I would say "some parts of mathematics" is an understatement. they are everywhere on mathematics, not especially on geometry, but especially in set theory
NOTES Spectrum of Rules of constant relations from which we perform deduction, induction, abduction, and guessing (trial and error). 1. Axioms must be declared: Ideal. Arbitrary. Presumed(declared) True. Used in formal Logic, Mathematics. 2. Premises may be assumed, and may be true, false, or unknowable. Pragmatic. Used in argument. 3. Laws (Theories) must be identified: Real. Laws are true with stated limits. Constrained. Used in Sciences. The most common problem I deal with correcting is the conflation of the three.
May I ask: what do you mean by “arbitrary” for axioms? How can you say an axiom is “arbitrary”? Surely there is a REASON a given axiom is chosen ? So why call it ARBITRARY?!
Good video! As a Math Degree student, I couldn't give a better definition of "Axiom". All in Maths is constructed either by axioms or by definitions, and in many cases you use "axioms" in order to define something. For example, if you want to give necessary condition for anything to be called "Set", you give a set of rules that must that must be verified (in this case, the ZFC axioms). It's not like an universal set of rules, but an universal set of rules that must be fulfilled if you belong to the class of "Sets". Similarly, the peano axioms give a necessary condition for anything to be a "natural number".
This is why I frequently refer to axioms with materialist atheists as 'articles of faith' & speak of traditional articles of faith as 'religious system axioms'.
@Intellect, reason&Logic Use your brain You give them too much credit implying belief re-evaluation & a personal existential connection to their worldview. Mostly they just get a bit huffy.
I guess materialist has something for axiom which can be observed in reality and which exist. Religious person has something for axiom which is just made up and has no relation to real world.
@@sasilik That rests upon the axiom of sensory trustworthiness & accuracy of conscious interpretation of the inputs. Religious system axioms and resulting structures are judged "by their fruit"; which show comparative multi-generational advantage against atheistic materialist societies, the latter consistently failing due to demographic collapse, social atomisation, existentialist angst & ennui.
This video explain axiom really well. But i want to ask something. Isn't the fact that we believe our minds are able to reason or find truth is an axiom by itself? We believe that our mind have the capability to find truth by the get go right? We assume that is true withouth any proof. And even if we try to find proof that support our assumption that our mind can find truth. It's going to end up in a contradiction. Because to find proof that our mind able to reason, firstly we have to assume the very thing we are trying to prove. So based on this, i conclude there is actually some axiom that we have to take.because without, we couldnt know or believe anything.
Welcome to philosophical skepticism. That is a classical skeptic argument against foundationalism. As a skeptic myself it is not concerning, but it is a big issue for most everyone else. :) ua-cam.com/video/YNFyQD8zxkM/v-deo.html
Good question. One way to think about this is to not put the epistemic cart before the metaphysical horse (ua-cam.com/video/fSGwUyfxgFM/v-deo.html). The metaphysical question is about truth, and metaphysically axioms and theorems are no different. Many think that things like logical or mathematical axioms are true independent of our beliefs about them. Before math was discovered, did 2+2=4? If you think yes, then logical and mathematical axioms are independent of our beliefs about them. So it does not matter if we prove them or assume them, they are true or false independent of our beliefs about them. The epistemic question is about our justification for believing these things. Here's where things become challenging for axioms. If they are assumed without argument, it seems like we have no justification for believing them. If everything we believe is built up from some set of axiomatic assumptions (ua-cam.com/video/YNFyQD8zxkM/v-deo.html), and those assumptions are unjustified, then everything we believe is unjustified. If justification is a prerequisite for knowledge, then we don't know anything. This is the case for philosophical skepticism. (ua-cam.com/video/S2sK_EOKb1Q/v-deo.html)
@@CarneadesOfCyrene Proper justification for any system of axioms cannot be found within the realm of the True, but rather the Good. Intuitively, to say something is "true" means it is straight, linear, not having deviatied from a single well defined trajectory, such as the path an arrow takes when fired from a bow. The realm of the True is concerned with the proper transformation of _meaning_ such that no information is gained or lost. Theorems of an axiomatic system are by definition the true statements, i.e. statements which do nothing but linearly extrapolate the explicit meaning of the axioms into new forms which better reveal all the hidden meaning which was implicit in the system taken as a whole, but not manifest in the statements of the axioms themselves. The realm of the Good concerns that which is favorable or virtuous with respect to some desired goal. For any axiomatic system, there are an infinite variety of systems (written in the same language) that are all equivalent in meaning despite vast differences in their explicit form. How then do we decide what the value of an axiomatic system is, so as to justify its use over others? As they say, the proof is in the pudding - the nature of the Good is not subject to logical analysis and must be borne out in time, but there are heuristic tools like Occam's razor which can help one avoid wandering blind through dark alleyways filled with gold. We want to be able to see the treasure hidden within - to understand what we have written and not just intellectually know it is in there by way of pure logic - so our goal is to find axioms written in a way which allows us to readily comprehend the underlying meaning and give us enough meaning to keep us interested, engaged, and occasionally pleasantly surprise us for the foreseeable future.
@@williamwesner4268 Can one then prove that Truth exists? If the point is to conserve knowledge, how would one ever actually reach the truth? Wouldn’t the search lead to something along the lines of a “knowledge regression?
I think the way this works is you make up whatever axioms make sense to you, then build your logic based on those axioms, if you find contradictions and paradoxes then you have to rethink your axioms.
they are ' subjetive ' only in the sense that everything in the theory comes from a 'Subject '; they are objective in the sense of their validity, ie, they are objective or, they have objectivity.
I personally find Tetralemma logic found in the east to be more viable and less rigid than the binary logic found in the west. It also helps in understanding quantum physics which wouldn’t make any sense using the rigid forms of binary logic.
Why can't this be an axiom: "something can exist" only the existence of that idea proves that it's correct. It doesn't need anything outside of it to be true
Axioms in mathematics is not particularly special to geometry. Most of mathematics work off axioms. Notable examples include the Peano axiom, the field axioms, and the Zermelo-Fraenkel axioms.
@Gurkirpa Singh The Peano axioms define what natural numbers are, the field axioms define what a field is, and the ZF axioms is the foundation for set theory. You can look up their Wikipedia page for more information.
Hey, I love your videos, I am learning so much from them. However I keep on stumbling on your claim that you are a sceptic. Something feels off about it. You said that as a sceptic, the axiomatic nature of logic is problematic. However, it seems to me, that scepticism itself rests on one or more axioms. The main axiom of a sceptic is that one should doubt claims, which one has not proven. This itself seems axiomatic to me. More then that, as it is an axiom, it is a self-contradictory one, because it claims that axioms themselves are not valid.
that's not the only thing that seems self contradictory to me Isn't the vary notion that we can reason /find truth an axiom by itself? And us doing anything that involves logic and reasoning implies that we adopt this axiom, therefore anything we conclude has a truth value means we have adopted the above axiom, even if we can prove that this is not the case we still have to take the assumption that we can find truth (since we would regard our proof to be true) What's also interesting is that I'm using reasoning to propose this as well, so the statement 'the fact we believe our mind can reason and find truth is an axiom' is built apon reasoning and logic
@@giventhamsanqa6517 I totally agree. The very act of reasoning presupposes that the mind is capable of recognizing true beliefs as true and false beliefs as false. I think a lot of the problems that scepticism adresses is based on the implicit assumption that reason is the only valid source of knowledge. Reason always argues for the truth of some A by means of some B. Of course you run into the problem of having to explain B with something other than a or b. The solution are axioms. No I think the error lies in assuming that axioms cannot be known. However there is no reason to justify that. Of course we can have intuitive or direct knowledge of something. Once you allow for knowledge that is not derived from reason all sorts of problems disappear. I can demonstrate that we actually do have knowledge that is not rationally aquired. Pinch yourself. You know that you feel what you feel. You did not arrive at this knowledge through reason. So we know that it is possible to have knowledge of something directly. Other things as well can in principle be knowable through direct knowledge. Reason then builds on these. Yes my example was one of sensation, but in principle the same thing can hold for objects of thought as it holds for objects of sensation. I think Descartes used this to start his axiomatic system. He knows that he had thoughts. Having thoughts he concluded that he must exist. I wouldn't agree with Descartes, that existence follows from the experience of thinking. The notion of existence might be an empty meaningles concept and as Buddhist point out personal identity might also be a false belief, but still He has a point at pointing out that he had knowledge about having experience. He knew that he was thinking.
Yeah, like how an aphorism can also be an idiom, like _a bad penny always turns up_ is an aphorism, but since it doesnt mean what the group of words literally means (a bad penny means a bad person) it's also an idiom. Isn't language fun? :)
I would like a presentation of Chrysippus' Dion/Theon identity puzzle, which Long and Sedley wrote about, putting special focus on making it more clear just what or who Dion and Theon are. That is, as I have read about it, it seems to be just a more confusing way of speculating on the identity of a person whose body at one point has two legs, and at another has but one - whether he is a "person" who had two legs and now one, or a person who had one leg throughout his existence, but did not exist until the two-legged body lost a leg.
That is the case for philosophical skepticism. You must assume axioms to prove theorems, but you have no basis for assuming those axioms, otherwise they would not be axioms. That lack of justification makes the case that we don't actually know any of those axioms, or the theorems based on them.
@@encouraginglyauthentic43 I'd imagine not, people in general conflate truth of fact versus conviction of opinion, and they don't understand what valid logic does and doesn't mean.
I have been using the term "axiom" for a while now, and i would like to hear if I am using it correctly. I say something like sports is an axiom, and the rules under a particular sport, like lets say baseball rules, are presumed to be true and not requiring proof. Also said baseball rules are only true within the axiom they are in, so baseball rules are only true within the axiom of baseball.
Hmm. Within the system of "The Rules of Baseball" rules which are stated explicitly could be loosely referred to as axioms. But rules that are not stated explicitly, but are rather proven from the existing rules would be theorems. The axioms are the ones that are written down that can't simply be derived from other rules. There's a deeper question here as to whether something like the rules of baseball can be true or false. If you are a coherentist about truth how they can be true or false seems pretty clear (ua-cam.com/video/Oyf0vHpdIFs/v-deo.html), but this is a harder claim to back up for someone that is a correspondence theorist (ua-cam.com/video/un0KbGfsdUM/v-deo.html). What thing in the world makes one set of rules true and another false? (Note that this is a different question from what makes us justified in believing one set of rules over another).
No. Game of baseball is built on axioms. You start with axioms (rules) and then you have many many ways to play the game within those rules. The correct sums of those combinations are called axioms. So, the game of baseball will require axiom (rules) but also c sets of those rules applied. Just because you did something that agrees with a rule of baseball (for example, throwing a ball according tithe rules) doesn't mean that you actually played a game of baseball. But, you can build a game of baseball by applying those axioms.
@@DennisPulido So basically, the Game of baseball is a Theorem created by applying rules of Baseball in a correct order (or multitudes of correct orders). Pitching a ball, catching a ball, running to a base etc. and there are many different orders which increase or decrease your chances of winning.
@@SabbatarianCalvinist thats a meta statement The advice he gave is to stay skeptical of all statemnts (first order) To be skeptical of staying skeptical is a second order thing - they aren't the same thing
0:37 not exactly: a logical system begins by defining the expressions that belongs to the language, ie , the so called well formulated formulas--wff--; axioms are not the rules, rules of inference have to be declared, and usually the rule is modus ponens or natural deduction rules like in Gentzen system. That the axioms are taken as primitive assertions is not related to a belief practice, it is more on the ' conventionallist ' nature of logical pre- structure work in mathematics. Since Euclides, the axioms are taken as true propositions, an aspect that was changed by David Hilbert axiomatic style.
I have to write a free essay after the holidays. The theme is, “Life is not an axiom. ” I know basically what an axiom is, but the subject itself doesn’t make any sense at all. Can someone help me there??? Because I can’t ask the teacher, because it’s holidays.
@@baikentram9992 they would simply not adopt that moral system as they reject its core axiom. This is why all moral systems are ultimately subjective--they all rely on axioms which are always a value judgement of some kind.
The axiom would not need proof, but because all moral systems rely on such axioms(which are all value judgements) all moral systems are ultimately subjective and cannot be proven "true" except within the system itself. If one rejects the axiom, one need not adhere to the system. That's my view. Cheers :)
I think a more accurate one would be this: Pain A should be avoided if and only if the potential happiness that comes from it doesn't outweight the pain. This also solves the masochist problem-the happiness that the masoschist experiences is better than the pain he or she experiences.
Hey Carneades, since all moral systems are based on a value judgement as an axiom (wellbeing should be enhanced, God's will is good, etc..) Doesn't that automatically rule out an objectively true and binding to all moral system? I see it as _if_ you accept the basic principle/axiom of a moral theory _then_ certain behaviors that are in line with that axiom are objectively preferable and behaviors contrary to that axiom are objectively wrong. But the moral theory itself is based on a value judgement, and is therefore subjective based on what one values. I think many people share many basic moral values based on our evolution as a social but not eusocial species, but that appealing to this fact to make some normative ethics "true" would be an appeal to nature fallacy. Lastly, no I do not think there is one true logical system. I am a logical instrumentalist just as I am a scientific instrumentalist....I value utility in navigating my experiences. I care not for what is "real", Matrices, Cartesion Demons and Solipsism be damned! :)
Morality = Reciprocity. And it has to be. Moral norms are members of a portfolio (network) that may be reciprocal or not. Moral intuitions vary by the individual's reproductive balance of reciprocity vs proportionality in the given set of moral norms. So whenever speaking of 'morality' which thing are you talking about? Ideal knowable (reciprocity). Ideal unknowable (anything not immoral and therefore irreciprocal is moral. What we mean is, what's good? Not what's moral?) Moral Norm (evolved market for prohibitions), Moral intuition (your bias given your reproductive and survival demands) - in other words, your tolerance for proportionality.
@@curtd59 except that morality does not equal reciprocity. Morality simple means any system of standards for right or wrong behavior. Divine Command Theory is a moral syatem that is not concerned with reciprocity, only duty to obey the perfectly moral commands of a God. To DCT, that is what determines right or wrong. A principle of reciprocity can be _a_ standard/axiom of morality but it is not _the_ standard. There are several competing moral theories and moral philosophy has yet to(and never will do, imo) find a One True Moral Theory or One True Moral Axiom. As Carneades said in the vid, the fact that axioms are assumed without proof disallows there _being_ a One True Morality.
@@munstrumridcully empirically, across all time and all civilizations, morality within the limits of proportionality available to th class consists of reciprocity. international law is governed by it. humans would find no rational value for cooperation otherwise. And we would not (and do not) cooperate under irreciprocity. So again morality equals reciprocity, and it would be interesting if you would try to find a case under which a tradition or norm or even law (not legislation, which is arbitrary), does not seek to produce reciprocity between people. You will find that what constitutes reciprocity within different social orders differs. But they will always be reducible to reciprocity. YOu may lack the knowledge to ascertain that on face value, but once you understand the economic system you'll rapidly see it's reciprocity. We envy one another and claim we demand POSITIVE freedom, and POSITIVE rights and POSITIVE morality but these are negotiation tactics. You are welcome to find evidence to the contrary.
@@curtd59 I dont think you understand what moral theories are or why there is no one true morality. One of the most popularly adopted moral theories today is utilitarianism, which does not adopt an axiom of reciprocity but rather three axioms : Pleasure or Happiness Is the Only Thing That Truly Has Intrinsic Value. Actions Are Right Insofar as They Promote Happiness, Wrong Insofar as They Produce Unhappiness. (Notice no mention of reciprocation. Increasing happiness via pure altruism without reciprocity is goid under this system) Everyone's Happiness Counts Equally.(Again, no mention of reciprocity, only that no one person's happiness is more important than another's, so maximizing your own happiness by inflicting pain on others is not cool) So, is utilitarianism a false morality? Please tell that to the moral philosophy journals, I'd love to see the peer review process on that :)
@@munstrumridcully Actions are right so long as they dont produce unhappiness in others. find me a case where unhappiness is not ir-reciprocity. find me a case where your unhappiness is not irreciprocity. if you engage in altruism (lets ignore for a moment that we may not do it ever) you are not acting irreciprocally although many people reject altruistic actions as attempts at debt creation. What is moral is whatever is not immoral. try to falsify that.
There are many axioms of logic, there is not just one. The rules of replacement and the rules of implication could be considered one set of axioms. Check out our series on the 100 days of logic for more (ua-cam.com/play/PLz0n_SjOttTcjHsuebLrl0fjab5fdToui.html)
Logic itself is basically the result of the majority's will to believe something to be true, I don't see any other way to prove it. if one doesn't conform with the belief of the majority then he/she will be considered illogical, but the question is, how much does the opinion of the majority actually matter? and is it fair for the majority to force their belief on the minorities? Logic is part of our existance.
Unfortunately, I don't feel that I'm yet well-read enough to weigh in on classic vs. non-classical logic, their popularity (or lack thereof), and how this is relevant to truth.
I am hoping to do a series on non-classical logic once we are done with set theory. The logic series generally take longer because they are so involved, but they are also so interesting.
@@CarneadesOfCyrene Well I'm looking forward to that; thank you very much. I agree. I also feel that you are providing invaluable insight with respect to logic. I feel incredibly thankful for Carneades.Org and the exceptionally apt breakdowns of logic that you provide. Besides making top-notch philosophy videos, I have yet to find another video creator who so articulately and passionately teaches in-depth logic lessons while also making said lessons particularly easy to digest, all things considered. I've always been impressed by this content and cannot find the words to accurately express my appreciation for the phenomenal work that gets done here with respect to both logic specifically and philosophy as a whole. BIG mahalo to you and everyone that makes this happen, my dude 🙌💯 sending much appreciation your way! 😁
Ik it’s outta place here, forgive me, but please read with an open mind The gospel, the good news is salvation from hell. And here’s how to get it, the Bible makes it as clear as can be. “Believe on the Lord Jesus Christ and thou shalt be saved”, acts 16:31. Words from your mouth don’t even need to be accompanied, just “believe on the Lord Jesus Christ and thou shalt be saved” from hell, it’s this easy!!
The challenge is that most axioms are stated very abstractly. You might get axioms in geometry that are not. E.g. A straight line may be drawn between any two points., but these are less common in logic.
In a way, operating under a logical system is like tentatively accepting new scientific propositions (or maybe even conducting basic scientific experiments). You start with what you've been given and then immediately interrogate reality to see its implications hold water. The moment something doesn't add up, you go back to the drawing board to see what can still be kept and what must be discarded. As long as the laws of identity, noncontradiction, and excluded middle - or rather the framework that they constitute - allows us to produce results that are can be verified in reality, we have all the more reason to trust that these axioms have us on the right path.
I couldn't understand a single frame from this video. Not the youtuber's fault, though. He seems to explain it thoroughly. I just couldn't understand this concept, unfortunately.
Axioms aren't things that are assumed to be true. They say that, for the moment, we are talking about any system that obeys the rules given by the axioms. If a system obeys the rules then some statements cannot avoid being true : they are the theorems. For instance, take the axiom There are at least three things. This is true of some subjects, false of others, and don't know for the rest. Now talk only of subject for which it is true. Then There are at least two things cannot avoid being true : it is a theorem (and you can prove it).
In abstract, one does not need to assume an axiom to be true to speak of validity of an argument. But no one outside the ivory tower cares that an argument is valid if it is not sound. For soundness, you must assume that the axiom is true of this system. Additionally, I think your definition will run into some problems with the Tortoise and Achilles (ua-cam.com/video/WS0bAKxmO_w/v-deo.html) i.e. we can't claim that a implies b without assuming that a and a implies b implies b and down the rabbit hole we go. Even to make claims about validity, you need to assume an infinite number of propositions.
When doing applied maths it is just as important to choose the right pure maths as it is to use the pure maths correctly. For instance, you can navigate round the British Isles using Euclid's axioms, but if you navigate from Britain to Australia you find that parallel lines cross each other. The video ends by asking if we can accept some axioms without proof. From this example the answer must be that it depends on the problem being investigated. If the chosen axioms agree with observation then they are useful. If they don't then they are not useful. But comparing with observation is not "proof" and for most problems there is no possibility of proof. Presumably "soundness" means you've used appropriate axioms in your applied maths problem. You don't "assume" they are true, you justify their use. Unfortunately, text books often omit the justification and just say assume so and so. This is just a teaching convention.
The Achilles and the tortoise problem demonstrates that a finite distance can be split into an infinite number of sub-intervals. The usual discussion then declares that a finite time cannot be split into an infinite number of time sub-intervals, hence the paradox. This is a very dubious argument.
‼️‼️Good News‼️‼️ The gospel, the good news is salvation from hell. And here’s how to get it, the Bible makes it as clear as can be. “Believe on the Lord Jesus Christ and thou shalt be saved”, acts 16:31. Words from your mouth don’t even need to be accompanied, just “believe on the Lord Jesus Christ and thou shalt be saved” from hell, it’s this easy!!
‼️‼️Great News‼️‼️ The gospel, the good news is salvation from hell. And here’s how to get it, the Bible makes it as clear as can be. “Believe on the Lord Jesus Christ and thou shalt be saved”, acts 16:31. Words from your mouth don’t even need to be accompanied, just “believe on the Lord Jesus Christ and thou shalt be saved” from hell, it’s this easy!!
Ugh! Axioms are not PRESUMED true. Axioms are true because they HAVE to be true, otherwise thought is impossible. Without the axiom of identity, nothing you say has any meaning--it refers to NOTHING (which is not understood until you understand SOMETHING--which has identity).
Several points. First, you beg the question against the skeptic. Simply because you need to assume X to prove some Z does not mean that X is true. I need to assume that I am omnipotent to prove that I am God, but it does not follow that I am omnipotent. Just because you need to assume some axioms to prove other claims does not mean that those axioms are true. If anything it means they are unjustified. As a skeptic, I doubt you can prove anything. Second, the basic laws of logic are rejected by many non-classical logics. Non reflexive logic, for example, rejects the law of identity. This does not destroy meaning or thought, it is simply a different logical system. In the same way that non-euclidean geometry does not make geometry impossible, non-classical logic does not make logic or thought impossible.
@@CarneadesOfCyrene I am not assuming anything! That's the point. You have lots of videos on here. None of them have ANY meaning without identity. i.e. you have a PERFORMANCE problem. You can't make any statement without using identity and that is why A=A is an axiom.
@@ParadymShiftVegan Can you explain your statement without using identity? Tautology has no meaning without identity. Nothing you say means anything without identity. It becomes jibberish. The word 'assertion' has no meaning without identity. Identity is necessary. If AA, you can't even formulate a tautology. If you want to give up A=A, then what is being said? This is the point of an axiom, and what Aristotle explained a long time ago. A=A is an axiom that bridges the metaphysical to the epistemological (what exists to awareness of existence). Without it you can't know anything, and thus can't say anything (of consequence or meaning), yet here you are attempting to say something of consequence and meaning. NOTE: this isn't a proof, (proof is a statement reduced to axioms), but rather a necessary fact about awareness. To be aware requires that you be aware of something, but in order to be something cognitively it has to have an identity. I will repeat the earlier statement. This is a USE or PERFORMANCE issue. You can't make a statement (any statement of consequence--which leaves jibberish) without using 'identity' which is why it is an axiom. It literally is the logical base one has to start with. Any argument put forward against this is performatively refuting itself. I will try this another way. I think you are treating A=A as an arbitrary predicate, but it isn't. What would 'Tautology' mean if Tautology Tautology?
@@nicosilva4750 The moon exists even if I can't describe it. There's no evidence that the things you are talking about do. There is no "identity" you're talking about that we have any objective evidence for. You're not talking about reality, you're talking about your attempt to understand it.
I believe there’re in fact axioms that cannot be accepted, otherwise, society couldn’t function. For example, much of modern gender theory is predicated on axiomatic conclusions, like people identify as and believing themselves to be a women (an axiom), yet can’t even explain what a women is (a definition). The world cannot function on axioms alone, as to do so would be incredibly intellectually regressive. For example, we assumed the world was flat at one point (something people believe to this day), yet we know very well that it isn’t, yet at one point, you’d of been fool to think to the contrary. We would still be in the Stone Age if all that we predicated our reasoning on were axioms.
That's fine and all, but you're advocating for either paralysis or submission to our instincts/proclivities which aren't driven by reason. The foundation for all currently in use systems of logic have to use some assumptions. If you're in a jury will you make it a hung jury under every circumstance that has existed in every justice system in the past, because you object to the validity of all presented induction and deduction?
@@christianbethel What I mean is that proving something requires a axiomatic standard, where you bring some statement or conclusion to compare and see if it holds true. For example, x=x. 1=2, 1=35, and 1=apple are all wrong, but only with respect to that axiom. Without it, they are all equally valid. So if we had absolutely *no* axioms. Every single statement would be equally plausible, and there would be no way to "prove" anything. At least that's how I see it.
Ik it’s outta place here, forgive me, but please read with an open mind The gospel, the good news is salvation from hell. And here’s how to get it, the Bible makes it as clear as can be. “Believe on the Lord Jesus Christ and thou shalt be saved”, acts 16:31. Words from your mouth don’t even need to be accompanied, just “believe on the Lord Jesus Christ and thou shalt be saved” from hell, it’s this easy!!
‼️‼️Good News‼️‼️ The gospel, the good news is salvation from hell. And here’s how to get it, the Bible makes it as clear as can be. “Believe on the Lord Jesus Christ and thou shalt be saved”, acts 16:31. Words from your mouth don’t even need to be accompanied, just “believe on the Lord Jesus Christ and thou shalt be saved” from hell, it’s this easy!!
‼️‼️Great News‼️‼️ The gospel, the good news is salvation from hell. And here’s how to get it, the Bible makes it as clear as can be. “Believe on the Lord Jesus Christ and thou shalt be saved”, acts 16:31. Words from your mouth don’t even need to be accompanied, just “believe on the Lord Jesus Christ and thou shalt be saved” from hell, it’s this easy!!
I would say "some parts of mathematics" is an understatement. they are everywhere on mathematics, not especially on geometry, but especially in set theory
are they on fractals tho?
@@Leleleleleleleleleo huh?
@@Leleleleleleleleleo I would believe so.
Also in real number system
Destiny lost in this debate
damn the intersection of the communities though
Lmao
An axiom is cool sounding word and its my favorite word.
NOTES
Spectrum of Rules of constant relations from which we perform deduction, induction, abduction, and guessing (trial and error).
1. Axioms must be declared: Ideal. Arbitrary. Presumed(declared) True. Used in formal Logic, Mathematics.
2. Premises may be assumed, and may be true, false, or unknowable. Pragmatic. Used in argument.
3. Laws (Theories) must be identified: Real. Laws are true with stated limits. Constrained. Used in Sciences.
The most common problem I deal with correcting is the conflation of the three.
May I ask: what do you mean by “arbitrary” for axioms? How can you say an axiom is “arbitrary”? Surely there is a REASON a given axiom is chosen ? So why call it ARBITRARY?!
Good video!
As a Math Degree student, I couldn't give a better definition of "Axiom". All in Maths is constructed either by axioms or by definitions, and in many cases you use "axioms" in order to define something.
For example, if you want to give necessary condition for anything to be called "Set", you give a set of rules that must that must be verified (in this case, the ZFC axioms). It's not like an universal set of rules, but an universal set of rules that must be fulfilled if you belong to the class of "Sets".
Similarly, the peano axioms give a necessary condition for anything to be a "natural number".
This is why I frequently refer to axioms with materialist atheists as 'articles of faith' & speak of traditional articles of faith as 'religious system axioms'.
@Intellect, reason&Logic Use your brain
You give them too much credit implying belief re-evaluation & a personal existential connection to their worldview.
Mostly they just get a bit huffy.
I guess materialist has something for axiom which can be observed in reality and which exist. Religious person has something for axiom which is just made up and has no relation to real world.
@@sasilik
That rests upon the axiom of sensory trustworthiness & accuracy of conscious interpretation of the inputs.
Religious system axioms and resulting structures are judged "by their fruit"; which show comparative multi-generational advantage against atheistic materialist societies, the latter consistently failing due to demographic collapse, social atomisation, existentialist angst & ennui.
@@GodsOwnPrototype I thought that you are sensible person but then you splattered this comment section with this BS....
@@sasilik
Not an argument / reasoned objection.
I think the best axiom is "whatever system can help us to best navigate experience is preferred"? Pragmatism, I guess?
Could you make a video on non-Aristotelian logics?
I second this request.
In his Map of Philosophy he went over some uncommon logics, if I remember correctly, but I dont think he made a specific video for any.
Have you read Science and Sanity?
I found this video while looking for examples of non-Aristotelian logic
This video explain axiom really well. But i want to ask something. Isn't the fact that we believe our minds are able to reason or find truth is an axiom by itself? We believe that our mind have the capability to find truth by the get go right? We assume that is true withouth any proof.
And even if we try to find proof that support our assumption that our mind can find truth. It's going to end up in a contradiction. Because to find proof that our mind able to reason, firstly we have to assume the very thing we are trying to prove.
So based on this, i conclude there is actually some axiom that we have to take.because without, we couldnt know or believe anything.
Welcome to philosophical skepticism. That is a classical skeptic argument against foundationalism. As a skeptic myself it is not concerning, but it is a big issue for most everyone else. :) ua-cam.com/video/YNFyQD8zxkM/v-deo.html
Also another question - since axioms are presumed, doesn't it make axioms subjective inventions rather than universal objective truths?
Good question. One way to think about this is to not put the epistemic cart before the metaphysical horse (ua-cam.com/video/fSGwUyfxgFM/v-deo.html). The metaphysical question is about truth, and metaphysically axioms and theorems are no different. Many think that things like logical or mathematical axioms are true independent of our beliefs about them. Before math was discovered, did 2+2=4? If you think yes, then logical and mathematical axioms are independent of our beliefs about them. So it does not matter if we prove them or assume them, they are true or false independent of our beliefs about them.
The epistemic question is about our justification for believing these things. Here's where things become challenging for axioms. If they are assumed without argument, it seems like we have no justification for believing them. If everything we believe is built up from some set of axiomatic assumptions (ua-cam.com/video/YNFyQD8zxkM/v-deo.html), and those assumptions are unjustified, then everything we believe is unjustified. If justification is a prerequisite for knowledge, then we don't know anything. This is the case for philosophical skepticism. (ua-cam.com/video/S2sK_EOKb1Q/v-deo.html)
@@CarneadesOfCyrene Proper justification for any system of axioms cannot be found within the realm of the True, but rather the Good.
Intuitively, to say something is "true" means it is straight, linear, not having deviatied from a single well defined trajectory, such as the path an arrow takes when fired from a bow. The realm of the True is concerned with the proper transformation of _meaning_ such that no information is gained or lost. Theorems of an axiomatic system are by definition the true statements, i.e. statements which do nothing but linearly extrapolate the explicit meaning of the axioms into new forms which better reveal all the hidden meaning which was implicit in the system taken as a whole, but not manifest in the statements of the axioms themselves.
The realm of the Good concerns that which is favorable or virtuous with respect to some desired goal. For any axiomatic system, there are an infinite variety of systems (written in the same language) that are all equivalent in meaning despite vast differences in their explicit form. How then do we decide what the value of an axiomatic system is, so as to justify its use over others? As they say, the proof is in the pudding - the nature of the Good is not subject to logical analysis and must be borne out in time, but there are heuristic tools like Occam's razor which can help one avoid wandering blind through dark alleyways filled with gold. We want to be able to see the treasure hidden within - to understand what we have written and not just intellectually know it is in there by way of pure logic - so our goal is to find axioms written in a way which allows us to readily comprehend the underlying meaning and give us enough meaning to keep us interested, engaged, and occasionally pleasantly surprise us for the foreseeable future.
@@williamwesner4268 Can one then prove that Truth exists? If the point is to conserve knowledge, how would one ever actually reach the truth? Wouldn’t the search lead to something along the lines of a “knowledge regression?
I think the way this works is you make up whatever axioms make sense to you, then build your logic based on those axioms, if you find contradictions and paradoxes then you have to rethink your axioms.
they are ' subjetive ' only in the sense that everything in the theory comes from a 'Subject '; they are objective in the sense of their validity, ie, they are objective or, they have objectivity.
Thank you for your contribution.
Thank you so much this made things vary clear
Logical systems are based
Based argument.
I personally find Tetralemma logic found in the east to be more viable and less rigid than the binary logic found in the west. It also helps in understanding quantum physics which wouldn’t make any sense using the rigid forms of binary logic.
How do we define _proof_ , without a system of axioms?
@Fajjat 420 No, facts are built from axioms.
Look at godel
Why can't this be an axiom: "something can exist" only the existence of that idea proves that it's correct. It doesn't need anything outside of it to be true
Axioms in mathematics is not particularly special to geometry. Most of mathematics work off axioms. Notable examples include the Peano axiom, the field axioms, and the Zermelo-Fraenkel axioms.
@Gurkirpa Singh The Peano axioms define what natural numbers are, the field axioms define what a field is, and the ZF axioms is the foundation for set theory. You can look up their Wikipedia page for more information.
@Gurkirpa Singh no probs :)
I've recently started to know what axioms are, I wanted to know if I really need to memorize them, I'm doing honours in mathematics
Hey, I love your videos, I am learning so much from them. However I keep on stumbling on your claim that you are a sceptic. Something feels off about it. You said that as a sceptic, the axiomatic nature of logic is problematic. However, it seems to me, that scepticism itself rests on one or more axioms. The main axiom of a sceptic is that one should doubt claims, which one has not proven. This itself seems axiomatic to me. More then that, as it is an axiom, it is a self-contradictory one, because it claims that axioms themselves are not valid.
that's not the only thing that seems self contradictory to me
Isn't the vary notion that we can reason /find truth an axiom by itself?
And us doing anything that involves logic and reasoning implies that we adopt this axiom, therefore anything we conclude has a truth value means we have adopted the above axiom, even if we can prove that this is not the case we still have to take the assumption that we can find truth (since we would regard our proof to be true)
What's also interesting is that I'm using reasoning to propose this as well, so the statement 'the fact we believe our mind can reason and find truth is an axiom' is built apon reasoning and logic
@@giventhamsanqa6517 I totally agree. The very act of reasoning presupposes that the mind is capable of recognizing true beliefs as true and false beliefs as false.
I think a lot of the problems that scepticism adresses is based on the implicit assumption that reason is the only valid source of knowledge. Reason always argues for the truth of some A by means of some B. Of course you run into the problem of having to explain B with something other than a or b. The solution are axioms. No I think the error lies in assuming that axioms cannot be known. However there is no reason to justify that. Of course we can have intuitive or direct knowledge of something. Once you allow for knowledge that is not derived from reason all sorts of problems disappear. I can demonstrate that we actually do have knowledge that is not rationally aquired. Pinch yourself. You know that you feel what you feel. You did not arrive at this knowledge through reason. So we know that it is possible to have knowledge of something directly. Other things as well can in principle be knowable through direct knowledge. Reason then builds on these. Yes my example was one of sensation, but in principle the same thing can hold for objects of thought as it holds for objects of sensation. I think Descartes used this to start his axiomatic system. He knows that he had thoughts. Having thoughts he concluded that he must exist. I wouldn't agree with Descartes, that existence follows from the experience of thinking. The notion of existence might be an empty meaningles concept and as Buddhist point out personal identity might also be a false belief, but still He has a point at pointing out that he had knowledge about having experience. He knew that he was thinking.
Hmmm I believe that there are things that are self-authenticating.
Foundationalism is a challenging position to defend. Here's the skeptic's argument against it. ua-cam.com/video/YNFyQD8zxkM/v-deo.html
Do a video on aphorisms
Yeah, like how an aphorism can also be an idiom, like _a bad penny always turns up_ is an aphorism, but since it doesnt mean what the group of words literally means (a bad penny means a bad person) it's also an idiom. Isn't language fun? :)
I would like a presentation of Chrysippus' Dion/Theon identity puzzle, which Long and Sedley wrote about, putting special focus on making it more clear just what or who Dion and Theon are. That is, as I have read about it, it seems to be just a more confusing way of speculating on the identity of a person whose body at one point has two legs, and at another has but one - whether he is a "person" who had two legs and now one, or a person who had one leg throughout his existence, but did not exist until the two-legged body lost a leg.
Thank you!
If Axioms are statements that are presumed true without proof. Then how can they be the basis for proving a theorem to be true?
That is the case for philosophical skepticism. You must assume axioms to prove theorems, but you have no basis for assuming those axioms, otherwise they would not be axioms. That lack of justification makes the case that we don't actually know any of those axioms, or the theorems based on them.
"true" is contextual.
It's not "A therefore B."
It's "If A then B."
You never prove A. You just prove B if A.
@@someonenotnoone Is this the common way of thinking about truth?
When I say common I mean the majority of the human population.
@@encouraginglyauthentic43 I'd imagine not, people in general conflate truth of fact versus conviction of opinion, and they don't understand what valid logic does and doesn't mean.
@@someonenotnoone Thanks for the reply.
I have been using the term "axiom" for a while now, and i would like to hear if I am using it correctly. I say something like sports is an axiom, and the rules under a particular sport, like lets say baseball rules, are presumed to be true and not requiring proof. Also said baseball rules are only true within the axiom they are in, so baseball rules are only true within the axiom of baseball.
Hmm. Within the system of "The Rules of Baseball" rules which are stated explicitly could be loosely referred to as axioms. But rules that are not stated explicitly, but are rather proven from the existing rules would be theorems. The axioms are the ones that are written down that can't simply be derived from other rules.
There's a deeper question here as to whether something like the rules of baseball can be true or false. If you are a coherentist about truth how they can be true or false seems pretty clear (ua-cam.com/video/Oyf0vHpdIFs/v-deo.html), but this is a harder claim to back up for someone that is a correspondence theorist (ua-cam.com/video/un0KbGfsdUM/v-deo.html). What thing in the world makes one set of rules true and another false? (Note that this is a different question from what makes us justified in believing one set of rules over another).
No. Game of baseball is built on axioms. You start with axioms (rules) and then you have many many ways to play the game within those rules. The correct sums of those combinations are called axioms. So, the game of baseball will require axiom (rules) but also c sets of those rules applied. Just because you did something that agrees with a rule of baseball (for example, throwing a ball according tithe rules) doesn't mean that you actually played a game of baseball. But, you can build a game of baseball by applying those axioms.
@@DataLog Ok, so if the game of baseball is made up of axioms, then what is the term I should use when referring to the game of baseball itself?
@@DennisPulido Maybe theorem? Not 100% sure but 99.9
@@DennisPulido So basically, the Game of baseball is a Theorem created by applying rules of Baseball in a correct order (or multitudes of correct orders).
Pitching a ball, catching a ball, running to a base etc. and there are many different orders which increase or decrease your chances of winning.
Action + Backround rationality that promotes said action
Random qwesh but what font is this video in? I just gotta know
Stay Skeptical , what a deep advice
It only begs the question of should one be skeptical about staying skeptical?
@@SabbatarianCalvinist thats a meta statement
The advice he gave is to stay skeptical of all statemnts (first order)
To be skeptical of staying skeptical is a second order thing - they aren't the same thing
🙏🙏🙏🙏 Well explained..
0:37 not exactly: a logical system begins by defining the expressions that belongs to the language, ie , the so called well formulated formulas--wff--; axioms are not the rules, rules of inference have to be declared, and usually the rule is modus ponens or natural deduction rules like in Gentzen system.
That the axioms are taken as primitive assertions is not related to a belief practice, it is more on the ' conventionallist ' nature of logical pre- structure work in mathematics. Since Euclides, the axioms are taken as true propositions, an aspect that was changed by David Hilbert axiomatic style.
I have to write a free essay after the holidays. The theme is, “Life is not an axiom. ” I know basically what an axiom is, but the subject itself doesn’t make any sense at all. Can someone help me there??? Because I can’t ask the teacher, because it’s holidays.
axiom is the base of a logical system
"Pain is bad" can be said to be an utilitarian axiom that doesn't needs proof?
What about masochists that enjoys and derives sexual pleasures from pain?
@@baikentram9992 they would simply not adopt that moral system as they reject its core axiom. This is why all moral systems are ultimately subjective--they all rely on axioms which are always a value judgement of some kind.
The axiom would not need proof, but because all moral systems rely on such axioms(which are all value judgements) all moral systems are ultimately subjective and cannot be proven "true" except within the system itself. If one rejects the axiom, one need not adhere to the system. That's my view. Cheers :)
@@munstrumridcully thanks for the input! I've always loved philosophy :)
I think a more accurate one would be this:
Pain A should be avoided if and only if the potential happiness that comes from it doesn't outweight the pain.
This also solves the masochist problem-the happiness that the masoschist experiences is better than the pain he or she experiences.
Hey Carneades, since all moral systems are based on a value judgement as an axiom (wellbeing should be enhanced, God's will is good, etc..) Doesn't that automatically rule out an objectively true and binding to all moral system?
I see it as _if_ you accept the basic principle/axiom of a moral theory _then_ certain behaviors that are in line with that axiom are objectively preferable and behaviors contrary to that axiom are objectively wrong. But the moral theory itself is based on a value judgement, and is therefore subjective based on what one values. I think many people share many basic moral values based on our evolution as a social but not eusocial species, but that appealing to this fact to make some normative ethics "true" would be an appeal to nature fallacy.
Lastly, no I do not think there is one true logical system. I am a logical instrumentalist just as I am a scientific instrumentalist....I value utility in navigating my experiences. I care not for what is "real", Matrices, Cartesion Demons and Solipsism be damned! :)
Morality = Reciprocity. And it has to be. Moral norms are members of a portfolio (network) that may be reciprocal or not. Moral intuitions vary by the individual's reproductive balance of reciprocity vs proportionality in the given set of moral norms. So whenever speaking of 'morality' which thing are you talking about? Ideal knowable (reciprocity). Ideal unknowable (anything not immoral and therefore irreciprocal is moral. What we mean is, what's good? Not what's moral?) Moral Norm (evolved market for prohibitions), Moral intuition (your bias given your reproductive and survival demands) - in other words, your tolerance for proportionality.
@@curtd59 except that morality does not equal reciprocity. Morality simple means any system of standards for right or wrong behavior. Divine Command Theory is a moral syatem that is not concerned with reciprocity, only duty to obey the perfectly moral commands of a God. To DCT, that is what determines right or wrong.
A principle of reciprocity can be _a_ standard/axiom of morality but it is not _the_ standard. There are several competing moral theories and moral philosophy has yet to(and never will do, imo) find a One True Moral Theory or One True Moral Axiom. As Carneades said in the vid, the fact that axioms are assumed without proof disallows there _being_ a One True Morality.
@@munstrumridcully empirically, across all time and all civilizations, morality within the limits of proportionality available to th class consists of reciprocity. international law is governed by it. humans would find no rational value for cooperation otherwise. And we would not (and do not) cooperate under irreciprocity. So again morality equals reciprocity, and it would be interesting if you would try to find a case under which a tradition or norm or even law (not legislation, which is arbitrary), does not seek to produce reciprocity between people. You will find that what constitutes reciprocity within different social orders differs. But they will always be reducible to reciprocity. YOu may lack the knowledge to ascertain that on face value, but once you understand the economic system you'll rapidly see it's reciprocity. We envy one another and claim we demand POSITIVE freedom, and POSITIVE rights and POSITIVE morality but these are negotiation tactics. You are welcome to find evidence to the contrary.
@@curtd59
I dont think you understand what moral theories are or why there is no one true morality. One of the most popularly adopted moral theories today is utilitarianism, which does not adopt an axiom of reciprocity but rather three axioms :
Pleasure or Happiness Is the Only Thing That Truly Has Intrinsic Value.
Actions Are Right Insofar as They Promote Happiness, Wrong Insofar as They Produce Unhappiness. (Notice no mention of reciprocation. Increasing happiness via pure altruism without reciprocity is goid under this system)
Everyone's Happiness Counts Equally.(Again, no mention of reciprocity, only that no one person's happiness is more important than another's, so maximizing your own happiness by inflicting pain on others is not cool)
So, is utilitarianism a false morality? Please tell that to the moral philosophy journals, I'd love to see the peer review process on that :)
@@munstrumridcully Actions are right so long as they dont produce unhappiness in others. find me a case where unhappiness is not ir-reciprocity. find me a case where your unhappiness is not irreciprocity. if you engage in altruism (lets ignore for a moment that we may not do it ever) you are not acting irreciprocally although many people reject altruistic actions as attempts at debt creation. What is moral is whatever is not immoral. try to falsify that.
Why is it so hard to find what the axiom for logic is? What is the axiom of logic?
There are many axioms of logic, there is not just one. The rules of replacement and the rules of implication could be considered one set of axioms. Check out our series on the 100 days of logic for more (ua-cam.com/play/PLz0n_SjOttTcjHsuebLrl0fjab5fdToui.html)
Logic itself is basically the result of the majority's will to believe something to be true, I don't see any other way to prove it. if one doesn't conform with the belief of the majority then he/she will be considered illogical, but the question is, how much does the opinion of the majority actually matter? and is it fair for the majority to force their belief on the minorities? Logic is part of our existance.
Randy Trail
Will Underpass
Is there some math/ logic that proof axioms?
No. Math also requires axioms.
2 + 2 = 4
Unfortunately, I don't feel that I'm yet well-read enough to weigh in on classic vs. non-classical logic, their popularity (or lack thereof), and how this is relevant to truth.
I am hoping to do a series on non-classical logic once we are done with set theory. The logic series generally take longer because they are so involved, but they are also so interesting.
@@CarneadesOfCyrene Well I'm looking forward to that; thank you very much. I agree. I also feel that you are providing invaluable insight with respect to logic. I feel incredibly thankful for Carneades.Org and the exceptionally apt breakdowns of logic that you provide.
Besides making top-notch philosophy videos, I have yet to find another video creator who so articulately and passionately teaches in-depth logic lessons while also making said lessons particularly easy to digest, all things considered.
I've always been impressed by this content and cannot find the words to accurately express my appreciation for the phenomenal work that gets done here with respect to both logic specifically and philosophy as a whole.
BIG mahalo to you and everyone that makes this happen, my dude 🙌💯 sending much appreciation your way! 😁
*will himself* 'Do not say "isn't it obvious", do not say "isn't it obvious".'
Ik it’s outta place here, forgive me, but please read with an open mind
The gospel, the good news is salvation from hell. And here’s how to get it, the Bible makes it as clear as can be. “Believe on the Lord Jesus Christ and thou shalt be saved”, acts 16:31. Words from your mouth don’t even need to be accompanied, just “believe on the Lord Jesus Christ and thou shalt be saved” from hell, it’s this easy!!
It would have been nice to see you use examples in your UA-cam video. Using variables are not examples!
The challenge is that most axioms are stated very abstractly. You might get axioms in geometry that are not. E.g. A straight line may be drawn between any two points., but these are less common in logic.
In a way, operating under a logical system is like tentatively accepting new scientific propositions (or maybe even conducting basic scientific experiments). You start with what you've been given and then immediately interrogate reality to see its implications hold water. The moment something doesn't add up, you go back to the drawing board to see what can still be kept and what must be discarded.
As long as the laws of identity, noncontradiction, and excluded middle - or rather the framework that they constitute - allows us to produce results that are can be verified in reality, we have all the more reason to trust that these axioms have us on the right path.
Can't we have a logical system with only definitions and rules of inference.
I couldn't understand a single frame from this video. Not the youtuber's fault, though. He seems to explain it thoroughly. I just couldn't understand this concept, unfortunately.
Paula Mountain
I’m so ducking confused. How is an axiom different than a physical law for example. Axiom is just a globally known truth.1 Apple plus 1 Apple is two.
Axioms are basic claims that are assumed without proof. Physical laws generally require some level of support or proof.
Robinson Brian Hall Frank Jones Elizabeth
wordle 4
Does a axiom require truth to be one?
Axioms is like faith in religion?
I am
Annamae Center
Axioms aren't things that are assumed to be true. They say
that, for the moment, we are talking about any system that obeys
the rules given by the axioms. If a system obeys the rules then
some statements cannot avoid being true : they are the theorems.
For instance, take the axiom
There are at least three things.
This is true of some subjects, false of others, and don't know
for the rest.
Now talk only of subject for which it is true. Then
There are at least two things
cannot avoid being true : it is a theorem (and you can prove it).
In abstract, one does not need to assume an axiom to be true to speak of validity of an argument. But no one outside the ivory tower cares that an argument is valid if it is not sound. For soundness, you must assume that the axiom is true of this system.
Additionally, I think your definition will run into some problems with the Tortoise and Achilles (ua-cam.com/video/WS0bAKxmO_w/v-deo.html) i.e. we can't claim that a implies b without assuming that a and a implies b implies b and down the rabbit hole we go. Even to make claims about validity, you need to assume an infinite number of propositions.
When doing applied maths it is just as important to choose the
right pure maths as it is to use the pure maths correctly. For
instance, you can navigate round the British Isles using Euclid's
axioms, but if you navigate from Britain to Australia you find
that parallel lines cross each other.
The video ends by asking if we can accept some axioms without proof.
From this example the answer must be that it depends on the problem
being investigated. If the chosen axioms agree with observation then
they are useful. If they don't then they are not useful. But
comparing with observation is not "proof" and for most problems
there is no possibility of proof.
Presumably "soundness" means you've used appropriate axioms in
your applied maths problem. You don't "assume" they are true, you
justify their use. Unfortunately, text books often omit the
justification and just say assume so and so. This is just a
teaching convention.
The Achilles and the tortoise problem demonstrates that a finite
distance can be split into an infinite number of sub-intervals.
The usual discussion then declares that a finite time cannot be
split into an infinite number of time sub-intervals, hence the
paradox. This is a very dubious argument.
The dependence on assumptions is what makes the logic a philosophy not knowledge.
@Nuclear Confusion An epistemic question with a big answer, that I am trying to find it.
I am not strong enough in epistemology yet, sorry.
‼️‼️Good News‼️‼️
The gospel, the good news is salvation from hell. And here’s how to get it, the Bible makes it as clear as can be. “Believe on the Lord Jesus Christ and thou shalt be saved”, acts 16:31. Words from your mouth don’t even need to be accompanied, just “believe on the Lord Jesus Christ and thou shalt be saved” from hell, it’s this easy!!
‼️‼️Great News‼️‼️
The gospel, the good news is salvation from hell. And here’s how to get it, the Bible makes it as clear as can be. “Believe on the Lord Jesus Christ and thou shalt be saved”, acts 16:31. Words from your mouth don’t even need to be accompanied, just “believe on the Lord Jesus Christ and thou shalt be saved” from hell, it’s this easy!!
??????
Re Er What?
Noice.
Ugh! Axioms are not PRESUMED true. Axioms are true because they HAVE to be true, otherwise thought is impossible. Without the axiom of identity, nothing you say has any meaning--it refers to NOTHING (which is not understood until you understand SOMETHING--which has identity).
Several points. First, you beg the question against the skeptic. Simply because you need to assume X to prove some Z does not mean that X is true. I need to assume that I am omnipotent to prove that I am God, but it does not follow that I am omnipotent. Just because you need to assume some axioms to prove other claims does not mean that those axioms are true. If anything it means they are unjustified. As a skeptic, I doubt you can prove anything.
Second, the basic laws of logic are rejected by many non-classical logics. Non reflexive logic, for example, rejects the law of identity. This does not destroy meaning or thought, it is simply a different logical system. In the same way that non-euclidean geometry does not make geometry impossible, non-classical logic does not make logic or thought impossible.
@@CarneadesOfCyrene I am not assuming anything! That's the point. You have lots of videos on here. None of them have ANY meaning without identity. i.e. you have a PERFORMANCE problem. You can't make any statement without using identity and that is why A=A is an axiom.
@@nicosilva4750 You're just tautologically asserting your conclusion.
@@ParadymShiftVegan Can you explain your statement without using identity? Tautology has no meaning without identity. Nothing you say means anything without identity. It becomes jibberish. The word 'assertion' has no meaning without identity. Identity is necessary. If AA, you can't even formulate a tautology. If you want to give up A=A, then what is being said? This is the point of an axiom, and what Aristotle explained a long time ago. A=A is an axiom that bridges the metaphysical to the epistemological (what exists to awareness of existence). Without it you can't know anything, and thus can't say anything (of consequence or meaning), yet here you are attempting to say something of consequence and meaning. NOTE: this isn't a proof, (proof is a statement reduced to axioms), but rather a necessary fact about awareness. To be aware requires that you be aware of something, but in order to be something cognitively it has to have an identity. I will repeat the earlier statement. This is a USE or PERFORMANCE issue. You can't make a statement (any statement of consequence--which leaves jibberish) without using 'identity' which is why it is an axiom. It literally is the logical base one has to start with. Any argument put forward against this is performatively refuting itself. I will try this another way. I think you are treating A=A as an arbitrary predicate, but it isn't. What would 'Tautology' mean if Tautology Tautology?
@@nicosilva4750 The moon exists even if I can't describe it. There's no evidence that the things you are talking about do. There is no "identity" you're talking about that we have any objective evidence for. You're not talking about reality, you're talking about your attempt to understand it.
I believe there’re in fact axioms that cannot be accepted, otherwise, society couldn’t function. For example, much of modern gender theory is predicated on axiomatic conclusions, like people identify as and believing themselves to be a women (an axiom), yet can’t even explain what a women is (a definition).
The world cannot function on axioms alone, as to do so would be incredibly intellectually regressive. For example, we assumed the world was flat at one point (something people believe to this day), yet we know very well that it isn’t, yet at one point, you’d of been fool to think to the contrary.
We would still be in the Stone Age if all that we predicated our reasoning on were axioms.
Every statement to be proven true _must have proof._ Period. Nothing should just be assumed to be true, no matter how self-evident it is.
That's fine and all, but you're advocating for either paralysis or submission to our instincts/proclivities which aren't driven by reason. The foundation for all currently in use systems of logic have to use some assumptions.
If you're in a jury will you make it a hung jury under every circumstance that has existed in every justice system in the past, because you object to the validity of all presented induction and deduction?
@@xenoblad No, but there has to be some standard when it comes to certitude. As the saying goes, nothing comes from nothing (except philosophy).
That's impossible, because it is impossible to prove anything without an assumption.
@@Naijiri. Explain, if you please.
@@christianbethel What I mean is that proving something requires a axiomatic standard, where you bring some statement or conclusion to compare and see if it holds true. For example, x=x. 1=2, 1=35, and 1=apple are all wrong, but only with respect to that axiom. Without it, they are all equally valid. So if we had absolutely *no* axioms. Every single statement would be equally plausible, and there would be no way to "prove" anything. At least that's how I see it.
Ik it’s outta place here, forgive me, but please read with an open mind
The gospel, the good news is salvation from hell. And here’s how to get it, the Bible makes it as clear as can be. “Believe on the Lord Jesus Christ and thou shalt be saved”, acts 16:31. Words from your mouth don’t even need to be accompanied, just “believe on the Lord Jesus Christ and thou shalt be saved” from hell, it’s this easy!!
‼️‼️Good News‼️‼️
The gospel, the good news is salvation from hell. And here’s how to get it, the Bible makes it as clear as can be. “Believe on the Lord Jesus Christ and thou shalt be saved”, acts 16:31. Words from your mouth don’t even need to be accompanied, just “believe on the Lord Jesus Christ and thou shalt be saved” from hell, it’s this easy!!
‼️‼️Great News‼️‼️
The gospel, the good news is salvation from hell. And here’s how to get it, the Bible makes it as clear as can be. “Believe on the Lord Jesus Christ and thou shalt be saved”, acts 16:31. Words from your mouth don’t even need to be accompanied, just “believe on the Lord Jesus Christ and thou shalt be saved” from hell, it’s this easy!!