Basically a hypothesis is a statement that can be true or false. That's it.
The reason I refer to science in this very technical way is because the we are tackling the problem of classification. We are asking the question what is computer science? So to answer the question we need to use very technical definitions where the boundaries of categorization are extremely clear.
Again, at a very technical level a hypothesis is simply a statement that is true or false.
> Basically a hypothesis is a statement that can be true or false. That's it.
No, a statement which can be true or false is just a proposition. The reason that we care about "why" is that a hypothesis has bearing on many falsifiable propositions. It's the difference between "the specific rock I dropped accelerated at 9.8 m/s^2" and Newton's law of universal gravitation.
No, that is a proposition, not a hypothesis.
And the requirement that hypotheses be explanatory has nothing to do with culture, it is the distinguishing feature of the scientific method. See: https://blog.rongarret.info/2024/03/a-clean-sheet-introducti...
https://www.sciencedirect.com/topics/mathematics/statistical....
When you cut through all the cultural and human stuff we place around the scientific method, in the end it is a statistics problem at the most technical level. Everything else makes it fuzzy and hard to define.
Then you made an assertion that a hypothesis "is a statement that can be true or false. That's it."
Now, you're asserting that a hypothesis "is defined by statistics". Never mind that humans did a bunch of science before statistics were developed, this is different than your prior statement ("true or false. That's it."), and you seem extremely confident in it.
You're acting as if you have certainty in a statement, but you did not arrive at it by a proof. You've claimed that only the falsifiability of a statement matter, not its explanatory structure, but your own statements about hypotheses are structural and definitional ("defined by statistics", "at the most technical level", "ignoring all the cultural stuff"). You've asserted that a hypothesis is falsifiable, and intrinsically statistical, but you bring no quantitative data in support of this.
I don't know what activity you're engaged in, but it doesn't seem like a rigorous and principled search for truth. And you seem to be more willing to preach about the importance of falsifiability than to apply that concept critically.
Yeah so? You can make a statement and the actuality of that statement is either true or false. But how you prove that statement to be true is NOT possible. That is my claim. I am also saying it is POSSIBLE to falsify the statement aka disprove it... All statements have this property.
>Now, you're asserting that a hypothesis "is defined by statistics". Never mind that humans did a bunch of science before statistics were developed, this is different than your prior statement ("true or false. That's it."), and you seem extremely confident in it.
Well you're using the "what came first argument" to say that the original scientific definition came before the statistical definition so it's more valid. I disagree.
Language emerges from concepts in attempt to explain things we only have vague understanding of. Concepts like Life and intelligence are ill defined and used for communication on topics we don't completely understand. It's useful to communicate this way but it's useful only because either we don't understand something completely or because we use it as a shortcut. Usually a new word starts off in this fuzzy state and as we understand things better the word takes on a more rigorous definition. Science started out without us understanding statistics, so that's why you have a lot of older definitions attached to it. The technical definition of hypothesis is part of mathematics. That is ultimately the most correct definition but it's not the definition with the most utility. If push comes to shove and we want to categorize a technical concept like computer science, then the technical definition is what matters more.
>You're acting as if you have certainty in a statement, but you did not arrive at it by a proof.
What. I never said this. You are entirely misunderstanding. I said statements can either be true or false. The proof of whether it's actually true or false is a separate issue. My original claim is that proving something true is impossible.
>You've claimed that only the falsifiability of a statement matter, not its explanatory structure, but your own statements about hypotheses are structural and definitional ("defined by statistics", "at the most technical level", "ignoring all the cultural stuff").
I didn't say only the falsifiability of a statement matters. I never said this. I said falsifying a statement is the only thing we logically have the ability to do. It still matters to do correlations and other types of things related to science but at a technical level we aren't proving anything. At a technical level things can only be falsified. This is not to say OTHER things don't matter. They do matter.
>You've asserted that a hypothesis is falsifiable, and intrinsically statistical, but you bring no quantitative data in support of this.
Did I not post a link to a resource stating this? This is Data supporting my point. If you want quantitative data for the English definition a word, I'm sorry but that's just not physically possible. English definitions cannot be quantified into numbers for any meaningful numerical analysis.
I know your question is just sort of rhetorical. Basically you think I'm being too pedantic and you're trying to illustrate a contradiction in my own logic. I don't deny it. In the end I'm using my own personal opinion here. But I share my opinion here because I believe if that the MAJORITY of people completely UNDERSTAND what I'm saying they will AGREE with me. That's all. But again opinion. And either way nothing can really be proven can it? Especially for english definitions.
>I don't know what activity you're engaged in, but it doesn't seem like a rigorous and principled search for truth. And you seem to be more willing to preach about the importance of falsifiability than to apply that concept critically.
What are you trying to say here? This is false. And it approaches the point of accusatory and a lie. I don't preach the importance of falsifiability. I am just saying that is the only possible technical thing we can do in terms of determining if something is true or false. I get technical because we ARE CATEGORIZING technical concepts and definitions so it's appropriate to DO THIS. If we are casually conversing or trying to understand concepts then of course we can revert to the more laid back way of communicating and fuzzy way of defining things.
But what's actually going on here is that we are determining whether or not a technical concept: "Theoretical computer science" is math or not? Such detailed and rigorous categorization REQUIRES the use of detailed and rigorous definitions.
A hypothesis is a statement that is TRUE or FALSE. And THIS is HOW it's defined by statistics.
>I'm not going to waste time debunking every half-baked idea you can come up with.
I'm sorry but this attitude is offensive and against the rules here. I can't participate in any further discussion with you because of this. Thank you for your time and good day.
But it must also be useful. We don't do science just to enumerate trivial true statements, after all.
To be useful it needs to predict things.
And when it's falsified (say your hypothesis explained why swans are white, but you found a black one), it doesn't get discarded immediately. It's still useful until someone comes up with a better hypothesis that fits with white swans and the occasional black swan.
Sure it can be useful. Think of it like a mathematical theorem. What’s the point of the theorem unless it’s useful? Why would a book define a theorem if it wasn’t useful?
So theorems in math need to be useful. But such a quality is human and fuzzy in nature. What does it mean to be useful? And everyone has a different definition of useful. That’s why the definition of a theorem doesn’t include the term useful Even though generally speaking it’s a bit of a requirement if an author were to define a theorem in a book.
The definition for hypothesis that I use follows the exact same process. It is a rigorous technical definition that we are using for rigorous and detailed categorization of another term: “Theoretical computer science”.
Thus in the face of such a task I use the most rigorous definition of hypothesis available. I discard fuzzy terms like usefulness or expositions into “why” to determine categorization.
The statistical hypothesis which defines the term hypothesis in a very technical way. In fact, in statistics, hypothesis testing is basically the technical definition of the scientific method. Following this definition we can clearly see the boundaries of things more clearly.
Theoretical computer science does not involve hypothesis testing. It is mathematics because it involves axioms and theorems.
