We are not sure if 1 or 2 are correctly defined or if they have an older meaning that was hidden from us by people who don't want us to know. How do we know that "one apple" is one apple if we don't know what one is and we don't know what an apple is?
Where is the proof that is based in reality and not made up bullshit? If "two" of "one" equals "two" then "two" is equal to "one" because "two" is "one"
Yes. I first put one apple on the desk in front of me and then I put another apple next to me. Then I count them and I will find I now have two apples.
2 years ago
Anonymous
Enlighten me Einstein, how exactly do you know that it's an apple and not an orange? How do you know you have "two" apples? It could just be "one" apple
2 years ago
Anonymous
>how exactly do you know that it's an apple and not an orange?
It doesn't matter what it is.
First I put one object in front of me and then I put another next to it (1+1). I then count them and find that I now have 2 objects (=2).
2 years ago
Anonymous
The base dishonestly here is saddening.
Want to convince them, just make it about money. The moment they get less than they are owed or taxed more is when they stop the stupid crap.
"Man", "Woman" and "Other" is a way to partition the set of all people. A biological male by default belongs to the set "Man" while a biological female by default belongs to "Woman". A person can choose to move from one set to another at their own choosing, for example a biological male can choose to belong to the set "Woman" instead of "Man".
2 years ago
Anonymous
>A biological male by default belongs to the set "Man" while a biological female by default belongs to "Woman". >presents a 5-year old male >I show you "A MAN"
2 years ago
Anonymous
Kek funny how the moron used "obvious cases to the contrary" to throw all the other criteria into the bin, yet, curiously, forgot to try and invoke the same hypothetical counter-scenario in the case of "obviously men" having the "inner woman" property, which would, by his criteria, also classify inner fender identity as unfit to determine who is and isn't a woman.
Apples come from Croatia, a white dominated country. This means apples are a symbol of white supremacy and should all be destroyed. Therefore, the correct answer is 1+1=0.Any other answer is unjust.
Formal logic is a field of math, and any application in philosophy is moronic self-refuting pseudointellectualism. There is nothing more cringe than a philosopher larping with logic in his infantile language games.
>Formal logic is a field of math
how does that contradict it being a field of philosophy. it is one of the most important elements of philosophy, and if you learn about philosophy, you have to learn about formal logic.
2 years ago
Anonymous
All "logic" in philosophy is a larp.
2 years ago
Anonymous
>hates philosphy so much he tries to convinve himself logic isn't even a field of it
2 years ago
Anonymous
philosophers desperately try to stay relevant by asserting that other fields actually depend on them. sad.
2 years ago
Anonymous
you learn it if you learn philosophy, and it's a branch of it. what are you going to say next, metaphyics isn't a part of philosophy? Ontology isn't a part of philosophy?
2 years ago
Anonymous
>you learn it if you learn philosophy
Why should I trust a philosopher? How do I know he isn't abusing his alleged epistemic authority to teach me something wrong?
2 years ago
Anonymous
This. They are never able to come up with relevant work done by actual philosophers in the last decades.
2 years ago
Anonymous
If any field could actually do anything meaningful without immediately veering into philosophy, we wouldn't have to remind you.
2 years ago
Anonymous
Logic in math: >rigorous >well-defined >yields powerful theorems and useful algorithms
"Logic" in philosophy: >hurr durr my baseless subjective opinion is an axiom now >I'll use this axiom to deduce the correctness of my baseless subjective opinion from it >am I being logical yet? >btw here's my false dichotomy between my baseless subjective opinion and an absolutely ridiculing strawman >therefore by law of excluded middle my opinion is true >I can't define "truth" in any meaningful way outside of math though
2 years ago
Anonymous
Logic in philosophy is every bit as rigorous as it is in math. At least that's what I gathered from the one modal logic course I was forced to take in undergrad as my gen-ed. We even proved that the axioms from theories T, S4 and S5 naturally arise from the type of relation R between the possible worlds W on a Kripke Frame <W, R>. What I'm trying to say is: it was really fricking fun and you should feel ashamed for badmouthing logic in any of its presentations.
2 years ago
Anonymous
I'd like to add that most logicians in the philosophy department of an uni are actually math PhDs.
Because it's circular. The only way to know that there's 2 apples on the right hand side of the equality is by counting them one by one, which is to say, by adding 1+1. Basically, everything that image is saying is 1+1=1+1. Also, Peano axioms tell us that s(1)=2, so 1+1=2 follows directly from that. If you want a more thorough proof starting from ZF, then I'm afraid I'm not smart enough to do that. Probably something to do with nested empty sets.
It really depends how you view an apple and what structure you endow it with. If we view an apple as a natural numbers object then we have to define a 1 or a 2 as for example In Principia Mathematica and follow this treatise to prove it. But you can also view an apple as a topological space embedded in R^3 with the standard topology and then you have to define what adding two apples is in this category. The plus sign in the OP picture is ambigous and intuitivelly it does make sense to add one apple to another and needs no explanation, but formally one has to define what operation and notion of equivalence is being used. The strict equality with apples is also ambigous because if you say one apple is equal to another then that is not the case because most apples aren't equal to each other as they come in different sizes and shapes. The sensible thing would be to talk about a homeomorphism of apples which is an another type of equivalence and different from the presented one in the picture. So the thing that matters the most is how you interpret an apple and what notion of equality and addition you define for them. But of course people who say proving this is crucial for completness or advancing mathematics is delusional, it is only important when doing a formal treatise of the subject.
I forgot, you can also use an equivalence relation where apples are members of an equivalence class of apples and then you can talk about equivalence with respect to the classes but this doesn't take into account the structure of distinct apples. But this falls under the special case of determining a general notion of equivalence
What you've got there, OP, is a model. Models are useful for checking that the arbitrary rules we invent to define how mathematical functions work give answers consistent with real world examples.
Likely because you don't accept any proof.
It is. Anyone claiming that 1+1=2 requires a proof is a pseud and should be avoided.
x+0'=x' does though
We are not sure if 1 or 2 are correctly defined or if they have an older meaning that was hidden from us by people who don't want us to know. How do we know that "one apple" is one apple if we don't know what one is and we don't know what an apple is?
We know all those things. 1 is 1 and an apple is an apple. What are you, moronic?
>1 is 1 and an apple is an apple
Can you prove either of those?
Just use the reflexive property
Where is the proof that is based in reality and not made up bullshit? If "two" of "one" equals "two" then "two" is equal to "one" because "two" is "one"
Yes. I first put one apple on the desk in front of me and then I put another apple next to me. Then I count them and I will find I now have two apples.
Enlighten me Einstein, how exactly do you know that it's an apple and not an orange? How do you know you have "two" apples? It could just be "one" apple
>how exactly do you know that it's an apple and not an orange?
It doesn't matter what it is.
First I put one object in front of me and then I put another next to it (1+1). I then count them and find that I now have 2 objects (=2).
The base dishonestly here is saddening.
Want to convince them, just make it about money. The moment they get less than they are owed or taxed more is when they stop the stupid crap.
That’s how we use the language, moron. Why would I care about a “hidden meaning” for the terms I and everyone else use daily?
i dont need to prove it. it's an axiom
>We are not sure if 1 or 2 are correctly defined
yes we are, we all collectively agree on the meaning of 1,2, +, = and apple.
um what if I take the seeds from the two apples and grow a tree and more apples? 1 + 1 apples = infinite apples.
Apples grown from seed are usually inedible.
>Apples grown from seed are usually unpalatable.
ftfy
what is "one"?
what is "plus"?
>what is a woman
"Man", "Woman" and "Other" is a way to partition the set of all people. A biological male by default belongs to the set "Man" while a biological female by default belongs to "Woman". A person can choose to move from one set to another at their own choosing, for example a biological male can choose to belong to the set "Woman" instead of "Man".
>A biological male by default belongs to the set "Man" while a biological female by default belongs to "Woman".
>presents a 5-year old male
>I show you "A MAN"
Kek funny how the moron used "obvious cases to the contrary" to throw all the other criteria into the bin, yet, curiously, forgot to try and invoke the same hypothetical counter-scenario in the case of "obviously men" having the "inner woman" property, which would, by his criteria, also classify inner fender identity as unfit to determine who is and isn't a woman.
What if I told you that 1+1=10?
What if I told you that both were correct?
Base 10 bot says you're not clever.
What if I told you 1+1=1?
What if I told you all 3 were correct?
Apples come from Croatia, a white dominated country. This means apples are a symbol of white supremacy and should all be destroyed. Therefore, the correct answer is 1+1=0.Any other answer is unjust.
ITT: an exploration of why philosophy has fallen from its once lofty perch and now is despised by the vast majority of humanity.
fomal logic is philosophy and has not fallen. It is a pillar of mathematics.
Formal logic is a field of math, and any application in philosophy is moronic self-refuting pseudointellectualism. There is nothing more cringe than a philosopher larping with logic in his infantile language games.
>Formal logic is a field of math
how does that contradict it being a field of philosophy. it is one of the most important elements of philosophy, and if you learn about philosophy, you have to learn about formal logic.
All "logic" in philosophy is a larp.
>hates philosphy so much he tries to convinve himself logic isn't even a field of it
philosophers desperately try to stay relevant by asserting that other fields actually depend on them. sad.
you learn it if you learn philosophy, and it's a branch of it. what are you going to say next, metaphyics isn't a part of philosophy? Ontology isn't a part of philosophy?
>you learn it if you learn philosophy
Why should I trust a philosopher? How do I know he isn't abusing his alleged epistemic authority to teach me something wrong?
This. They are never able to come up with relevant work done by actual philosophers in the last decades.
If any field could actually do anything meaningful without immediately veering into philosophy, we wouldn't have to remind you.
Logic in math:
>rigorous
>well-defined
>yields powerful theorems and useful algorithms
"Logic" in philosophy:
>hurr durr my baseless subjective opinion is an axiom now
>I'll use this axiom to deduce the correctness of my baseless subjective opinion from it
>am I being logical yet?
>btw here's my false dichotomy between my baseless subjective opinion and an absolutely ridiculing strawman
>therefore by law of excluded middle my opinion is true
>I can't define "truth" in any meaningful way outside of math though
Logic in philosophy is every bit as rigorous as it is in math. At least that's what I gathered from the one modal logic course I was forced to take in undergrad as my gen-ed. We even proved that the axioms from theories T, S4 and S5 naturally arise from the type of relation R between the possible worlds W on a Kripke Frame <W, R>. What I'm trying to say is: it was really fricking fun and you should feel ashamed for badmouthing logic in any of its presentations.
I'd like to add that most logicians in the philosophy department of an uni are actually math PhDs.
Proof?
Because it's circular. The only way to know that there's 2 apples on the right hand side of the equality is by counting them one by one, which is to say, by adding 1+1. Basically, everything that image is saying is 1+1=1+1. Also, Peano axioms tell us that s(1)=2, so 1+1=2 follows directly from that. If you want a more thorough proof starting from ZF, then I'm afraid I'm not smart enough to do that. Probably something to do with nested empty sets.
It really depends how you view an apple and what structure you endow it with. If we view an apple as a natural numbers object then we have to define a 1 or a 2 as for example In Principia Mathematica and follow this treatise to prove it. But you can also view an apple as a topological space embedded in R^3 with the standard topology and then you have to define what adding two apples is in this category. The plus sign in the OP picture is ambigous and intuitivelly it does make sense to add one apple to another and needs no explanation, but formally one has to define what operation and notion of equivalence is being used. The strict equality with apples is also ambigous because if you say one apple is equal to another then that is not the case because most apples aren't equal to each other as they come in different sizes and shapes. The sensible thing would be to talk about a homeomorphism of apples which is an another type of equivalence and different from the presented one in the picture. So the thing that matters the most is how you interpret an apple and what notion of equality and addition you define for them. But of course people who say proving this is crucial for completness or advancing mathematics is delusional, it is only important when doing a formal treatise of the subject.
I forgot, you can also use an equivalence relation where apples are members of an equivalence class of apples and then you can talk about equivalence with respect to the classes but this doesn't take into account the structure of distinct apples. But this falls under the special case of determining a general notion of equivalence
its not that trivial in math. This stuff actually requires a rigorous proof
required*
Okay, we proved it 100+ years ago rigorously. No we dont need to know the proof, lets just move on and do some real math. Hilbert was right.
so, 1+1=11 ?
You know, it's really just a definition of 2
>1+1 = 2 because... 1+1=2
Basic addition is usually defined axiomatically
What you've got there, OP, is a model. Models are useful for checking that the arbitrary rules we invent to define how mathematical functions work give answers consistent with real world examples.