What constitutes "proof"? Some people see proof as something with various requirements, others see no problem with "proving" some conjecture or premise, as soon as they see or read, something that might at least constitute the proof they want to see. They conjure up facts and actualities, from the slightest sniff, the merest waft of any breeze that tells them, "you have it now". Some others, being aware of the "proof is where you see it" phenomenon, will know that those seeking "the truth", of some conjecture, prosaic or otherwise, will be applying certain internal algorithms to determine certain patterns. That some who seek such things are eager to find the required resonance, as we sometimes do when reading something that someone else has invented - produced or projected, so to speak - we invent a "local production" somewhere. This is (of course it is), in keeping with the understanding that thought is the product of a human mind, which resides in a brain, mostly (for most of us), that a human brain behaves a lot like a system with its own resonances. That behaves algorithmically. We know about mathematics because our minds are inescapably mathematical. This field of study (Mathematical Science) is abstract, numbers exist in our brains as 'stable states', they are maintained by a biological computer, which is electronic, and biochemical. Like most things, there are two things that make the engine go. The neural electronic network requires the biochemical one, because a brain needs a body too. The thermodynamics is very inefficient, the computer doesn't 'go fast' except in a parallel sense. Those who have studied computing, networking, distributed and parallel systems, who know about algorithms, know that brains run on two circuits, that one sustains the other, and the brain has its own set of biochemical networking. Biochemistry study helps with that, since the undeniable computability, of biochemical systems has brought molecular computing (with modified DNA) to the lab bench. With brains, the whole thing is a dual processor, in a top-down sense, but both engines - the things that compute - are different, the network is heterogenous. So, if you know people who think proving things is about rabbiting on about how much mathematics they can do, point out to them that their computer is doing it (the neuro-biochemical one), so could they please adjust the ego function?
Logic is everything. There have been discussions here where people completely disregard logic on the basis that logic is irrelevant. Logic is the only relevance. It is the only way to prove things. You use logic in your proof, and people respond that your proof is irrelevant because logic is irrelevant. You cannot have a legitimate discussion or prove anyhting when people act like that.
Hmmmm....not so sure that logic provides the proof. What about love? Do you demand from your lover the logic that proves their love for you or does a smile, a soft lingering kiss, warm hug or intimate embrace just do it every time, even if you consider yourself unlovable. I would think not. :shrug: Same goes for religion. What logical proof, and yet the irony is that we will fight, and wage war and risk death for those two afore aspects without the logic being overtly clear. In a way, I wouldn't have it any other way Please Register or Log in to view the hidden image!
Note the two bolded statements. If you use logic 'in' yourproof, then the proof must include other things. Logic alone cannot be enough. We do not use (only) logic when we read and understand an argument. It is not enough. We need to check the words with the things they refer to. In part this MUST be an intuitive process. Logic alone is math. Once you try to connect a set of statements to the world you have to go beyond logic. Logic is insufficient. So is reason. Unless your definition of reason includes intuition.
Perhaps you don't but that would be the preferred method of reasoning. That would be part of the same process. Please Register or Log in to view the hidden image! Complete rubbish. That's where the distinction between the rational and the irrational becomes indistinguishable for the person using intuition. Theists use this method to support their arguments, allowing them to justify anything they want. They are pretty much opposite ends of that spectrum as far as methods are concerned.
Since this is a place of science, I'm going to respond only in the context that applies to discussions on SciForums, except those in the religion and crackpottery subforums where the rules of science are relaxed for our entertainment. As has been pointed out, abstractions can be proven true. Mathematics is the obvious example. Math deals entirely with abstractions and a hypothesis may be conclusively proven to be true according to the rules we have devised for those abstractions. (Although that proof may not be easy and we have to wait generations for some hypotheses to be proven true or false.) The abstractions of mathematics are useful in dealing with the physical universe, so we can say it is proven that two cats plus two cats equals four cats, and this can give rise to the assumption that non-mathematical hypotheses about the physical universe can also be (or have been) proven true. This assumption is invalid but it's common among laymen. The broader category of logical abstractions also supports proof. "If A then B" does not imply "If not A then not B," is true, period, because it has been proven true by the rules of logic. There is no circumstance under which this statement is false, and we can say with unassailable confidence that there never will be such a circumstance, because the statement deals entirely with abstractions. But scientific hypotheses can only be proven false. Because they are based on observations of the behavior of the natural universe, they are limited by the extent of our observations, and can never be completely proven true. After hundreds of years of testing a hypothesis energetically and repeatedly, actively looking for falsification and never finding it, we can invoke the language of the law and say that it is "true beyond a reasonable doubt," and elevate it to the status of a scientific theory. This is a safe thing to do because even though one of these canonical theories is in fact occasionally proven false, it happens so infrequently that it does not bring the canon crashing down. But this is not the same thing as proving it true.
But it is true that mathematics, studying it and using it, is algorithmical. The brain is too - there is far too much evidence supporting the 'singing neurons' idea - that thoughts are like a superposition of different 'waves' of co-operative activity between transient clusters of neurons (i.e. circuits). EEG waves are a 'coarse-grained' measurement, the brain isn't active in one dimension, like EEG graphs are, for starters. The first things you get taught - multiplying and dividing, counting - are algorithms or procedures. A mathematical formula - finding a solution - is a procedure. Our brains use internal procedures to 'map' the world constantly. When you 'do math' you're projecting algorithms onto something. It's abstracted usually, like writing down results of some measurement and applying some formula is an abstraction of a real event or series of events. These algorithms might have been learned but it's because of the way our brains work that we 'understand' how they work. Even that we understand what abstraction is.
Vkothii-Proof is relative to all parties involved. The fact that you have caused text to be recorded here is not proof enough that you exist. Can you be proven to exist to my satisfaction? So long as I don't show you what I would accept as proof, any attempt you make will be in vain.
What can you do, to identify this "proof" you say can't ever be satisfactory, what do you think it looks like? Seeing how you've made an assumption that you can't do so, because then I would "know" how to provide it? There's a way to prove to you I exist, to your satisfaction, but if you say what it is I'll know what you'll "accept"? But I can't prove (to myself) that you exist, either?
Vkothii-Precisely. Proof is MOST important in the eyes of the person something is being proven to. Thus, if I tell you that proof of your existence to me would be for you to come to my house, theoretically, you could do just that. Let's say that proof of your existence, for me, would be that the moon reversed it's orbit around the earth? Now the bar is set unreasonably, and you would not try to prove your existence at all. Knowledge of what the provee would accept as proof is a powerful tool to the prover.
Sorry, there going beyond logic is a different story. While there are metalogical concepts, logic is what humans use to prove things. Logic is 100% faith based. Logic is an assumption. However, intuition, non-logical irrationality, or anything else does not lead to proof. There is only logic under the only 2 possible conditions. 1. Either true. Or 2. Either false.
However, you can prove, using logic, that logic exists and that only certain logical 'arguments' are valid.
With only logic you cannot verify if the propositions are correct. Logic cannot relate a word to what it refers to. Logic cannot determine if a word is being used beyond its scope. Logic cannot tell whether the grammar of the language it is being used in is limiting. Logic said things could not be both waves and particles. This seemed logically obvious. Unfortunately it was not true. To connect logic and language to reality you must use non-logical tools. And please note, they are not illogical.
Implicit ad hom. You cannot determine the meaning of words and if they are being used correctly using just logic. For example. Please Register or Log in to view the hidden image! another implicit ad. hom. No. Logic really only helps you given that all the words are correctly applied, given that the grammar is not misleading us because language can mislead us about reality, for example. Validity can be checked logically. Determining truth requires other tools, in addition. They are both necessary in most investigations. You have to connect language to reality and do checks to see if it is correct. This does not involve logic. Logic can work via deduction or induction. This process is neither.
