Implication (Propositional Logic)
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- čas přidán 7. 09. 2024
- An explanation of the implication operator in propositional logic (100 Days of Logic and 90 Second Philosophy).
Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more!
Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more!
Wow, this appeared so much more convoluted when someone else was explaining it to me. Now, I get it.
I suppose the confusion was when the statements don't seem to entail each other, for example, "if superman exists then spiderman also exists," rather than "If you mow my lawn then I will pay you $20"
Glad to help!
Read through up to 5 pages of a cheesy handout and didn't get it. But this opened doors for me. Thank you. Subscribed.
Thank you so much, I’ve actually spent quite a while in attempt at gaining an understanding of this concept and you’ve clarified it in a quick and to the point way!!
I don't understand why many people hate this video. It's not very in-depth, true. But it's sure as hell very easy to understand.
lol this is just one piece of a whole logic series. It's merely one of the definitions provided 😆
thanks God that there is a speed controller in CZcams... : )
Note to self:
Affirming the antecedent = modus ponens = valid
Negating the consequent = modus tollens = valid
Denying the antecedent = logical fallacy
Affirming the consequent = logical fallacy
Denying the antecedent:
P1) If X, then Y
P2) Not X
C) Not Y
Affirming the consequent:
P1) If X then Y
P2) Y
C) X
excellent, thank you
Crystal clear explanation, thank you sir.
Wonderful. Glad it was helpful. Thanks for watching!
I think it helps if you think about the overall statement in terms of valid/invalid, rather than true/false
No, that would not be a useful way of thinking of it. Valid means that the syllogism has no contradictions, meaning that there are no propositions that are both affirmed and not affirmed, which is related to the truth value of those propositions.
So, you can see why using the word "valid" in the place of true would be problematic since it conflates to distinct logical concepts.
edit clarification
THANK YOU VERY MUCH!
+ArmenianGOD No problem, thanks for watching!
I thought the video was decent, so much hate lol.
Thanks. I don't know why certain videos seem to garner so much disdain. But then again, as a skeptic I don't know anything ;)
THANKS
1:34
I don´t understand how p being true and q being true implies that the implication is true. When I say "If I wear a red shirt then I am a man" I am aware that both statements are true but I don`t reckon that me wearing a red shirt IMPLIES that I am a man, for I can wear a blue shirt and still be a man, and woman wear a red shirt and still be a woman. For a more technical example, a company lowers its production and starts hiring women. The company then sees they are lowering their income, do to the lowering of its production. Can then the company conclude that hiring women implies that they will lower their income. It would seem to me, that for an implication to be true, it must be that (sorry I´m new into this) P1) p and q
P2) ¬p and ¬q
If I´m using this wrong, what I mean to say is that if I am now wearing a red shirt and am a man, and when I decide to change to a blue shirt I turn into a woman, THEN I can conclude that the blue shirt was causing me to be man and therefore wearing a red shirt IMPLIES me being man.
I would really appreciate it if you could answer this question. I love your videos!! ;)
-Cano
btw I get why the second one is false, I just don´t get why the other ones are true.
Remember that propositional logic is to do with structure. The only way something is False here is if it is inherently wrong. In other words, we're not examining the actual content of a statement here, but merely the possibility that any proposition P can imply any proposition Q. For some statements, we could say "this isn't true, but if it were true then this would be the case" and there is nothing inherently wrong with that form of argumentation. However, saying that P would lead to Q if true, that P is true, but that Q is false, is inherently contradictory, so we mark it as false. Hope that helps!
***** Is correct. I'll just add my two cents. You are correct that Logical Implication is very divorced from the idea of causality that we usually associate with if then statements. If your statement is "If I wear a red shirt then I am a man" this would only be correct if only men can wear red shirts, or if by wearing a red shirt you become a man. The point is that your implication is false as there is a case in which you can wear a red shirt and be a woman (antecedent true, consequent false).
However, there are a number of logicians out there that have the same intuition you do, that logic does not completely describe what we mean by implication. They have come up with other versions of logic than classical logic which have different understandings of what Implication is. Here's a link to a pdf paper on one:
folk.uio.no/josang/papers/JE2011-FUSION.pdf
And here's a link to the SEP on the logic of conditionals:
plato.stanford.edu/entries/logic-conditionals/
Hope that helps, thanks for watching!
Thanks for your responses! I'll rewatch the videos and read the links ;)
Carneades.org Okay, so if I have a red shirt on, I am a man. But if I am a woman and have a red shirt on, I am not a man. And if I do not have a red shirt on I may be a man or a women so both can be true?
That the antecedent and consequent are true proof that the implication is true?
Suppose my argument is:
I am in front of my pc
I'm sitting
therefore if i am in front of my pc then i am sitting
At this point, the premises of my argument are true, but I don't see how that proves the implication to be true. I've been standing in front of my pc.
I suppose an implication means that whenever the antecedent is true, the consequent would be true, but I don't think that a case where both are true proves that it will always be so.
It is not raining
If it was raining then I would have my umbrella
Why is the if then statement true?
Note that your statement is importantly different than the statement in the video. The statement in the video says "If it IS raining, then I HAVE my umbrella" Since it is not raining, there is no way to make this statement false. The statement you give would require a temporal operator e.g. H(R>U) For all past situations, if it was raining, then I had my umbrella. To disprove this in the same way you try to here, we would need H(~R) e.g. it has never rained. In which case the statement would be true, since there is again no way to make it false, since it has never rained (depending on exactly what you mean you might also want to add a G(R>U) it will never rain too). For more on Temporal logic check out this series: czcams.com/play/PLz0n_SjOttTca6krPm5TKsYDaBO6qjOP3.html
@@CarneadesOfCyrene ok sorry, it’s not raining, but if it is raining, then I would have my umbrella. U say there’s no way to make the statement false so it must be true. But what if there’s no way to make the statement true? Does that mean it’s false? Hence a contradiction? Would that mean we need to find a way to make the statement true? You could try to say the statement is already not false so it must be true. But what if I just said the statement is already not true so it must be false?
@@CarneadesOfCyrene Thanks a lot, I get it now!!
⊃
Ooo, fancy :)
;)
do you have an alt code for that?
P-> q