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Ayn Rand has the best moral philosophy ever invented. Karl Popper has the most important breakthrough in epistemology. Most Objectivists seem to think that Popper and Rand are incompatible, and Popper is an enemy of reason. They have not understood him. These lists are intended to help explain my motivation for integrating Rand and Popper, and also to help highlight many similarities they already have. Points Popperian epistemology and Objectivist epistemology have in common. In Popperian epistemology I include additions and improvements by David Deutsch and myself: - opposition to subjectivism and relativism - fallibilism - says that objective knowledge is attainable (in practice by fallible humans) - realism: says reality is objective - connected to reality: we have to observe reality, keep our ideas connected to reality - asserts there is objective truth - attention to context ("problem situation" or sometimes "problem" is the common Popperian term meaning context. E.g. a Popperian will ask "What is the problem this is addressing?" and be asking about context.) - pro-science - opposition to positivism - opposition to the language analysis school of philosophy - say that most professional philosophers are rather crap - opposition to both skeptical and authoritarian schools of epistemology - keeps our concepts "open-end[ed]" (ITOE). That means: possible to improve in the future as we learn more. - says that there are objective moral truths - does not seek a "frozen, arrested state of knowledge" (ITOE) - written clearly and understandably, unlike much philosophy - says epistemology is useful and valuable to real people; it matters to life; it's practical - you can't force an idea on someone. they can choose to accept it or not - you can't implant an idea in someone. you can't pour it in, stick it in with surgery, make them absorb it, etc. they get to think, interpret, choose. - free will - people are not born with some unchangeable nature and innate ideas. we can be self-made men. we can learn, change, improve, progress - emphasis on active use of one's mind, active learning - no inherent conflicts due to objective truth - understanding of unconscious and inexplicit ideas - if two ideas contradict, at least one is false - integration of epistemology with morality, politics, and more - rejection of authority - full rejection of idealism, solipsism - strong emphasis on clarity - rejection of limits on human minds - reject probabilistic approaches to epistemology - looks at man as rational and capable - value of critical thinking including self-criticism Strengths of Objectivist epistemology: - stolen concept - package deal - check your premises - ideas about integrating all one's knowledge and removing all contradictions - measurement omission and concept formation ideas both worthwhile, though flawed - good criticisms of many opponents of reason - good understanding of essentials vs non-essentials, e.g. for definitions - idea about automating some thinking - good explanation of what objectivity is - Judge, and be prepared to be judged Strengths of Popperian epistemology: - evolution creates knowledge - conjectures and refutations method - piecemeal, incremental method. value of every little improvement - identification of, and solution to, justificationism - addresses induction - conjectural, fallible, objective knowledge - idea that we progress from misconception to better misconception - myth of the framework - value of culture clash - emphasis on bold highly-criticizable claims, sticking your neck out to learn more - no shame in mistakes - value of criticism. criticism is a gift - understanding of rationality as being about error correction - unimportance of starting points. you can start anywhere, improve from there - criticism of definitions - criticism of foundations, bases - criticism of essentialism - criticism of manifest truth (and self-evidence, obviousness, etc) - static and dynamic memes - structural epistemology - coercion and common preferences - understanding of conflict and symmetry - applications to parenting, education, relationships - understanding of tradition - explanation of value of external criticism (if everyone has some blind spots, but some people have different blind spots then each other, then it's productive to share criticism with each other. a little like comparative advantage) - emphasis on critical method, criticism (ideas stand unless refuted) - let our ideas die in our stead Some of you are now wondering about details. I know. But it's so much! Let's do it like this: if you are interested in one of the topics, ask about it and I can elaborate. If you would preference a reference to existing material on the topic, that's fine too.
There are two particularly hard parts of explaining why induction is false. First, there are many refutations. Where do you start? Second, most refutations are targeted at professional philosophers. What most people mean by "induction" varies a great deal. Most professional philosophers are strongly attached to the concept of induction and know what it is. Most people are strongly attached to the word "induction" and will redefine it in response to criticism. In *The World of Parmenides*, Popper gives a short refutation of induction. It's updated from an article in Nature. It involves what most people would consider a bunch of tricky math. To seriously defend induction, doesn't one need to understand arguments like this and address them? Some professional philosophers do read and respond to this kind of thing. You can argue with them. You can point out a mistake in their response. But what do you do with people who aren't familiar with the material and think it's above their head? If you aren't familiar with this argument against induction, how do you know induction is any good? If you don't have a first hand understanding of both the argument and a mistake in it, then why take sides in favor of induction? Actually, inductivists have more responses open to them than pointing out a mistake in the argument or rejecting induction (or evading, or pleading ignorance). Do you know what the other important option is? Or will you hear it for the first time from me in the next paragraph, and then adopt it as your position? I don't recommend getting your position on induction from someone who thinks induction is a mistake – all the defenses I bring up are things I already know about and I *still* consider induction to be mistaken. Another option is to correctly point out that Popper's refutation only applies to some meanings of "induction", not all. It's possible to have a position on induction which is only refuted by other arguments, not by this particular one. I won't help you too much though. What do you have to mean by "induction" to not be refuted by this particular argument? What can't you mean? You figure it out. Popper argues against induction in books like LScD, C&R, OK, RASc. Deutsch does in FoR and BoI. Should I repeat points which are already published? What for? If some inductivist doesn't care to read the literature, will my essay do any good? Why would it? I recently spoke with some Objectivists who said they weren't in favor of enumerative induction. They were in favor of the other kind. What other kind? How does it work? Where are the details? They wouldn't say. How do you argue with that? Someone told me that OPAR solves the problem of induction. OPAR, like ITOE, actually barely mentions induction. Some other Objectivists were Bayesians. Never mind that Bayesian epistemology contradicts Objectivist epistemology. In any case, dealing with Bayesians is *different*. One strategy is to elicit from people *their* ideas about induction, then address those. That poses several problems. For one thing, it means you have to write a personalized response to each person, not a single essay. (But we already have general purpose answers by Popper and Deutsch published, anyway.) Another problem is that most people's ideas about induction are vague. And they only successfully communicate a fraction of their ideas about it. How do you argue with people who have only a vague notion of what "induction" is, but who are strongly attached to defending "induction"? They shouldn't be advocating induction at all without a better idea of what it means, let alone strongly. There are many other difficulties as well. For example, no one has ever written a set of precise instructions for how to do induction. They will tell me that I do it every day, but they never give me any instructions so how am I supposed to do it even once? Well I do it without knowing it, they say. Well how do they know that? To decide I did induction, you'd have to first say what induction is (and how it works, and what actions do and don't constitute doing induction) and then compare what I did against induction. But they make no such comparison – or won't share it. Often one runs into the idea that if you get some general theories, then you did induction. Period, the end. Induction means ANY method of getting general theories whatsoever. This vacuous definition helps explain why some people are so attached to "induction". But it is not the actual meaning of "induction" in philosophy which people have debated. Of course there is SOME way to get general theories – we know that because we have them – the issue is how do you do it? Induction is an attempt to give an answer to that, not a term to be attached to any answer to it. And yet I will try. Again. But I would like suggestions about methods. Induction says that we learn FROM observation data. Or at least from actively interpreted ideas about observation data. The induced ideas are either INFALLIBLE or SUPPORTED. The infallible version was refuted by Hume among others. As a matter of logic, inductive conclusions aren't infallibly proven. It doesn't work. Even if you think deduction or math is infallible (it's not), induction STILL wouldn't be infallible. Infallible means error is ABSOLUTELY 100% IMPOSSIBLE. It means we'll never improve our idea about this. This is it, this is the final answer, the end, nothing more to learn. It's the end of thinking. Although most Objectivists (and most people in general) are infallibilists, Objectivism rejects infallibilism. Many people are skeptical of this and often deny being infallibilists. Why? Because they are only infallibilists 1% of the time; most of their thinking, most of the time, doesn't involve infallibilism. But that makes you an infallibilist. It's just like if you only think 1% of haunted houses really have a ghost, you are superstitious. So suppose induction grants fallible support. We still haven't said how you do induction, btw. But, OK, what does fallible support mean? What does it do? What do you do with it? What good is it? Support is only meaningful and useful if it helps you differentiate between different ideas. It has to tell you that idea X is better than idea Y which is better than idea Z. Each idea has an amount of support on a continuum and the ones with more support are better. Apart from this not working in the first place (how much support is assigned to which idea by which induction? there's no answer), it's also irrational. You have these various ideas which contradict each other, and you declare one "better" in some sense without resolving the contradiction. You must deal with the contradiction. If you don't know how to address the contradiction then you don't know which is right. Picking one is arbitrary and irrational. Maybe X is false and Y is true. You don't know. What does it matter that X has more support? Why does X have more support anyway? Every single piece of data you have to induce from does not contradict Y. If it did contradict Y, Y would be refuted instead of having some lesser amount of support. Every single piece of data is consistent with both X and Y. It has the same relationship with X and with Y. So why does Y have more support? So what really happens if you approach this rationally is everything that isn't refuted has exactly the same amount of support. Because it is compatible with exactly the same data set. So really there are only two categories of ideas: refuted and non-refuted. And that isn't induction. I shouldn't have to say this, but I do. That is not induction. That is Popper. That is a rejection of induction. That is something different. If you want to call that "induction" then the word "induction" loses all meaning and there's no word left to refer to the wrong ideas about epistemology. Why would some piece of data that is consistent with both X and Y support X over Y? There is no answer and never has been. (Unless X and Y are themselves probabilistic theories. If X says that a piece of data is 90% likely and Y says it's 20% likely, then if that data is observed the Bayesians will start gloating. They'd be wrong. That's another story. But why should I tell it? You wouldn't have thought of this objection yourself. You only know about it because I told you, and I'm telling you it's wrong. Anyway, for now just accept that what I'm talking about works with all regular ideas that actually assert things about reality instead of having built-in maybes.) Also, the idea of support really means AUTHORITY. Induction is one of the many attempts to introduce authority into epistemology. Authority in epistemology is abused in many ways. For example, some people think their idea has so much authority that if there is a criticism of it, that doesn't matter. It'd take like 5 criticisms to reduce its authority to the point where they might reject it. This is blatantly irrational. If there is a mistake in your idea it's wrong. You can't accept or evade any contradictions, any mistakes. None. Period. Just the other day a purported Objectivist said he was uncomfortable that if there is one criticism of an idea then that's decisive. He didn't say why. I know why. Because that leaves no room for authority. But I've seen this a hundred times. It's really common. If no criticism is ever ignored, the authority never actually gets to do anything. Irrationally ignoring criticism is the main purpose of authority in epistemology. Secondary purposes include things like intimidating people into accepting your idea. But wait, you say, induction is a method of MAKING theories. We still need it for that even if it doesn't grant them support/authority. Well, is it really a method of making theories? There's a big BLANK OUT in the part of induction where it's supposed to actually tell you what to do to make some theories. What is step one? What is step two? What always fills in this gap is intuition, common sense, and sometimes, for good measure, some fallacies (like that correlation implies or hints at causation). In other words, induction means think of theories however (varies from person to person), call it "induction", and never consider or examine or criticize or improve your methods of thinking (since you claim to be using a standard method, no introspection is necessary). For any set of data, infinitely many general conclusions are logically compatible. Many people try to deny this. As a matter of logic they are just wrong. (Some then start attacking logic itself and have the audacity to call themselves Objectivists). Should I go into this? Should I give an example? If I give an example, everyone will think the example is STUPID. It will be. So what? Logic doesn't care what sounds dumb. And I said infinitely many general conclusions, not infinitely many general conclusions that are wise. Of course most of them are dumb ideas. So now a lot of people are thinking: induce whichever one isn't dumb. Not the dumb ones. That's how you pick. Well, OK, and how do you decide what's dumb? That takes thinking. So in order to do induction (as it's just been redefined), in one of the steps, you have to think. That means we don't think by induction. Thinking is a prerequisite for induction (as just redefined), so induction can't be part of thinking. What happens here is the entirety of non-inductivist epistemology is inserted as one of the steps of induction and is the only reason it works. All the induction stuff is unnecessary and unhelpful. Pick good ideas instead of dumb ones? We could have figured that out without induction, it's not really helping. Some people will persevere. They will claim that it's OBVIOUS which ideas are dumb or not – no thinking required. What does that mean? It means they can figure it out in under 3 seconds. This is silly. Under 3 seconds of thinking is still thinking. Do you see what I mean about there are so many things wrong with induction it's hard to figure out where to start? And it's hard to go through them in an orderly progression because you start talking about something and there's two more things wrong in the middle. And here I am on this digression because most defenses of induction – seriously this is the standard among non-professionals – involve a denial of logic. So backing up, supposedly induction helps us make theories. How? Which ones? By what steps do we do it? No answers. And how am I supposed to prove a negative? How do I write an essay saying "induction has no answers"? People will say I'm ignorant and if only I read the right book I'd see the answer. People will say that just because we don't know the answer doesn't mean there isn't one. (And remember that refutation of induction I mentioned up top? Remember Popper's arguments that induction is impossible? They won't have read any of that, let alone refuted it.) And I haven't even mentioned some of the severe flaws in induction. Induction as originally intended – and it's still there but it varies, some people don't do this or aren't attached to it – meant you actually read the book of nature. You get rid of all your prejudices and biases and empty your mind and then you read the answers straight FROM the observation data. Sound like a bad joke? Well, OK, but it's an actual method of how to do induction. It has instructions and steps you could follow, rather than evasion. If you think it's a bad joke, how much better is it to replace those concrete steps with vagueness and evasion? Many more subtle versions of this way of thinking are still popular today. The idea of emptying your mind and then surely you'll see the truth isn't so popular. But the idea that data can hint or lead or point is still popular. But completely false. Observation data is inactive and passive. Further, there's so much of it. Human thinking is always selective and active. You decide which data to focus on, and which ways to approach the issue, and what issues to care about, and so on. Data has to be interpreted, by you, and then it is you interpretations, not the data itself, which may give you hints or leads. To the extent data seems to guide you, it's always because you added guidance into the data first. It isn't there in the raw data. Popper was giving a lecture and at the start he said, "Observe!" People said, "Observe what?" There is no such thing as emptying your mind and just observing and being guided by the data. First you must think, first you must have ideas about what you're looking for. You need interests, problems, expectations, ideas. Then you can observe and look for relevant data. The idea that we learn FROM observation is flawed in another way. It's not just that thinking comes first (which btw again means we can't think by induction since we have to think BEFORE we have useful data). It also misstates the role of data in thinking. Observations can contradict things (via arguments, not actually directly). They can rule things out. If the role of data is to rule things out, then whatever positive ideas we have we didn't learn from the data. What we learned from the data, in any sense, is which things to reject, not which to accept. Final point. Imagine a graph with a bunch of dots on it. Those are data points. And imagine a line connecting the dots would be a theory that explained them. This is a metaphor. Say there are a hundred points. How many ways can you draw a line connecting them? Answer: infinitely many. If you don't get that, think about it. You could take a detour anywhere on the coordinate plane between any two connections. So we have this graph and we're connecting the dots. Induction says: connect the dots and what you get is supported, it's a good theory. How do I connect them? It doesn't say. How do people do it? They will draw a straight line, or something close to that, or make it so you get a picture of a cow, or whatever else seems intuitive or obvious to them. They will use common sense or something – and never figure out the details of how that works and whether they are philosophically defensible and so on. People will just draw using unstated theories about which types of lines to prefer. That's not a method of thinking, it's a method of not thinking. They will rationalize it. They may say they drew the most "simple" line and that's Occam's razor. When confronted with the fact that other people have different intuitions about what lines look simple, they will evade or attack those people. But they've forgotten that we're trying to explain how to think in the first place. If understanding Occam's razor and simplicity and stuff is a part of induction and thinking, then it has to be done without induction. So all this understanding and stuff has to come prior to induction. So really the conclusion is we don't think by induction, we have a whole method of thinking which works and is a prerequisite for induction. Induction wouldn't solve epistemology, it'd presuppose epistemology. What we really know, from the graph with the data points, is that all lines which don't go through every point are wrong. We rule out a lot. (Yes, there's always the possibility of our data having errors. That's a big topic I'm not going to go into. Regardless, the possibility of data errors does not help induction's case!) And what about the many lines which aren't ruled out by the data? That's where philosophy comes in! We don't and can't learn everything from the data. Data is useful but isn't the answer. We always have to think and do philosophy to learn. We need criticisms. Yes, lots of those lines are "dumb". There are things wrong with them. We can use criticism to rule them out. And then people will start telling me how inconvenient and roundabout that is. But it's the only way that works. And it's not inconvenient. Since it's the only way that works, it's what you do when you think successfully. Do you find thinking inconvenient? No? Then apparently you can do critical thinking in a convenient, intuitive, fast way. At least you can do critical thinking when you're not irrational defending "induction" because in your mind it has authority.
Karl Popper is often misunderstood because he says the debates for several major philosophy issues involve a false dichotomy. The question is misconceived; both sides are wrong; a new way is needed. (Whether there are exactly two standard positions, or actually more in some cases, doesn't affect my point.) Popper's epistemology is the most innovative epistemology of note. By that I mean it changes more from prior epistemology than any of its rivals do. It's the most different. That makes it harder to understand. (Also, to be clear, Popper personally is not important. Like all philosophers, different people have read his books and interpreted him to be saying a variety of different things. I am interested here only in what I regard as the correct, best interpretation. This includes refinements by David Deutsch and myself.) What commonly happens is Popper (or a Popperian, or a person advocating a Popperian idea, whatever) says a particular epistemology idea is mistaken and tries to explain why. Then people usually interpret Popper as being on the other side of the dichotomy from them, because he's disagreeing with them. "If he says I'm wrong, he must be on the opposing side from me!" That's an easy conclusion to reach when you don't fully understand the point being made. But actually Popper is taking neither of the standard sides. It's hard conceiving of a new way of looking at an issue. That's harder than understanding that someone has an opposing position which you've heard before and have arguments about. The standard opponent is within your framework, which is easier to deal with. Look at it another way. For many issues, there are two sides which disagree but also have some points of agreement. For example, they agree on what the right question or dichotomy is, but give opposing answers to it. When popper says that not only is their answer wrong, but also their question is wrong, Popper is disagreeing with them more than their opponents do! So he could be misunderstood as an even more disagreeable version of their opponents, even though he isn't. This is relevant to Objectivism because Objectivists have misunderstood Popper, and their criticisms of Popper rely on misunderstanding his positions. There aren't any Objectivist refutations of the Popperian ideas I'm advocating. (Nor are there Objectivist answers to Popper's actual criticisms of some Objectivist positions, like induction). Popperian epistemology does not contradict all of Objectivist epistemology. There are many points in common, such as valuing clarity and accepting the possibility of humans attaining objective knowledge. But there are some major points of disagreement such as induction and self-evident axioms. Objectivists have the opportunity to learn something, and should be happy about that (just as, for example, Popperians could and should learn a lot from Objectivist morality and politics). Let's look at some example issues where there is a false dichotomy which Popper rejects: certainty and proof, induction, justification, support. Take certainty or proof: there is a false dichotomy between having certainty and not having knowledge. There is an assumption, shared by both sides, that certainty is a requirement of knowledge. Popperian epistemology rejects that package deal, and offers a new way: a non-authoritarian, fallibilist way to gain objective knowledge. Take induction: the two main positions both center around the problem of induction. One position is that we can solve the problem of induction (some claim they already did solve it, some expect it to be solved any decade now). Another position is that the lack of solution to the problem of induction presents a big problem for epistemology. The popperian position is that it's the wrong problem, the wrong question. Popper instead raised a different better question and solved it. Take justification: there is a false dichotomy between "yes we can justify our beliefs/ideas/knowledge" and "no we can't, justification fails due to regress [and several other arguments], therefore knowledge is impossible". The Popperian view is that both of these positions are wrong. They both agree on an incorrect concept of what justification is and why we need it. They package justification together with knowledge. Take support: consider the idea that we can support our beliefs with evidence and arguments. Some people say we can't, therefore our beliefs are irrational. Some people say we can, and it makes our beliefs rational. Both sides have accepted that we need to support our beliefs with evidence and argument for them to be rational. Popper disagrees with both standard sides. He says we don't have to support our beliefs with evidence and argument for them to be rational; that isn't actually how you get rational knowledge; but there is a different way of getting rational knowledge. There is a package deal combining rationality and support. And it creates a false dichotomy where either you have both rationality and support, or neither. Popperian epistemology is a complex subject requiring study to understand well. I cannot cover it all here. I'm going to talk about one example in more detail to give you a sample. Do we have to support our beliefs with evidence and arguments for them to be rational? Pretty much everyone agrees the answer is "yes". That includes both people who think we can do this and thereby get rational knowledge, and also people who think that our inability to do this prevents us from getting rational knowledge (skeptics). The Popperian view is that rationality is not about support. It is achieved by a different method. Rational ideas are ideas which are open to criticism. If there's no way to improve an idea, it's stuck, it's bad, it's irrational. If it's open to improvement via criticism – if it's open to reform, refinement, error correction – then it is rational. Whether ideas are open to error correction does not depend on how much support they have. That is not the issue. (And actually, sometimes when people say, "I've proved my case with all this supporting evidence," it can indicate they are not open to criticism.) Think, for a moment, about what we want to accomplish in epistemology. For example: we want to sort out good ideas from bad ideas. We want to improve our ideas. We want to get knowledge – ideas that are connected to reality and effective in reality. Trying to support ideas was a false goal. It's not really what we wanted. It was a way of getting something else. It had indirect value. It's important to identify this gap and separate the concepts. We can reject support but still find a different method to get the useful stuff support was intended to achieve. Supporting ideas is meant to sort out good ideas from bad ideas. The ones with more support are good. This method does not work. One unsolved problem with it is to define exactly when, why and how much any given idea supports any other ideas. A second problem is whether a less supported idea could be the best one. If it can, what does it really matter that it's less supported? However, a different method of sorting out good ideas does work: criticism. Ideas which are not refuted by criticism are sorted out from those which are refuted by criticism. (These critical classifications are always open to revision in the future as we learn more.)
Objectivists accuse Popperians of being skeptics. Popperians accuse Objectivists of being infallibilists. Actually, both philosophies are valuable and largely compatible. I present here some integrating ideas and then a mistake that both philosophies share. Knowledge is contextual, absolute, certain, conclusive and progressive. The standard of knowledge is conclusiveness not infallibility, perfection or omniscience. Certain means we should act on it instead of hesitating. We should follow its implications and use it, rather than sitting around doubting, wondering, scared it might be wrong. Certain also means that it is knowledge, as opposed to non-knowledge; it denies skepticism. Absolute means no contradictions, compromises or exceptions are allowed. Contextual means that knowledge must be considered in context. A good idea in one context may not be a good idea when transplanted into another context. No knowledge could hold up against arbitrary context switches and context dropping. Further, knowledge is problem oriented. Knowledge needs some problem(s) or question(s) for context, which it addresses or solves. Knowledge has to be knowledge about something, with some purpose. This implies: if you have an answer to a question, and then in the future you learn more, the old answer still answers the old question. It's still knowledge in its original, intended context. Consider blood types. People wanted to know which blood transfusions were safe (among other questions) and they created some knowledge of A, B, AB and O blood types. Later they found out more. Actually there is A+, A-, B+, B-, AB+, AB-, O+ and O-. It was proper to act on the earlier knowledge in its context. It would not be proper to act on it today; now we know that some B type blood is incompatible with some other B type blood. Today's superior knowledge of blood types is also contextual. Maybe there will be a new medical breakthrough next year. But it's still knowledge in today's context, and it's proper to act on it. One thing to learn here is that a false idea can be knowledge. The idea that all B type blood is compatible is contextual knowledge. It was always false, as a matter of fact, and the mistake got some people killed. Yet it was still knowledge. How can that be? Perfection is not the standard of knowledge. And not all false ideas are equally good. What matters is the early idea about blood types had value, it had useful information, it helped make many correct decisions, and no better idea was available at the time. That value never goes away even when we learn about a mistake. That original value is still knowledge, considered contextually, even though the idea as a whole is now known to be false. Conclusive means the current context only allows for one rational conclusion. This conclusion is not infallible, but it's the only reasonable option available. All the alternative ideas have known flaws; they are refuted. There's only one idea left which is not refuted, which could be true, is true as far as we know (no known flaws), and which we should therefore accept. And that is knowledge. None of this contradicts the progressive character of knowledge. Our knowledge is not frozen and final. We can learn more and better – without limit. We can keep identifying and correcting errors in our ideas and thereby achieve better and better knowledge. (One way knowledge can be better is that it is correct in more contexts and successfully addresses more problems and questions.) The Mistake Peikoff says that certainty (meaning conclusive knowledge) is when you get to the point that nothing else is possible. He means that, in the current context, there are no other options. There's just one option, and we should accept it. All the other ideas have something wrong with them, they can't be accepted. This is fine. Peikoff also says that before you have certainty you have a different situation where there are multiple competing ideas. Fine. And that's not certainty, that's not conclusive knowledge, it's a precursor stage where you're considering the ideas. Fine. But then Peikoff makes what I think is an important mistake. He says that if you don't have knowledge or certainty, you can still judge by the weight of the evidence. This is a standard view held by many non-Objectivists too. I think this is too compromising. I think the choices are knowledge or irrationality. We need knowledge; nothing less will suffice. The weight of the evidence is no good. Either you have knowledge or you don't. If it's not knowledge, it's not worth anything. You need to come up with a good idea – no compromises, no contradictions, no known problems – and use that. If you can't or won't do that, all you have left is the irrationality of acting on and believing arbitrary non-knowledge. I think we can always act on knowledge without contradictions. Knowledge is always possible to man. Not all knowledge instantly, but enough knowledge to act, in time to act. We may not know everything – but we don't need to. We can always know enough to continue life rationally. Living and acting by reason and knowledge is always possible. (How can we always do this? That will be the subject of another essay. I'm not including any summary or hints because I think it's too confusing and misleading without a full explanation.) Knowledge doesn't allow contradictions. Suppose you're considering two ideas that contradict each other. And you don't have a conclusive answer, you don't have knowledge of which is right. Then using or believing either one is irrational. No "weight of the evidence" or anything else can change this. Don't pick a side when you know there is a contradiction but have not rationally resolved it. Resolve it; create knowledge; learn; think; figure it out. Neither idea being considered is good enough to address the contradiction or refute the other idea – so you know they are both flawed. Don't hope or pray that acting on a known-to-be-flawed idea will work out anyway. Irrationality doesn't work. That's not good enough. If you discover a contradiction, you should resolve it rationally. If you fail at that – fail at the use of reason – then that's bad, that's a disaster, that's not OK. Karl Popper made the same mistake in a different form. He said that we critically analyze competing ideas and the one that best survives criticism should be acted on. Again this is too compromising. Either exactly one idea survives criticism, or else there is still a contradiction. "Best survives criticism", and "weight of the evidence", are irrational ways of arbitrarily elevating one flawed idea over another, instead of using reason to come up with a correct idea. (For some further discussion about weighing ideas, see also the choices chapter of The Beginning of Infinity by David Deutsch.)