if 2+2=5 then 2+3=6 but 2+3=/=6 hence 2+2=/=5

4) if 2+2=4 then 2+3=6 but, 2+3=/=6 hence 2+2=/=4

Which of the above are valid and which are not.

An explanation will help a lot.

Thanks
 
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1) Incorrect
2) Correct
3) Correct
4) Correct

You can do these by truth tables (without using Natural deduction) let say you have A and B as two predicates then,

A B A=>B

T T T
T F F
F T T
F F T

Now try ~A and ~B and you should end up with ~B=>~A iff A=>B. In English if you make a statement saying if it rains then it is wet, then if it is dry, it has not rained.

Hope this helps
 
Did you learn about truth tables? Can you write down the truth table for A => B and see how that helps you (dis)prove them?

By the way, this is a good exercise. It points out an important mistake made by many people, who start to learn writing down proofs.
 
What people do before the truth tables or what other formalistic commodities where discovered? Where in the dark?? MUST ilearn now whatever you call it logic to evaluate those arguments? I KNOW that an argument is valid when the premises of the argument supports the truthfulness of the result,therefor No1 argument is valid
 
I am sorry to say that truth tables and natural deduction sounds Chinese to me.
Isnt there another way to evaluate those arguments?
 
peos69 said:
What people do before the truth tables or what other formalistic commodities where discovered? Where in the dark?? MUST ilearn now whatever you call it logic to evaluate those arguments? I KNOW that an argument is valid when the premises of the argument supports the truthfulness of the result,therefor No1 argument is valid
No one argument basically says that if it has rained then it is wet, and then it observes that it has not rained. Now you can't say that it is not wet, because rain is not the only thing that causes things to get wet. For truth tables go on http://en.wikipedia.org/wiki/Truth_table . Make sure you look at the examples, they are pretty simple. Some tips,
If A then B is the same as saying A=>B (that is A implies B)
and iff is if and only if which says A=>B and B=>A.

No1 is definitely false, no doubt about it. If you don't understand why, think about it. Rather I should say its not a tautology (which means its not always true).
 
Surely if it rains is going to get wet .Those things are interrelated,but the sentences in my examples are not.To oppose your argument i can produce the following argument.
If i am reach i can buy Kennedy Airport,but since i am not reach i cannot buy the said airport
 
That's logically false :)
You could get a bank to loan you money and still buy it.
It would be different if you said:
"If and only if (i.e. precisely if, i.e. either both, or neither) I am rich, I can buy Kennedy airport."
Then from "I am not rich" you can draw the conclusion that you can't buy it. But it follows from the "only if" part, not the "If" part.
 
Mention The Bank I Will Pay Them A Visit Tomorrow
 
  • #10
And again you did not answerer my question what people did before all those logical commodities were discovered
 
  • #11
I am sorry to say i do not understand
 
  • #12
Implication that is A=>B (If A then B) is true if A is false, regardless of if B is false or not. So if you are not rich then the statement is true regardless if you can buy the airport. The statement would be false if you are rich but you cannot buy the airport.

If you say, I am rich if and only if I can buy the airport, then if you are not rich, you cannot buy the airport.
 
  • #13
.

.[/QUOTE]If you say, I am rich if and only if I can buy the airport, then if you are not rich, you cannot buy the airport.[/QUOTE]

I am sorry i DID NOT say that
 
  • #14
peos69 said:
If i am reach i can buy Kennedy Airport,but since i am not reach i cannot buy the said airport
That is what i said
 
  • #15
It is only true if you say "if and only if" not just "if".
 
  • #16
Would you also agree then that

"If I am rich I can buy a cup of coffee but I am not rich so I cannot buy a cup of coffee"?
 
  • #17
Hallsofivy, i agree...it's all relative!
 
  • #18
A cup of coffee is not the Kennedy Airport
 
  • #19
I am sorry for the mistake in spelling. it is "rich" instead of "reach"
 
  • #20
peos69 said:
A cup of coffee is not the Kennedy Airport
And your point is what? I was under the impression we were talking about airports. Are you now saying that we were only talking about airports?

The discussion at the point where you wrote "If I am rich I can buy the Kennedy Airport" implied "if I am not rich I cannot buy the Kennedy Airport" while everyone had been telling you that "if A then B" does NOT imply "if not A then not B". My point was that your example is not general.
 
  • #21
If you can prove Godels theorems and the consistency of set theory i will jump over the cliff but since you cannot prove them both you saved my life
 
  • #22
And your contention is not general
 
  • #23
NOT everyone ...
 
  • #24
Er, are you feeling well?
 
  • #25
* Wondering if this thread can still be saved?
 
  • #26
SURE perfect after all i am not going to jump over the cliff
 

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