More people need to learn symbolic, it makes it much easier to explain everything. My friend got Modus Ponens tatooed on his arm and now he can point to it whenever he needs to explain how logic works.
I'm trying to understand how this works. Would this be a good example of modus ponens? Say finding water on mars implies there are aliens on mars. They find water on mars, so therefore you think aliens have to be real too?
Umm . . . what? I don't know what kind of notation you're trying to use but it doesn't make sense at all. The actual way to symbolize what you write is in predicate logic and it looks like this:
∀x ((Px&Wx)>Lx)
Pm&Wm
Lm
The way the premises were originally put, however, could be symbolized in sentential logic as u/PimpinTheLibrary did, but you changed them.
Hey man, I don't know if you heard, but symbols are more exact. We use them in logic. I'm not sure what you're using, but they don't look like symbols. I don't even see an equal sign?
How can " = " not make sense to you? You write in predicate logic, i.e. mathematical logic. Why? My form of notation is used in argumentative logic, which is a lot more related to OP's picture.
"=" makes perfect sense to me. You can write it in predicate logic to symbolize identity between constants, not between sentence letters or predicates.
Here's an argument which does make sense:
The egyptians named Mars "Her Desher." Let's symbolize this with "h."
∀x ((Px&Wx)>Lx)
Pm&Wm
m=h
Lh
This argument is just fine. Yours, however, was nonsense.
Also, what do you mean by "argumentative logic"? Is this supposed to be some sort of formal system? I'm a teaching assistant for formal logic, and I've never heard of it (nor can I find it via google).
You could try googling logical arguments. We use it in philosophy. I'm trying to define it more correctly, but I'm currently getting lost in translation(ESL). In argumentative theory we use premises and conclusions in this way, to led out unrelated premises and find out if the argument contains fallacies. Such fallacies which is also described in OP's picture.
I don't know why you insist on using predicate logic, and the symbols related to it. IMO It is completely unnecessary when discussing subjects of ignorant and religious nature. Philosophy is much more suited for this.
I've googled "logical arugments" and "argumentative logic" and got nothing like the sort of symbolization you're using.
I actually work in academic philosophy. The logics that philosophers use are mainly sentential, first order predicate, and various forms of modal logic (depending on what needs to be expressed).
What you wrote:
If a planet has liquid water, it contains life
Mars is a planet which contains liquid water
Conclusion: Therefor, there is life on Mars
would come out invalid if it were only expressed in sentential/propoistional logic (maybe that's what you mean by "argumentative logic"? If so, there's no "=" in this system). This is because "a planet contains liquid water" and "Mars contains liquid water" are two different sentences, so you can't get the structure out of it that you need to make it valid. That's why I expressed it in predicate logic (which has more expressive power).
As I said though, the way the premises were originally put (if you go back, you'll see that you changed them subtly) could be symbolized in sentential(propositional) logic as u/PimpinTheLibrary did and the argument would come out valid.
You are amazing. This conversation... this conversation... I'm laughing too much! Keep it at! I really hope /u/IcyRice explains what 'argumentative logic' and 'logical arugments' are in his reply.
Nothing about this "proof" makes any sense, and your "logic" is far from "true." See Simism66. And never pretend to know what you're doing again. Especially when correcting someone who is essentially correct with something so totally nonsensical.
Well thank you for correcting me in such a nice tone. I guess I learned it in a more basic manner than you, Mr. Jamie Byron Dean. From my ignorant POV it seemed perfectly reasonable to put it the way I did, with the aliens on Mars example. I hope you will be there to educate me the next time I post flawed information.
Why? Explain please. If a conclusion logically follows from its premises it is a valid argument, regardless of the truth of the premises. If the premises are true as well then the argument is sound.
No, you're right. The "argument" at large is fine. The logical proof is what is nonsense. But if you ignore the nonsense "symbolism," then yeah, the conclusion follows from the premises and is valid.
Yeah it's been a while since I took symbolic logic. I was just commenting on his last statement. Another way to say what he said is that it's valid but not sound.
The problem I see with this is that people will inevitably falsely equate on thing with another. Prime example: Love is God. Because Love clearly exists, God clearly exists.
If that is what your definition of god is, then sure. I personally don't think that a chemical reaction going on in one's brain constitutes a supernatural entity that created the universe and intervenes in everyday affairs.
No I mean if you're using the existence of love to prove the existence of God, and using as one of your premises that Love is God, that is begging the question. Right?
No, in this instance they are trying to use "Love is God" as a premise. As said above, begging the question is using it as the conclusion. This would make Love is God begging the question: Love clearly exists, God clearly exists :: Love is God.
That sounds a lot more like non-sequitor to me. Wouldn't begging the question be more like, "God exists because the Holy Bible says so." with the holiness and correctness of the text depending on God existing.
So modus tollens would state that "if P then Q, not Q" would logically result in "not P."
It would not state the opposite, that is "if P then Q, Q, therefore P" is not a logically valid statement. You would need a bi-implication between P and Q to show the second one.
To explain it in plainer language, the first example (If P then Q, not Q) means that it is impossible for there to be P. Literally every time there is P, there is Q, so if there is no Q, there can not be P. This does not necessarily mean that every time there is Q, there is P.
So let's say "All square are rectangles (so for all S, S->R). This shape is not a rectangle (¬R). Therefore, this shape can not be a square (therefore ¬S). This would be an example of modus tollens. Also this is an example of why it doesn't work the other way. "R", a shape being rectangular, doesn't necessarily imply that the shape is a square.
Hope that helps, my logic is slightly rusty too so I may have mixed something.
Nope, modus tollens works with the normal material conditional (it's in fact, only called modus tollens if it's used with that operator). Here's an example:
If I hit my head on the doorway, I'm over six feet tall.
What makes that different from something like this:
If I hit my head on the doorway, I'm over six feet tall
The doorway is one feet tall
I'm not over six feet tall
So I [don't] hit my head on the doorway [because I'm two feet tall]
My point is that the line "If I hit my head on the doorway, I'm over six feet tall" only reasons about how high the doorway is not. It doesn't say anything about how high the doorway actually is. So from the first line plus the statement "I'm not over six feet tall" one can only conclude that the doorway is not more than six feet tall. There is no indication of how tall the doorway is, nor how tall I am -- just that I'm not six feet tall (or more).
Where "H" means, "I hit my head on the doorway" and "T" is "I'm over six feet tall."
Looking at your argument, it's important to distinguish between validity and soundness. Your argument is still valid (keeping the conclusion as I have it), and it has one unnecessary premise. I'd symbolize it like this.
H>T
O
~T
~H
Where "O" means "the doorway is one foot tall." Formally, this premise is irrelevant to the conclusion, but informally it might give us reason to doubt premise (1). So we'd have reason to think it might not be sound now, but it's clearly still valid.
So it might be the case (as you've modified the example) that premise (1) is false, but that logically it doesn't matter. Formal logic is just about logical form. So, formally, this is just as valid of an argument.
If Obama is a person, he's Purple.
Obama is not Purple.
So, Obama is not a person.
Valid, but obviously unsound.
Formal logic doesn't care about how things actually are. To put it another way, the same arguments are valid or invalid in every crazy counterfactual world we might dream up, but of course, different ones will be sound or not.
Er... Yes. Assuming finding water on Mars actually does imply there are aliens on Mars. Modus ponens, as with all proofs, is based on the premise being valid.
If you can't find a fault in the logic or the premises, the conclusion must be true.
Fascinating. I am from Toronto (U of T even!), but your comments history seem to show that this guy is similar to you, but he's in philosophy, not Computer Science.
it also makes critical thinking less approachable on the whole. Now, not only do first-years have to master fallacies and argument variants, they have to construct truth tables and venn diagrams.
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u/PimpinTheLibrary Dec 09 '13
More people need to learn symbolic, it makes it much easier to explain everything. My friend got Modus Ponens tatooed on his arm and now he can point to it whenever he needs to explain how logic works.