h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: Truth and Validity - A763779
Author: Lost Vagrant - U195902

Hmm.. here's my first entry. The spelling should be all accurate, as should the grammar. Hope you enjoy it

I think you've got some of these mixed up:

"If a car has the word FORD on it, then it is a Ford.
This car does not have the word Ford on it. Therefore, it is not a Ford!"

In symbols, you've got:

A=>B
not(A)
Therefore: not(B)

This is not a valid argument, as you point out later. It is possible for a Ford car to have the word removed, and it would still be a Ford car.

Later on:

"Invalid Argument Form Number 1: Affirming the Consequent

If x, then y.
x.
Therefore, y.

This form of argument is often a common logical mistake. It seems to make sense, doesn’t it? It is invalid because the conclusion does not follow in order after the premises, even if it is a true statement. It is very easy to mix this form up with the Modus Ponens form. Here’s an example:

If I am happy, then I am with the one I love. I am happy. Therefore, I am with the one I love."

This argument is valid, and is exactly modus ponens (unless I'm going crazy ). If the first statement is true, then being happy necessitates that you are with the one you love. You're right that the result isn't true in real life because you could be happy for some other reason. The first sentence would more likely fit with reality if it were the other way round:

"If I am with the one I love then I am happy."

Then again, it's the night before a big exam, maybe I am going loopy

You had some good points about the Ford, that was a bad example. Thanks for the critiqueing anyways. However, it seems that in some ways Logic has no logic to speak of at all... interesting stuff anyways. Good luck on the finals

Hi LV!

Good to see more philosophers around!

A couple of suggestions:

1. It might be worth making the difference between validity and truth clear much earlier on in the entry. It seems to come in near the end. I think it makes your later discussion much clearer for non-philosophers to follow. Something like:

Truth and validity are not the same thing. Validity is a property of arguments, truth is a property of propositions (premises or conclusions). A conclusion can be true, but the argument invalid [example], and conclusion can be false and the argument valid [other example]

2. "A valid argument contains a universal truth: If the premises are all true, then the conclusion is true as well."

I'm really not sure about the "universal truth" bit. Perhaps "a valid argument contains a neccesary truth if (and only if) the premises are true. If the premises are true, and the argument is valid, then the conclusion logically cannot be anything other than true" Or something.

3. I think you need to say more about Modus Tollens, and the difference between:

A, if B
A, if (and only if), B

A good subject for a guide entry, though!


Otto

Ah, thank you for all these great suggestions. Very helpful What articles have you written? I'd be interested to see them.. Thanks!
Chris

I think you need to differentiate between necessary and sufficient conditions.
ie "Y can only be if X" (X is necessary)
or "if X, then Y must be" (X is sufficient)

Hi Chris,

If you click on my name (above), it'll take you to my H2G2 homepage, which will have links to whatever else I'm up to at the time!

My only solo guide entry is "How to be a Philosopher", for which there's at least one link at my homepage. I've tried not to write exclusively about philosophy, although I have something in the pipeline on Rawls. Along with several other things I keep starting and not finishing!

Otto

Seem to be bugs in the examples... someone's already commented on the FORD one. Here're others:

>>If a kiwi is a fruit, then it can walk. A kiwi is a fruit. Therefore, a kiwi can fly.
>>As you can see, there is an obviously false conclusion, even though the argument form is valid.

The argument form is invalid because 'fly' and 'walk' have been mismatched, no?

>> If I am happy, then I am with the one I love. I am happy. Therefore, I am with the one I love.
>> It is invalid because the conclusion does not follow in order after the premises

I don't think so. It's a valid argument, but it's untrue because the premise (If I am happy, then I am with the one I love) is untrue.

>> If children run, then pigs can wallow. Children cannot run. Therefore, pigs cannot wallow.
>> Even though both of the premises are true

Nope, I don't think the second premise (children cannot run) is true in this world, because children certainly can run (in general).

The first premise is true provided you take "if A then B" to mean "A logically implies B" (but not if you take "if A then B" to be a statement about counter-factuals). I think you'd be wise to dodge the entire issue by not using if...then constructions, lest you open worm cans.

--

>> Part Two: Invalid Arguments

You've said this twice...
You should mention that there are many other forms of invalid arguments (aka logical fallacies). For example, A688287 - Circular Reasoning. It'd be good to link to such entries.

-Martin

Hey there Lost Vagrant, are you with us? Or you lost? I'm tempted to take this entry but would ideally like you to address the points made by Lucinda in this 'ere thread.

If Lost Vagrant is genuinely lost to us - maybe lying on some Moscow park bench, wrapped in old issues of Pravda, sipping vodka, leafing through a battered copy of 'Crime and Punishment' - can this go in as it is? I don't really understand the subject so I require help in making a judgement call. Cheers.

Personally, I don't think so. The few points I made wouldn't take a long time to fix, but they do need to be fixed. At the moment, the entry is claiming that children can't run, for example...

-Martin

OK, let's see if Lost Vagrant get's back - I'll give him to the end of the week. If by that time we hear nothing, I propose we move the entry out of here and in to the Flea Market. Thanks for your help. And how are your toes?

A lot cleaner than they were after softball!
-Lucinda

It's not claiming that children can't run, it's just saying that if children couldn't run then...

Definitely cannot go in as is. Get someone who knows what they're talking about to adopt it, if we've lost a vagrant.

OK.

Right, in the absence of the aptly-named author, and listening to the advice proffered in this 'ere thread, I've decided to move the entry to the Flea Market, to see if any one or more of our young philosophers want to have a go (if they think they're hard enough).

Sam.

Does the week end a lot earlier in the BBC than the rest of the world?
-MyRedDice

I can take this one. Like Lucinda said, it only needs some polishing. Well, it needs new examples, and some rewriting, and some polishing. Regardless, I've never adopted an entry from flea market before, and this one just looks so sad, with those big droopy eyes!

So, how does this work? I post to Lost Vagrant's space, indicating that I've got his child, and where he can leave the money, right? Then I go to the test-page, copy the code, and paste it into my own entry, being sure to share author credit? Sounds jolly.


GTB

New location: A813025

Say, what happens to this thread now?