/sci/ - Science & Math

[Anonymous No.4704823]

Is logic worth learning?

[Anonymous No.4704856]

>>4704823
Logic is the ONLY thing worth learning!

[Anonymous No.4704873]

how does one lrn2logic?

[Anonymous No.4704868]

Logically, logic is worth learning,
according to logic.

[Anonymous No.4704885]

>>4704873
According to logic you can only learn logic if you leave 4chan because its full of non-logical candyasses

[ad hoc name No.4704920]

Ofc logic is worth learning.

One learns logic by reading e.g. a logic textbook. Copi's is the usual choice, but given what i know, Meaning and Argument sounds like a better choice.

Perhaps read something like Logic: A very short introduction, first. Even tho i read it was mediocre. Graham Priest has some cool ideas, even if it turns out that he is wrong.

[Anonymous No.4704925]

http://mind.ucsd.edu/podcasts/ Found this series of lectures on an introduction to logic on reddit.com/r/philosophy. Might not be exactly what you want, but they might be helpful.

[Anonymous No.4704929]

Prove the following statement: "Logic is the only way to prove something".

[Anonymous No.4704933]

Only if it's real <span class="math"> \bf{ Mathematical } [/spoiler] Logic. None of the bullshit fake logic in philosophy or CS.

[Anonymous No.4704935]

>>4704929
Only if you prove the statement "It is possible to prove something"

[ad hoc name No.4704955]

Let me know if u want me to send u some textbooks or otherwise guide u.

[Anonymous No.4704983]

>>4704933
better be trolling

[Anonymous No.4704990]

>>4704929
>>4704935

All mathematical proofs require a set of axioms.... so you are asking us to prove this in what?

[Anonymous No.4704995]

>>4704933
>None of the bullshit fake logic in philosophy or CS.
You know computer scientists study the exact same logic as mathematicians, right?

[Anonymous No.4705012]

Logic fails to describe the nature of existence, e.g., it is inapplicable to the concept of an ultimate cause for reality's being physical.

[Anonymous No.4705019]

>>4705012
Elaborate, please?

[Anonymous No.4705020]

>>4705012

Depends what logic you'd be referring to. There are countless forms of what constitutes logic.

[Anonymous No.4705023]

>>4704933
>None of the bullshit fake logic in philosophy or CS.
>bullshit fake logic in CS

wat

[Anonymous No.4705039]

>>4705020
>>4705019
A "first cause" is never the first. It is an effect of some previous cause, which is an effect of some previous cause, repeat ad nauseum.

[Anonymous No.4705047]

>>4705039
Needs more turtles.

[Anonymous No.4705049]

>>4705039
Ok then, what makes you think reality has a beginning?

[Anonymous No.4705058]

>>4705049
Wat? I'm pointing out that it can not, when thought about logically. How could you infer I did?

[Anonymous No.4705064]

>>4705058
>Logic fails to describe the nature of existece

[Anonymous No.4705083]

>>4705064
Yeah?
If you want me to say it I don't think there is a beginning to physical reality. Existence is eternal from one's ontological perspective.

[Anonymous No.4705102]

>>4705083
So.. Logic CAN describe the nature of existence?

[Anonymous No.4705118]

>>4705102
Wtf? A reason for causation is illogical at best, so I assume the contrary where no initial cause is there, a logical explanation for eternal recurrence seems more logical in itself, so maybe.

[Anonymous No.4705124]

>>4705102
Less convoluted answer: Yes, but not one for a beginning.

[Anonymous No.4705177]

>>4704995
>>4704983
>>4705023
>You know computer scientists study the exact same logic as mathematicians, right?

You know that truth tables and De Morgan's law in discrete 'math' barely count as real logic? Can you prove that König's lemma and Compactness theorem are the equivalent as well as prove each of them? Or even state the significance of Gödel's Completeness theorem and Soundness theorem? Did you ever have to prove Cantor-Bernstein-Schroeder or even Cantor's theorem on a CS exam?

[Anonymous No.4705215]

>>4705177
>You know that truth tables and De Morgan's law in discrete 'math' barely count as real logic?
I wouldn't say it barely counts as real logic, but it is completely elementary, yes.
>Can you prove that König's lemma and Compactness theorem are the equivalent as well as prove each of them?
Sure.
>Or even state the significance of Gödel's Completeness theorem and Soundness theorem?
Of course.
>Did you ever have to prove Cantor-Bernstein-Schroeder or even Cantor's theorem on a CS exam?
I can't say I have.

Why are you choosing your examples from so narrow a component of mathematical logic, incidentally? For example, I studied a lot of type theory and its reductions from various logics (mostly constructive), and I don't see you mentioning anything of that sort.

[resident /sci/ economist !!0CqB7P/574e No.4705228]

This shit aint logical.

>>4704995

Yeah, I like what you said.

I had to remind someone just the other day. There is only one kind of logic. There is no diversity in reason. Its universal and absolute. Thats kind of a nice feature.

[Anonymous No.4705423]

OP: mfw I forgot about this thread and refreshed it 4 hours later

[Anonymous No.4705451]

>>4705177

ur a fagget

>>4705215

ur cool

[Anonymous No.4705515]

OP:

I'm starting with "Logic for Dummies" by Mark Zegarelli. You have to crawl before you can walk. I'll learn the very basics without being completely discouraged.

I might move on to A Concise Introduction to Logic by Patrick J. Hurley after that and then maybe ease into a mathematical treatment.

Anyone have some input on a course of study? I'm quite serious about learning this subject well.

[Anonymous No.4705520]

>>4705451
ur jelly?

[Anonymous No.4705523]

biology is applied chemistry, chemistry is applied physics, physics is applied math, math is applied logic

so probably

[Anonymous No.4705521]

OP: I'm starting with "Logic for Dummies" by Mark Zegarelli. You have to crawl before you can walk. I'll learn the basics without being completely discouraged. I might move on to "A Concise Introduction to Logic" by Patrick J. Hurley after that and then maybe ease into a more mathematical treatment.

Anyone have some input on a course of study? I'm quite serious about learning this subject well. I'm not sure how I should progress.

[Anonymous No.4705525]

[Socrates !!T+RffVQayfz No.4705529]

You don't need logic, I mean, the entire GOP and Neocon voter base seems to get by okay without it. As do the people who deny climate change.

[resident /sci/ economist !!0CqB7P/574e No.4705532]

>>4705529

Ayn Rand once said that "The unexamined life is not worth living" and I basically agree.

[full !metalHJfCs No.4705543]

>>4705532
>Ayn Rand
>I basically agree.
oh god.

Also to actually make a statement instead of being an asshole

what if you led a life that had tremendous effect without anyone knowing (being a guy who points the way to a cure for cancer, or who develops a method for vastly improving ion propulsion and not being given credit, or a person who accidentally stops an assassination by chance etc etc)

if none of those things are worth living for then, well, what is?

[Anonymous No.4705546]

>>4705532

0/10

[resident /sci/ economist !!0CqB7P/574e No.4705554]

>>4705543

I actually think Ayn Rand is ridiculous. I dont give her any legitimacy at all. I was joking because the quote actually belongs to Socrates, who this trip named socrates seemed to disagree with.

>Thats the Joke

But nonetheless I agree with the statement. But to respond to your point:

1. If I lived a life curing cancer, that would be examined. The quote means I examine my own life and how to go about it. It doesnt mean other people examining my life.

2. I dont think the best life is necessarily one that has the most tremendous effect.

[Anonymous No.4705558]

>>4705529
Woah argumentum ad populum everywhere. How ironic.

OP, I see logic (and philosophy) as a sort of mortar to the bricks of science. You can build a reasonably sound house with bricks alone, but logic is what dictates the interactions of the sciences.

Why should we pursue the sciences? How do we know which science to apply in a scenario? Why is it that engineers are inherently gay and biologists not real scientists? Logic and argumentation will provide the answers to these questions and many others concerning interactions involving (but not necessarily limited to) the hard sciences.

[Anonymous No.4705560]

>>4704823
Logic is not only worth learning, it is worth using in pretty much everything you'll encounter.

>>4705012
log·ic
noun
1. the science that investigates the principles governing correct or reliable inference.
2. a particular method of reasoning or argumentation: We were unable to follow his logic.
3. the system or principles of reasoning applicable to any branch of knowledge or study.
4. reason or sound judgment, as in utterances or actions: There wasn't much logic in her move.
5. convincing forcefulness; inexorable truth or persuasiveness: the irresistible logic of the facts.

You clearly do not understand logic, what it means, nor do you have a single fucking clue about what you're saying.
You hate the word "logic" because you've been slapped down in the past for not using any, I'd bet.

captcha: arose ourturd

[resident /sci/ economist !!0CqB7P/574e No.4705571]

>>4705558

>.OP, I see logic (and philosophy) as a sort of mortar to the bricks of science. You can build a reasonably sound house with bricks alone, but logic is what dictates the interactions of the sciences.

But I think what you are saying isnt true.

Science, for the most part, is just very convincing inductive reasoning. Inductive reasoning being limited in its capacity. Evolution for example isnt proven, it just a great variety of observations fail to disprove evolution.

A lot of cosmology operates the same way. We make observations and then we which conclusions the observations fail to disprove (higgs bosons, curved space, dark matter). For a long time even gravity was just inductive reasoning, just the observation that I repeatedly fail to float away without any rhyme or reason to that observation.

[Anonymous No.4705585]

i hope at least that guy who gave the 0/10 realised that wasn't ayn rand quote but socrates

[Anonymous No.4705590]

>>4705560
>>4705558

I knew I had to study it in depth once I understood what validity and soundness were. It's powerful knowing that something must be true if the premises are true and the structure of your argument is correct.

[Anonymous No.4705608]

>people disregarding philosophical logic as illegitimate
>honestly can't tell if trolling

Seriously /sci/, please give me a glimmer of hope for humanity. Please tell me you're trolling.

[resident /sci/ economist !!0CqB7P/574e No.4705615]

>>4705590

>It's powerful knowing that something must be true if the premises are true and the structure of your argument is correct.

This is so true. During high school I went through a pretty emotional period that involved that realization.

[Ramblings. No.4705607]

For the harder sciences, I believe it is necessary to learn logic and to learn it well. There exists certain facets of logic which have practically no placement in mathematics, however.

I remember being in my logic course and I thought that it would help me out immensely in writing proofs; I was wrong. I just ended up devising truth tables, truth trees, derivations and manipulating conditionals, negations, etc.

The quantifiers section was nice, however. I learned how to develop very nice counter-examples, which translates well into mathematics which I need to disprove something.

[Ramblings. No.4705618]

>>4705607
My professor also had me do an extra credit project in possible world semantics which is, by the way, very cool. I'm thinking about writing a paper on philosophical mathematics and the Geometries.

[Anonymous No.4705626]

>>4705607

OP: What facets of logic should I study if I want to better understand proofs and how to write them?

[Anonymous No.4705628]

>>4705615
That was OP BTW.

[Anonymous No.4705661]

OP: I've vaguely understood what logic is for a while, but I never actually took the time to learn it. I've actually been obsessed for a while about how we know something is true. I felt like I should be able to get underneath it all and finally get some answers. I discovered axioms and realized that we can only dig so far. I think logic is the closest I can get to that.

[Ramblings. No.4705678]

>>4705626
In all honesty, I don't know. The logic course I took didn't really help me out in writing proofs. It did, however, help me in how to parse information. I'm able to look at a conditional and think of various ways to restate it and see if I can find something striking in the NEW statement that I can prove.

Derivations kind of help you see how a proof should go, but it can't help too much. It helps, but not completely. Truth trees can be useful because you break down certain things in a fashion similar to proofs whereby you're able to see each step, how one thing can lead to the next, etc. There's a point, however, where it becomes useless because you're not really incorporating any mathematics.

For any math major looking to increase their proof writing skills in a Logic course, focus on these: Rewriting statements(conjunctions, disjunctions, conditionals, biconditionals, etc), derivations, some truth trees, quantifiers(Logic courses actually handle these REALLY well; most math courses just give a 10 min explanation and that's it).

Regardless, I enjoyed the course.

[Ramblings. No.4705685]

>>4705678
Also, counter-examples. Those kind of come up on the fly, though. I was able to write mathematical statements in my other courses effortlessly and devise counter-examples pretty swiftly. Logic, like I said, helps you parse information better mentally and it restricts you to thinking of the subject at hand. I can see why people call logicians/hardline mathematicians cold; everything must take a second step in order to think clearly.

[Anonymous No.4705693]

>>4705685
>>4705678

I can't say I understand completely what you're talking about, but are you kind of saying that logic shows you how to move forward with what you have but not how to get where you want to go?

[Ramblings. No.4705760]

>>4705693
Pretty much.

A conditional P -> Q can be written as:
~Q -> ~P.
~P v Q.

So, you have three ways to prove the statement: The conditional, the contrapositive or the equivalent disjunction. The logic course doesn't really teach you a set way of proving it, though. It helps you indirectly by parsing the information in a structured format, but you can't translate the information you learn from a Logic course to, say, proving the isomorphism theorem in group theory. It just helps you categorize information better, mentally.

[Anonymous No.4705794]

>>4705760

This has nothing to do with what you just said, but I was curious.

Validity relies on the structure of an argument, so does this imply that there must be a connection to the the content of the preceding premise.

I guess what I'm wondering is if logic can teach you the limits of what you can say after your first premise. That is, the limits of what you can possibly connect to that first premise.

I'm sorry if that sounds ridiculous. XD

[Ramblings. No.4705817]

>>4705794
It doesn't. Someone asked that same very question in the fourth or fifth week of class.

The answer to that question is yes, BUT it depends. Derivations rely on the preceding/assumptions, but let's say I wanted to prove "If there is a city in a state of America, then that city is in America" I could say something like..

1. So, city is in state of America.
2. Dogs have wings, pigs fly and EK is attractive.
3. Since the city is contained in the state, and the state is in America, by transitivity, the city is in America
4. -> The city is in America.

The argument is valid, but obviously statement #2 isn't(it's a joke, EK. :P). It still doesn't detract from anything. 3 follows from 1. Nothing is wrong with it. It's not aesthetically pleasing, of course, but it's fine as far as I'm concerned.

Now, you cannot infer certain other things in your argument that are 'open ended' or can be false. Like.
1. The city is in a state of America.
2. The city is New York City.
3. New York City is in America.
-> Every city in a state of America is in America.

The argument falls apart at 2 because 2 does not follow from 1 at all. Even if the consequent is correct, the argument is wrong. I cannot infer that the city in question is NYC, or Kansas City, etc.

[Anonymous No.4705839]

>>4705817
So, at the end of the day, you must have a statement that follows or the argument is invalid.

Basically, you can have a lot of bullshit in between, but the argument must still have proper structure?

[Ramblings. No.4705857]

>>4705839
Of course. That was one of the first things I learned in my mathematics proof classes, actually.

Everything must be substantiated by a previous step and/or axiom. Nothing can just be developed randomly. That's one of the things that people miss when they start writing mathematical proofs for the first time. I made that mistake myself.

[Anonymous No.4705869]

>>4705857
I think that's going to be the tough transition for me. I can generally see how to progress using statements in English, and sort of see how to manipulate statements in symbolic logic, but mathematical statements seem tricky to me.

This might be stupid example, but for instance a statement like:

y = mx + b

That is a true statement, yes? How do I derive things from that? Is the structure of an argument different when you're dealing with mathematics as opposed to English statements or symbolic logic?

[Anonymous No.4705872]

Logic is like diet math. Instead of a lot of values, there is just one value that you follow over the course of a derivation or whatever: is the argument TRUE or FALSE. That's it.

Except when you're doing symbolizations. Then "doing logic" means "translating natural English sentences into this hokey made-up language with only 8 words"

[Anonymous No.4705875]

>>4705869
>y = mx + b

is an identity, not an argument

[Anonymous No.4705880]

>>4705875

Like I said, it might be a stupid example.

[Ramblings. No.4705881]

>>4705869

Technically, that's an identity in mathematics. Secondly, it's true .. but, in what context?

It's true in R^2 for a linear line. It is not true for R^1 or in R^2 when you're dealing with a line that is not linear.

Also, what do you want to derive from that? This is where Logic and Mathematics get a bit dicey because you're diverging from pure logic and into pure math by asking mathematical questions. These can't be answered by logic alone.

[Anonymous No.4705883]

>>4705869
Logic is really, really easy. If you can tie your shoes by yourself you can do predicate logic. Hundreds of thousands of desperate ghetto negro philosophy majors complete mandatory predicate logic courses every year.

A perfectly adequate introduction to predicate logic is Terence Parsons' totally free textbook, the first chapter of which is found at this link
www.ucs.mun.ca/~arthurs/Text0.pdf

[Ramblings. No.4705885]

>>4705883
It depends.

Certain truth trees and derivations can be hard. Truth trees are fine for me, but truth derivations can be a bitch because they require some creativity and a lot of rules.

That whole quantifier, truth table stuff is easy though.

[Anonymous No.4705886]

>>4705881
Well, saying I have a lot to learn is the understatement of the century.

What else do you need besides logic to answer mathematical questions? I know you need statements, true or false depending on what you're trying to do, and understanding of the statements that you're working with. Is that what you mean?

[Anonymous No.4705890]

Didn't Godel's incompleteness theorem pretty much prove that logic proofs only work because you can't prove his logic proof? viz. logic is only a system that makes sense because of its own rules, it's not some fundamental truth.

anyways: a is b if c is d
>not paying attending to 'is'
Being is not fully understood, unless you've read heidegger.

[Anonymous No.4705893]

>>4705890
lol wat....

philosophy students always make me laugh when they talk about godel or his work.

[Anonymous No.4705896]

>>4705893
math students always make me laugh when they say godel doesn't make sense.

>mathematical sense
>which was his point

[Anonymous No.4705901]

>>4705893

I always thought it was consistency and completeness.

If the system is complete, then you can derive statements that are inconsistent in the system. If the system is consistent, then it can never be quite complete.

I'm sure that's the Sesame Street version of it anyway.

[Anonymous No.4706452]

>>4705901
Yeah, that's true as far as I can tell.
The insight behind it is that there will always be a "godel sentence" in a complete system; that is, a sentence that is conditional upon its own truth value For example, "This sentence is false" is a godel sentence.