You can’t disprove a definition… you can prove that someone isn’t using the correct definition or is contradicting himself… but you can’t disprove a definition.
This must be it.
So we’ve covered material implication and logical implication. What about causal implication, or implication that rests on entailment?
I think what I mean by causal implication is pretty obvious (but ask me if it’s not). What I mean by implication that rest on entailment is a conditional statement that is meant to be interpreted such that the antecedent entails the conclusion (i.e. there is some connection between the two). For example: if the victim was killed at 2:00 AM, then the murderer must be Joe Schmoe. In other words, it could not be possible that the victim was killed at 2:00 AM and the murder is not Joe Schmoe.
Note how this differs from Uccisore’s example: if I scratch my head, then a quasar somewhere emits high energy protons. My head scratching and the protons emitted by the quasar have absolutely nothing to do with each other. We’re only able to say if the one is true then the other is true because they both so happen to be true in the same world, but not because the one causes the other, or even that the one entails that the other must be true.
What I’m asking is, does the truth table for conditionals also apply to causal or entailment implications?
The truth table applies to all implications… because they can all be translated to ~(P^~Q)
Why do you ask?
Because it seems to me that with causal/entailment conditionals, you can get the kinds of absurd statements that I thought we were dealing with at the start of this thread. If we take Uccisore’s example: if I scratch my head, then a quasar somewhere will emit high energy protons, and we say this as a causal statement (i.e. scratching my head causes some quasar to emit high energy protons), then the truth table for conditionals tells me this is a true statement:
If [I scratch my head] (<-- let’s say this is true–I am scratching my head), then [some quasar will emit high energy protons] (<-- this has got to be true somewhere in the universe). ← the whole statement is true because it takes the form: if [true] then [true].
But if this is meant as a causal implication, then to say that it is true is to say that scratching my head does cause some quasar somewhere out there to emit high energy protons–which seems absurd.
The truth table doesn’t tell you what kind of implication it is, though… you don’t see if something is a causal implication any more than you see if its a logical one from looking at the truth table.
You need to justify/explain them separately…
It shouldn’t matter whether the truth table can tell me what kind of implication it is; if the truth table applies to all types of implication, then it should apply to causal implication. So if I have P → Q, and that’s meant to be interpreted as P causes Q, then the truth tables tells me that such a causal statement will always be true so long as P and Q are true. So I could say “If I scratch my head, a quasar somewhere emits some high energy protons,” and mean that my scratching my head causes a quasar somewhere to emit some high energy protons, and the truth table tells me that’s true.
I see what you’re saying… and don’t get me wrong, this is a hard subject… and I’m kinda impressed that you care to ask and learn, most people find this stuff dry and boring.
Anyway… in standard Logic “P causes Q” is not equivalent to “P->Q” You can conclude “P->Q” from “P causes Q”… but you cannot conclude “P causes Q” from “P->Q”
So in effect if you say “If I scratch my head, a quasar somewhere emits some high energy protons” and mean it as a causal implication you are saying:
- We live in a world where Scratching my head causes a quasar somewhere to emit some high energy protons (this is a premise you have to defend separate from the following)
Therefore - the material implication “If I scratch my head, a quasar somewhere emits some high energy protons.” is true (yet it could be true irrespective of the truth of the previous premise)
I have seen some people express the first premise as (P c Q) as in P causes Q and I personally prefer that symbol… yet there’s no formal “cause” symbol that I know of… and if there is I think it’s “c”
However another way of expressing it would be
W => P->Q
W
Therefore P->Q
Where W is the the world you think we live in.
Not me. I freakishly find logic fascinating. It was my best subject in school, and I once solved a problem on an assignment on which the instructor wrote “brilliant!” Obviously, I’m forgetting much of it–it was a long time ago.
I see. So the truth table for conditionals does not apply to P c Q.
And I’d assume something similar can be said about entailment implication, by which I mean implications meant to be read as the antecedent entailing the consequent. Ex: if the murder took place at 2:00 AM, then Joe Schmoe is the murderer. So the murder taking place doesn’t cause Joe Schmoe to be the murderer, but it entails it (i.e. maybe because it was proved that everyone else was asleep at 2:00 AM and that Joe Schmoe was still up and about in the vicinity). So we might write that as P e Q (where e stands for “entails”), but the truth table for conditionals doesn’t apply to P e Q, but it does apply to the material implication P → Q which can be deduced from P e Q.
That’s awesome! I’m the same way… I love “systems” of any kind… All Logics like Math, Programing Languages, Electronics, quantum… you name it…
I have my dad to thank for that… he’s an electronic engineer and he used to give me puzzles, those old school circuit board designs he used to work on, and ask me to find the flaw in the system as a kind a challenge…
But just as a defense of my dad… he did not do this against my will as some kind of parenting technique… we had a computer back then and I desperately wanted to “play” with it, but all he had installed were the programs used to design the systems so… he made up a game for me… and I loved it.
Nor does it technically apply to definitions that we use to conclude logical implications.
The problem seems to be that we can’t look at the truth table for implications as a “confirmation” of the kind of implication we’re talking about… since it just shows AN implication is true/false.
So we still have to actually define/defend what kind of implication we’re talking about…
It can be fun challenging your kids with intellectual puzzles. I once tried to teach my daughter (4 years old at the time) the theory of relativity. I used the most simplistic example: what if, when you’re walking down the sidewalk, it isn’t really you walking but the sidewalk moving backwards? What if, when you’re spinning, it isn’t really you spinning but the world spinning around you? She kind had a “woaw, deep thoughts” moment, and then came up with examples of her own: What if my toys were really books? What if this bread I’m eating was really chicken? To which I said “uh… yeah, we’ll work in that.” 
But yeah, I like playing with logic. It’s one of the things I do here. I like to pick apart the logic of people’s arguments and point out any holes or inconsistencies I see. I’ve been accused by atheists of being a theist because I pointed out some holes in their atheist arguments. I’ve been accused by theists of being an atheist because I pointed out some holes in their arguments. Really, I don’t always care much for one position or another, I just like playing with the logic of the arguments I hear.
Most of my time on ILP is spent reading what others write… I’m not the most prolific member… but the few times I do feel like getting involved is when I notice someone making a logical error like you say, or when the subject is something I happen to know well.
@ Gib or someone else
Would you mind responding James’ post ( viewtopic.php?f=1&t=185298#p2456603 ) ?
Yes, you did. Excuse me!
Then take this:
If 3 x 3 = 10, then the earth is a planet.
[size=150]?[/size]
Thank you!
Regards!
So if [false] then [true]? ← Well, it’s true! If 3 x 3 = 10, then the Earth is a planet.
As Uccisor would say: In all case in which 3 x 3 = 10, the Earth is a planet.
Or as Mad Man would say: It is not the case that 3 x 3 = 10 and the Earth is not a planet.
The statement of a logical implication is false then and ONLY then, if the first part of the statement is true and the second part of the statement is false.
Jimmy’s post is nonsense… nothing in that post has anything to do with logic and he got literally everything wrong except the truth table.
Yes… yes it is.
Says the one who couldn’t get any of it right after several pages. 
So you are saying: Logic is nonsense. — Why? Because James’ post is refering to logic and nothing else.
Logic isn’t nonsense, but: Your statement is nonsense. It has nothing to do with logic, nothing to do with philosophy, nothing to do with science, nothing to do with life, nothing to do with anything because it is absolutely absurd, it is just false.
Maybe you didn’t or couldn’t read James’ post. In that case I forgive you, but your statement is stupid. Your statement is mad too, Mad Man P., and laughable ( ), but also dangerous ( 
) because it is a subjective one which indicates that you are merely a hater.
Try to read James’ post: viewtopic.php?f=1&t=185298#p2456603
If you can not understand logic, I wonder why are you posting here because: the most important discipline of philosophy is logic.
[size=120]I love philosophy, especially logic.[/size]
Exercise example:
Mad Man P
Posts: 2342
Joined: ?
Location: Denmark
If this one is a woman, (he / ) she persecutes logicians.
Help!
Code of practice:
p _ q _ p → q
F _ F _ T
F _ T _ T
T _ F _ F
T _ T _ T
Regards.