P@NTH3ON

@Harrison Danneskjold That video presents ideas for the amelioration of senescence or aging and only to a certain extent, not a cure. The Chief Science Officer of the organization behind that video once stated that the word "cure" has done more harm than good with respect to educating people about aging. The word "cure" implies that aging is a disease, which is something that some people get throughout their lives and some don't. That's not what aging is. It's a side-effect of being alive in the first place and there is no evidence that it can be fully stopped.

So based on reading some of the discourse you guys went through, when I was discussing forming the concept “length,” I think that what I really had in mind was actually “extension,” I was just using the word “length.” It looks like the concept “length” is derived from the concept "extension." I think @merjet made a good distinction between length and extension. I also think that length can be thought of as “the longest spatial dimension of an object” and “extension” is just “a spatial dimension of an object.” I wanted to try expressing my main point with the examples I gave last time but this time I wanted to compare them more explicitly. I want to start with the concept “blue” and go through the cognitive process that Peikoff has identified in words. I’m gonna paraphrase what he said because now I cannot find the exact quote: “To form the concept blue you observe one blue object (blue1) and another blue object (blue2) AS OPPOSED TO A RED OBJECT.” You observe the similarity between the TWO blue objects, abstract, designate a word to use to refer to the group, and you have formed the concept blue” (again I’m paraphrasing this into my own words because I cannot find the quote) Notice that to form the concept blue there are three existents involved: blue1, blue2, and red. Also notice that the existent that serves as the unit that the units of the concept are differentiated from is “red.” So there are THREE existents but only TWO of them get integrated into the concept. Now I want to present an exact quote of the cognitive process he identified in words to form the concept “length:” Notice that in order to form the concept “length,” THREE existents are also involved: match, pencil, stick. HOWEVER, WE DO NOT FOLLOW THE SAME PROCESS THAT WE FOLLOWED TO FORM THE CONCEPT BLUE. It’s not like it was with the concept “blue” in which we were dealing with Existent1, Existent2, and we differentiated Existent1 (blue1) and Existent2 (blue2) from Existent3 (red). We do not differentiate a match and a pencil from a stick to form the concept length, as we differentiated blue1 and blue2 from red to form the concept “blue.” Also notice that for the concept “blue,” the first two existents were integrated into the concept while the third existent (red) was EXCLUDED from the concept. But that is not the case with the concept “length.” For the concept “length,” ALL THREE existents were integrated into and included in the concept “length” WITHOUT ANY EXISTENT BEING EXCLUDED. Ayn Rand is supposed to be presenting a SINGLE theory of concept formation. These differences that I’ve called out between the process of forming the concept “blue” and the concept “length” are CAUSING ME TO DOUBT that a SINGLE theory of concept formation was used to form them. Again just to summarize the differences that are tripping me up: For the concept “blue,” three existents were involved with two of them being integrated into the concept, and the one that was excluded was differentiated from the former two and it was COMMENSURABLE with the former two unlike for the concept “length,” in which three existents were involved with ALL THREE integrated into the concept, all were commensurable and NO EXISTENT WAS EXCLUDED. I was hoping that somebody could reconcile these differences that I have pointed and explain to me WHY the SAME, SINGLE theory of concept formation is still being used to form both the concept “blue” and the concept “length.” I find it very hard to believe right now that the underlying mechanics are the same in both cases. It seems to me that our minds might be forming different concepts differently. I tried to apply Ayn Rand’s theory of concept formation to validate my concept of (and these are just some random examples) “exam”. To form the concept “exam,” I go to school and observe Exam1 and Exam2 and a Quiz. I differentiate Exam1 and Exam2 from a Quiz to and integrate them to form the concept “Exam.” To form the concept “Car,” I observe Car1, Car2, differentiate them from a Truck, and integrate them to form the concept “Car.” And notice what I’m doing here. I am following the format that Peikoff followed when he identified the cognitive process of forming the concept “blue” in words, i.e observe blue1, blue2, as opposed to red and so on and so forth… As I mentioned before, I’ve had very limited success with this like with the concept “Color.” I tried to follow the same format (like with the concept “blue” that I just discussed): Observe Color1 (red), Observe Color2 (blue) and that’s far as I’ve gotten because the rule that Ayn Rand stated is that the third existent has to be COMMENSURABLE with the first two but I can’t figure out what to choose to be that third existent. If I am following the SAME process as I did for the concept “blue,” the third existent will be something that I will differentiate the former two from, in this case Existent1 (red) and Existent2 (blue). And what about a very abstract concept such as the concept “culture?” If I were to try to apply Ayn Rand’s theory as I understand to form the concept “culture,” I would say in social studies class I observe Culture1 (some civilization) and I observe Culture2 (a different civilization) and I differentiate the two of them from something else that is commensurable to them and integrate them to form the concept “Culture?” I had an additional question about the necessity of doing any of this in the first place and I wanted to start it off a Peikoff quote. He makes this statement close to the beginning of his lecture on concepts and he purposely makes it close to the beginning to emphasize the weaknesses that knowledge would have if he simply stopped there: Later on in the lecture he makes another statement: How can this be true? Is he saying here that you can form a concept without knowing how to form a concept? That sounds like a self-contradiction? Then later he makes another statement: This is where I wanted to ask my other major question: Is it really true that without Ayn Rand’s Theory of Concept Formation we would REALLY NOT KNOW that concepts were valid? If Ayn Rand never existed and her theory was never developed, would our knowledge really not be validated as such, as Peikoff stated? Is it really true that before Ayn Rand people did not know ENOUGH about concepts to know that they were grounded in reality? Do we really need to go as far as the measurement omission theory to be certain that concepts are grounded in reality? I wanted to present an argument without using Ayn Rand’s theory for a moment just to argue that concepts are grounded in reality. Just pretend we are in a world in which Ayn Rand’s theory of concept formation didn’t exist. I would argue the following: “We may not know how we form concepts but we do know that all of the concepts we have are formed AFTER observing reality. All the ideas we have about how the world around us works were developed AFTER observing the world. I didn’t get the ideas I have about how the world works from anywhere but from observing the world. Additionally, we can use the concepts we have formed to make predictions about what we will observe in certain situations and when our predictions come true, that implies that the concepts that we have are really describing how the world works, so they are AT LEAST grounded in reality and NOT ARBITRARY as some people try to assert.” In my hypothetical argument above, I’m not trying to suggest my own theory of concept formation, I’m only saying that even without a theory of concept formation we can know that our concepts are valid, i.e grounded in reality and not arbitrary. Is there anything wrong with my preceding argument about how we can know that concepts are grounded in reality? And lastly, if I want to pursue and claim VALID knowledge about various topics, am I now obligated to go through every concept I have and identify IN WORDS how I have formed those concepts in accordance with Ayn Rand's Theory of Concepts (as I have been trying to do)? If, for some reason, I can't do that, like if I encountered the problems that I discussed with concepts like "color" and "length," does that mean that I actually don't have those concepts formed? Does it mean that my knowledge pertaining to those concepts is not valid (if I can't identify IN WORDS how I formed those concepts as Peikoff did for "blue" and "length")?

@dream_weaver Page 132 of ITOE. She doesn't say this herself but she does respond "That's right" after the person she is having a discussion with states "For instance, in the case of concrete versus entity, the units are the same, but the concept entity distinguishes entities from attributes, while the concept concrete distinguishes entities from abstractions." To this statement, Rand responded "That's right. @merjet Yes it is possible to form higher-level concepts before you form lower-level ones and Rand does discuss the possibility of a child doing this at some point in ITOE. I think she also mentions that this is possible only up to a certain level in the conceptual hierarchy. I think she says the determining factor regarding the level that you start at when you form concepts is going to be "what is available to your observation." But again, I think she said, there is a limit at how high of a level you can start at.

@Grames In that quote in your response I called it an existent. But I do see earlier in my post I called it a "unit" and this was a mistake on my part. I thought calling it an existent was a better choice of words because I didn't know what other word to refer to it by. What would you call the "redness" when you are using redness to differentiate two shades of blue from in the process of forming a concept of blue? I think of it as "what you are using to differentiate blue from." And it doesn't have to be red it could be green right? Rand said you need something COMMENSURABLE that you can look at and use to differentiate the units of your concept from. So I'm wondering what did we use to differentiate the units of various concepts from? What did we differentiate red and blue from when we formed the concept "color?" What did we differentiate a thud and a ring from when we formed the concept sound? I'm wondering if I'm being unclear in my questions or if I misunderstood Rand or Peikoff about concept formation. When you're dealing with ostensive units it seems to be easy to identify "what you are using to differentiate the units of your concept from." Like when you form the concept "cat" by observing two cats and a dog and omitting parricular measurements and differentiating the cats from the dog. But "color" and "sound" are more abstract. So I'm wondering what did we use to differentiate various colors such as "red" and "blue" from that is commensurable with red and blue in order to be able to form the concept "color" in the first place? I can't think of it. Also isn't a force primarily a push or a pull? You can't form the concept force unless you form the concept of push and pull first right? It would be like forming the concept furniture before forming the concept chair and table, right? I agree it's very primary. Force is directly perceptible and that's why I was saying you experience two different particular pushes and a pull and after omitting measurements you differentiate the pushes from the pull and integrate them into the concept "push" and vice versa for the concept "pull." Then after that you're ready to form the concept force, which is on a level that is higher from "push" and "pull." That's my understanding.

@merjet I'll check out that document. But I wanted to respond first to what you mentioned: How do you know that the x's and non-x's satisfy "a more abstract, wider, less specific, category" if that category corresponds to a higher-level concept which you have not formed yet? In your example, you're trying to form the concept of X, but you're using the higher-level concept that subsumes the X's and Non-X's to guide you in forming the concept X. And you're using that higher-level concept when you impose the requirements that the x's and non-x's "should satisfy a more abstract, wider, less specific category." It seems like you're stealing the higher-level concept to form the lower level one... And by the way, since you mentioned color, can you tell me what existent did you differentiate red, blue, and green FROM to form the concept "color?"

I had a question about the way in which we form concepts. The definition of a concept is “a mental integration of TWO OR MORE units possessing the same distinguishing characteristics, with their particular measurements omitted.” However, when I listen to Peikoff’s lectures about how to form concepts, his examples always involve something more than just the two units. It involves something else to differentiate the units from. For example, he explains how to form the concept blue by observing two particular instances of blue, one shade of blue and a slightly different shade of blue and omitting their particular shades while retaining the characteristic “BLUE” and distinguishing them from red. This third unit serves as what you use to differentiate the former two units from and there are rules that have to be followed regarding this unit. He mentions seeing “two blue objects AS OPPOSED TO RED.” So there’s always something more included in the conceptualization process than just the two or more units. The rule that stands out the most to me is that the characteristic that you are using to differentiate the former two units from the third has to be “commensurable” with the former two units. I am trying to see how the concepts I have measure up against Rand’s theory of concept formation but I am having difficulties doing this with many of the concepts I have. My biggest problem so far is I don’t understand what commensurable existents I am differentiating the units of my concepts from. How did I form the concept “color?” At first I thought I saw a red object and I saw a blue object and I omitted the particular colors in question and integrated them into the concept “color.” But I’m missing a key piece in the process of concept formation (which by the way is not mentioned in the definition of the concept, as a I stated above). I am missing the COMMENSURABLE existent that I need to differentiate the two units FROM. I am trying to figure out what that existent is. I was thinking maybe it could be a *ring of a phone or a particular instance of “sound.” So I observed blue and red and I heard a *ring and I realized that blue and red were far more similar to each other than they both are to a *ring, so I integrate them into the concept “color” and I differentiate them from a *ring of a phone. But am I wrong about this because a *ring is not COMMENSURABLE with red or blue? And this is just one example. I don’t understand how I formed the concept “sound” for the same reasons. I was thinking I heard two different sounds, like a *ring and a *thud, but I dont know what existent I differentiated them from? The other day I read that Rand formed the concept “entity” by observing two separate entities and DISTINGUISHING THEM FROM THEIR ATTRIBUTES. How does she know that their attributes are the commensurable existents that she is supposed to use to differentiate them? I mean now that I think about it, I can maybe understand that an entity is commensurable with its attributes because it could be thought of as a collection or more precisely an integration of its attributes, but I’m still struggling with this. For pretty much every concept I have, I can’t identify what existent I distinguished the units from and this is making me wonder “If I can’t do this, does this mean that I haven’t actually formed the concepts that I thought I formed?” And if I haven’t formed the concepts that I thought I formed, how am I able to even think about the referents that I am thinking about? This seems to me to be a dumb question but I’m seriously wondering about this. I think I’ve succeeded with a couple concepts, the concept of “pushes” and “pulls.” You observe pushes and pulls, you observe Push1 and Push2 and omit the particular magnitudes of the pushes while distinguishing them from a pull to form the concept “push.” You do the same thing vice versa for the concept “push.” But that’s as far I can go. I can’t even form the concept “force” in a physical context because I can observe a “push” and then a “pull” but again I don’t know what commensurable existent to differentiate them FROM to form the concept force? I was hoping somebody could help me solve these problems? And also, could someone tell me, why isn’t that third existent that you are using to differentiate the “two or more units” from included in the definition of a concept? It seems to be an essential piece of the conceptualization process and therefore shouldn't it be included in the concept's definition?

@Grames I think I get what you're saying I just want to affirm a couple things. I noticed you stated "proof of induction." I think you might have made a typo here. What I was referring to was Peikoff's "inductive proof of causality." My understanding is (or was) that Peikoff was not "proving induction," he was using induction to induce (prove) causality. This was my previous understanding of what was happening. And now from you I'm understanding that it was not a proof of causality but a nifty horizontal integration of "identity" and "causality." Is this an accurate understanding of what you are saying? And one more thing, you mentioned "not applicable to axioms and first level concepts." So that's exactly what I was wondering about horizontally integrating "identity" with "causality." If the way that you horizontally integrate concepts is by vertically integrating to something in common, I was just saying you can't do that with "identity" and "causality" because you can't get beneath them. So I was thinking that there is no way to horizontally integrate "causality" and "identity" but again you're saying that in that older lecture I referred to about induction, peikoff presents another way to horizontally integrate "causality" and "identity," that doesnt involve vertical integration to something in common, right?

@Grames If they are horizontally related through some other concepts that are hierarchically prior to both, how can causality and identity be horizontally relatable? What concept is there that is "hierarchically prior" to identity? I thought identity was the most fundamental concept anyone can form. There shouldn't be anything hierarchically prior to "identity" right?

@Grames I was not aware that Peikoff changed his mind about this. This is causing me to have a few questions that I was hoping to get some answers to. Is Peikoff basically saying that his inductive proof of causality that he goes over in a course called "An Inductive Approach to Philosophy" is wrong? He mentions in the lecture that it essentially involves 3 concepts: entities, identity, and action i.e. entities with identities acting in a particular kind of way in accordance with their identities. What is wrong with this understanding? What is improper about this understanding of causality? Did Peikoff ever mention what his reason was for later rejecting the proof that he himself gave? And lastly, I suspect my understanding of "horizontal integration" is not up to par so could you explain what "horizontal integration" is? Maybe give an example of it and how it differs from "vertical integration?"

And I already mentioned the ability to create new life does not imply that you can indefinitely extend a given life. The idea that you can "apply" that ability to indefinitely extend a given life is flawed.

You missed the part where I told you about the arrow-of-time, non-equilibrium nature of living beings. Replacement of anything cannot happen instantaneously, whether its living or non-living. At every single instantaneous moment of your existence, your internal energy states are being taken from an ordered non-equilibrium state to a disorded equilibrium state until an equilibrium configuration is reached. As soon as a moment passes, your fundamental life generating/life sustaining processes are already busy bringing you closer to equilibrium in your next moment of existence. This is where the nature of all non-equilbrium processes comes in effect and it differentiates you at one moment from you at every other moment of your existence. This fundamentally disallows a certain amount of any kind of repair/replacement. Remember I mentioned your example with the muscles and food. The food doesnt just become waste, the muscles themselves change during every moment of your existence in accordance with the irreversible, non-equilbirum processes they have to undergo.

Nothing that I have argued is refuted by the ability of life to create NEW INDIVIDUAL SYSTEMS. Entropy based on internal energy state configuration and the necessary life-sustaining irreversible processes that continuously cause it to rise over time are defined ONLY FOR AN INDIVIDUAL ENTITY/SYSTEM. During the creation process of a NEW INDIVIDUAL, those continuous, irreversible processes have not yet been set in motion inside the new individual. It is a new, separate system with it's own, different identity which is getting all of its initial energy states built up and constructed during its creation process as all of its atoms/molecules get assembled. It doesnt detract from anything I've argued. A living individual with a mind can be conceptually identified as a quasi-stable non-equilibrium open thermodynamic system which needs to undergo continuous irreversible processes to continue to exist. Those irreversible processes by their very nature eventually doom an individual living entity to death by aging or cancer, like Masel said. In order to stay alive, the living entity's internal energy states have to continue to get closer and closer to an equilibrium configuration (increasing the number of equivalent microstates that correspond to an individual organism's momentary macrostate) over time, per the irreversible processes that cause that. At the individual entity level, that continuous approach to an equilibrium energy state configuration eventually manifests itself as aging damage or cancer, per the irreversible processes that cause that. Self-generating/self-sustaining the life of a given individual entity and creating a new, separate individual entity are two different processes which should not be conflated. The ability to create new individual entities does not serve as evidence for the possibility of a given individual's indefinite life. It is an impossibility.

@StrictlyLogical Instead of “entropic” I should have been more precise and used the word “irreversible.” The irreversible processes that have to occur in living entities in order for living entities to continue to exist do result in an internal energy state configuration change from non-equilibrium to equilibrium that manifests as decay/damage/deterioration. It isn’t like the ideal engines we learned about in school, the ones with no internal rireversibilities. We made simplifying assumptions in school that allowed us to show that something like a diamond engine can be thermally and mechanically loaded and then it can be allowed to cool and then afterward its entropy can maybe be equal to what it was before it was loaded, only the environment is different. In real life it isn’t like that. In reality, that thermal and mechanical loading is irreversibly transferred throughout that engine and that process is producing internal energy state configuration changes in that engine. The bonds between all of its atoms are weakening over time as the engine’s internal energy disperses. Eventually, after enough loading, that engine would suffer what is called “widespread fatigue damage” and break down. Widespread fatigue damage/decay/deterioration is a manifestation of an entity’s entropy increase from irreversible changes in its internal energy state configuration. It is a result of irreversible processes occurring in the entity. It’s not wrong to classify damage/decay/deterioration as a source of entropy. In an atomic/molecular context, entropy unsurprisingly is defined differently from how it’s defined macroscopically. At the atomic level, entropy is quantified by the number of equivalent energy microstates that characterize an entity’s macrostate. Basically, this means the number of ways that energy can be distributed throughout a system in a particular macroscopic state. A damaged/decayed/deteriorated entity which is closer to an equilibrium energy state configuration has a lot more ways that its internal energy can be distributed than an undamaged/undecayed/undeteriorated entity, i.e. a higher entropy. So strictly speaking, entropy itself may not necessitate damage, decay, or deterioration, but the irreversible processes that result in damage, decay, or deterioration (which are a source of entropy) do necessitate it. And in living entities, those irreversible processes have to continuously happen in order for you to exist from one moment to the next and all throughout your life. In your example about muscles, it’s not just the food that becomes waste, the muscles themselves are changing over time in accordance with the irreversible processes they continuously have to undergo. Even cell division is an example of an irreversible process that disperses a living entity’s energy. Uncontrollable cell division, like cancer, is a little different from damage/decay/deterioration, but it also irreversibly changes a living entity’s energy state from non-equilibrium to equilibrium. I came across an article that quoted an evolutionary biology professor named Joanna Masel. She said this about aging and cancer: So even a renewed cell is not necessarily a good thing. And Nasif Nahle strongly emphasizes that living systems are not isolated systems. He conceptualizes them as quasi-stable non-equilibrium open thermodynamic systems and he conceptualizes death as equilibrium. And I’m not sure about this being a philosophical or technical issue but the philosophical significance I would attribute to it is this: It is in the identity of the continuous irreversible processes that living beings have to undergo to change their energy state configuration from a non-equilibrium energy state configuration to an equilibrium energy state configuration over time.

It may have repaired an injury or something like that but the fact remains that a living being is still older than it was after it healed than it was before it healed. In order to sustain its life, it went through irreversible, entropic processes that drove its healing but still resulted in an overall energy state configuration closer to equilibrium.

You cannot apply the same argument to a messy room because a room does not need to go through continuous entropic processes in order to continue to exist. It is not an oversimplification. And even during the process of creating a new human being, that human being does not exist yet during that creation process, so that concept would not apply. It's only after the human's continuous, entropic, and self-sustaining processes start that that concept would apply. I don't know if this is something that is "in principle" like you said. There is a biologist whose name is Nasif Nahle and he explains this alot better than I could. He applies inductive first followed by deductive scientific methods in his work. He discusses the conception of man (and all other living beings) as quasi-stable non-equilibrium systems. These are systems that continuously increase their entropy up to a maximum value in order to stay in existence.

@StrictlyLogical I agree with what you said about life being a natural process and I do agree what you said about repairs not being possible if no energy is available. But what I'm saying is "deterioration" itself can be conceptualized as a bodily high entropy state and a "repair" can be conceptualized as a lowering of that entropy. And what i'm saying is because a living human body's basic function essentially and continuously increases entropy (to make you change over time in the first place, i.e. arrow of time), a certain amount of that entropy cannot be lowered (repaired) even if you had energy available. You can repair excessive/unnecessary high entropy such as an injury or hunger. What you can't repair (even if you had available energy) is the entropy associated with how long you've been in existence. What I think is interesting is that overall bodily entropy (which continuously increases over time) can serve as an objective indicator of how long a particular living individual with a mind has been in existence.

@StrictlyLogical Well I agree. Although, I would be a little bit careful about the way you think about eating or breathing. The actions of eating and breathing are actions that are under your higher-level conscious control, more or less. Also, neither of those are necessary for a living being to exist from moment to moment. You can stop breathing for minutes and you can still exist throughout that entire temporal duration. I think the longest record someone held their breath was 22 minutes but that's beside the point. And eating you can stop for weeks and continue to exist. So there some differences in the nature of these actions and the actions that your living body continuously does from moment to moment and all throughout your entire life without your conscious control. It's these lower-level bodily metabolic and neural actions that drive your ability to choose to eat or breathe in the first place and it's these actions that are continuously operating and piling on more and more entropy (bringing the body from a non-equilibrium to an equilibrium state) and they can't be interfered with.

@StrictlyLogical But there is always an inherent limit with all living beings. The living human body is a far from equilibrium thermodynamic system that actively undergoes a continuous progression from non-equilibrium energy state configuration (low entropy) to equilibrium energy state configuration (high entropy). This is a defining characteristic of all living things. It's the reason that you're able to actively change over time in the first place. There's a certain amount of irreversibility that cannot be reversed. A certain amount of that progression cannot be halted otherwise you wouldn't be alive in the first place.

@StrictlyLogical Can you please clarify what you mean by "indefinite life" and why you say it is "possible?" The "slow transformation" would still have to be occurring like you said. "Slow" still implies a definite lifespan. The transformations would have to completely stop for it to be indefinite. Now maybe it can slowed down to the point that you'd still be around when the heat death of the universe comes about, but it still wouldn't be indefinite.

@ StrictlyLogical No that is not at all what I am proposing. I am simply saying that if somebody makes a claim that contradicts an axiom (which we have validated by evidence plenty of times) that claim is not merely arbitrary but more importantly, it is a metaphysical impossibility. That's what I'm saying. I think it's important that we answer a few questions before we go any further if it wouldn't be too much trouble. 1. What does it mean to "prove" something? 2. What does it mean to "validate" something? I ask this because I'm not sure if "validate" means the same as "prove" and Objectivists use the word "validate" a lot. 3. Do you know something ONLY IF you prove it? The reason I ask this is because when we observe something we gain knowledge. We learn. We know stuff from observing stuff. But do we "prove" anything when we observe and gain knowledge from observation? I say no but I think the answer to this will depend on what it means to "prove" something? 4. Can claims be BOTH ARBITRARY AND self-contradictory (incoherent or self-refuting)? Arbitrary because they have no evidence to support them (definition of arbitrary) AND self-contradictory because they contradict themselves. There are statements that are arbitrary and your statement "nothing can leave behind evidence" is an arbitrary claim. I agree with you. But it also implies a metaphysical contradiction. "Nothing" by definition is a non-existent. There is no such thing as "nothing." To exist is to be and to be is to be something. "Nothing" is that which is not anything at all, which means it cannot DO ANYTHING AT ALL. It has no capabilities whatsoever including the capability to "leave behind" ANYTHING AT ALL, let alone evidence. This is why I say it also implies a contradiction. The act of making a claim requires you to mean something by the words that you state to make the claim. When you analyze the meaning behind the word "nothing" in your claim, you can show that that claim is ALSO self-contradictory. That's all I'm saying. @Veritas I agree with you about proofs having to pertain to reality. At this point, I am reluctant to take a position on your "Karl-in-the-room" example because I am not sure at this moment if any axioms get contradicted if we see an empty room but Karl is still inside the room. In order to apply the "proof of contradiction" that I mentioned to the Karl-In-The-Room example, the negative of Karl not being in the room would have to be assumed and, from that assumption, a metaphysical contradiction would have to be deduced. "Proof by contradiction" is mostly a mathematical technique and it applies mostly because math is a very delimited subject with pretty much every claim being reduced to an axiom. But this is not the case in everyday life, although it is the case for claims such as the one that StrictlyLogical proposed.

What about the method of Proof By Contradiction? Assuming the opposite of a proposition is true and then demonstrating that such an assumption leads to a contradiction is a way to prove a negative. @StrictlyLogical I agree with you that any claim is made has to be based on SOME evidence. And that is exactly why whenever anyone makes any meaningful claim they are at the very least implicitly making an assertion that is NOT ARBITRARY on some level. And in those cases, if an any assertion made either implicitly or explicitly implies a contradiction, the claim can be dismissed as FALSE. Take for example your statement about the fact that a nonexistent thing CANNOT leave behind any evidence. How did you know that? What evidence do you have to support that claim that it CANNOT leave behind any evidence? You know because the opposite proposition implies a contradiction.