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William O

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William O last won the day on March 24

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  1. I'm asking how modus ponens is justified. I am not (knowingly) asking about child psychology or the history of logic. It is fair to ask of any item of knowledge "how do we know X?" The reason for this is that there is no such thing as innate knowledge or divine revelation, which means that all knowledge must be traceable by some series of steps back to observation (the given). So for example, "how do we know the earth is round?" and "how do we know concepts are formed by measurement omission?" are fair questions. I'm just substituting modus ponens for X in this formula. Yes, I made a mistake in the OP. What I tried to do if you look back is to stipulate that "the Objectivist answer" means either the answer given by Rand or the answer given by an Objectivist intellectual. This was a bad idea on my part and it has contributed to considerable confusion since it directly contradicts the correct definition of Objectivism as the philosophy of Ayn Rand. Overwhelmingly, philosophers have maintained that logic and mathematics are not justified by observation and induction. That is what I meant, although naturally logic itself is much less controversial than philosophy of logic.
  2. I don't see how modus ponens is justified here, since you haven't mentioned modus ponens at all. If you're saying that Aristotle's work contains a justification of modus ponens, my understanding is that he thought the categorical syllogism (e.g. Barbara: "All As are B, and all Bs are Cs, therefore all As are Cs") was the only form of logical inference. So I'd be very surprised to find out that he justified modus ponens. Before I started this thread, I was very unclear about the epistemology of logic. That is, I was not sure how we arrive at the knowledge that the forms of inference are true using only observation and induction. Presumably this isn't just stupidity on my part, since virtually nobody outside of Objectivism would say it's possible to get logic from observation and induction. This has been partially ameliorated by MisterSwig's short derivation of modus ponens from the law of identity. I am still not happy with the particular way he defends the law of identity, but that's a different topic really, and there can be no doubt of the law of identity itself.
  3. I paid $7 for it, so it would be an expensive preview. At any rate, there is definitely a new Kindle book over a hundred pages long sitting on my computer right now.
  4. ...huh. You're right. And the link I posted in the OP is no longer working. Well, since I've personally read the Kindle version, which I assure you cannot be 512 pages of normal size, all I can say is that it used to be available as I described it. I don't know what's up with that.
  5. Thanks for responding. I attempted to explain what I meant by "how we come to know modus ponens" in an earlier post: "Objectivism holds that all knowledge originates from perception, meaning that our knowledge of modus ponens has to arise from perception. In other words, there has to be some series of observations and inferences leading to the conclusion that modus ponens is valid. So I'm asking for a detailed description of that series of observations and inferences." Another way of putting it is that I'm asking for a reduction of modus ponens to observation. I think the derivation from the law of identity that MisterSwig gave earlier was pretty good, though.
  6. This is not the Objectivist position. More importantly, it does not work in its own right. First, this isn't the Objectivist position: "[An axiomatic concept] is the fundamentally given and directly perceived or experienced, which requires no proof or explanation, but on which all proofs and explanations rest." http://aynrandlexicon.com/lexicon/axiomatic_concepts.html Induction would be a form of "proof," which Rand denies is applicable to axioms above. There is also a passage in OPAR where Peikoff explicitly denies that axioms are based on induction. I don't have OPAR with me, though. Second, your explanation does not work in its own right because it is impossible to perform induction without presupposing the law of identity. The law of identity is presupposed in the process of concept formation that leads up to induction, since every concept is the concept of something with a determinate identity. The law of identity is also presupposed by the law of causality on which induction depends, since causality is a corollary of identity. You also say that the law of identity is "contextually valid," which leads straight to skepticism since there is no rational way of delimiting the context of the law of identity. How would you ever know whether you were within the context? For example, if you're reasoning about cats, what would a cat that isn't a cat look like? Even if you did prove something - say, cats have kidneys - how would you know whether or not cats also lacked kidneys on that premise? And what if cats are cats today but not tomorrow? You cannot prove anything without absolutely ruling out the possibility of a contradiction in reality ahead of time.
  7. Thanks for responding. I have a couple of follow-up questions. First, what does this explanation add to modus ponens? Why isn't it just a repetition of the rule? Second, how do we know through observation that the law of identity holds universally? I know my second follow-up question is a bit of digression. However, it's something that I've been wondering about in its own right, and answering it is technically necessary in order to derive the universality of modus ponens from the law of identity.
  8. Thanks for responding, it shows me what I need to clarify. p and q are variables that represent propositions. I could also have used any lowercase letter (a, b, c..., y, z). For example, p could stand for "the streets are wet" and q for "it rained last night." I'm under the impression that this is standard in formal logic. I agree that modus ponens is a valid form of deductive inference - if 1 and 2 are true for some value of p and q, then 3 is always true. My question is how we know that according to Objectivism. Objectivism holds that all knowledge originates from perception, meaning that our knowledge of modus ponens has to arise from perception. In other words, there has to be some series of observations and inferences leading to the conclusion that modus ponens is valid. So I'm asking for a detailed description of that series of observations and inferences.
  9. Modus ponens is, of course, the following pattern of inference: If p, then q. p. Therefore, q. What is the Objectivist position on how we come to know this inference rule? "The Objectivist position" here can mean either the position taken by Rand or the position taken by an Objectivist intellectual. I am pretty sure Rand never addressed this in the official Objectivist literature. Thanks in advance.
  10. Thanks to Dr. Odden's suggestion that I write out the actual axiomatic propositions, it occurs to me that "self" (or "I have a self") is another axiom pertaining to consciousness. It has to be, since the term "I" appears in nearly all of 1-11. "Knowledge" (or "I have knowledge") is another one.
  11. You're right, I listed axiomatic concepts rather than axioms as I defined the term. The axiomatic propositions (what I called axioms in the OP) would be: I am conscious. I can perceive the world. I have free will. My concepts, beliefs, and thoughts have intentionality. I have the faculty of introspection. I can understand things. I can form concepts. I can form beliefs. I have the faculty of memory. I can think. I have the faculty of reason. I see now that not stating these as axiomatic propositions in the OP was a major mistake - the process of translation is more complex and error prone than I realized. It's not mechanical. The IEP explains the concept of intentionality pretty well. I assume you are already familiar with this concept, but other people might not be: "If I think about a piano, something in my thought picks out a piano. If I talk about cigars, something in my speech refers to cigars. This feature of thoughts and words, whereby they pick out, refer to, or are about things, is intentionality. In a word, intentionality is aboutness." https://www.iep.utm.edu/intentio/ It seems clear how intentionality is conceptually distinct from free will given this characterization.
  12. Right, that did cross my mind when I wrote the OP. One thing that I would like to be able to say here is that there's a concept of "consciousness on the human level" which is convertible with some of 1-11. For example, we might think that "reason" is convertible with "consciousness on the human level." I didn't say that because "consciousness on the human level" sounds more like a cross-classification than an actual distinct concept. Like, what's the difference between that and just substituting any conscious organism for X in "consciousness on the X level?" Why say "the human level" and not just state that humans have concepts, propositional thought, reason, and all of the other components of human consciousness? Aristotle's concept of the rational soul might be of use here. I'm influenced by Binswanger there. Consciousness is metaphysically active. If an entity is just pulled along by external forces, and has no capacity to initiate its own thought or action, it is not conscious. This is why I don't think computers are conscious. So I'd say either cockroaches aren't conscious (in other words, they are little robots), or they have some limited capacity to make free choices. What's the distinction you're drawing between free will and volition? I've always used those terms as synonyms. This is interesting. I think the concept of a goal (or desire or inclination) has to be related to the concept of reason, because reason is goal directed. So I think those concepts are likely axiomatic as well. I can't personally make that case for pain or pleasure.
  13. Let's define an axiom as a self evidently true proposition that serves as the foundation of all other knowledge. I've noticed that there are a lot of axioms pertaining to consciousness: Consciousness (trivially) Perception Free will Intentionality Introspection Understanding Concept Belief Memory Thought Reason That's eleven. It is self evident that each of these exists, and the denial that any one of them exists is self refuting (I assume the latter is obvious with a little reflection, but I can prove it if necessary). Also, each of 1-4 (consciousness, perception, free will, and intentionality) is "convertible" with the concept of consciousness. If you have any of 1-4, then you have consciousness; and if you have consciousness, then you have all of 1-4. Maybe one of you can argue that some of 5-11 are convertible with the concept of consciousness too, although I can't. I found this interesting, so I thought I'd share it. If you can refute me or add something to what I've said then I'd appreciate it.
  14. This book provides transcripts of many of Peikoff's podcasts. I've bought the Kindle version and I'd say it's pretty good. https://www.amazon.com/dp/B07P5TWX4J/ref=nav_ya_signin?#reader_B07P5TWX4J
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