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StrictlyLogical

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  1. Man IS the rational animal, but His capacity for INSANITY is unbounded.
  2. Thank you Boydstun. Another interesting twist. You seem to indicate that a string of words can be meaningful and a sentence if it tries to state something about an identifiable referent... even if that something is inapplicable, or nonexistent. The result is a sentence which is false. "This sentence" is surely a referent. The purported something about the sentence, is its truth or falsity. Let us consider what "truth" or falsity" is. Objectively it identifies a state of the relationship between the "something said" and the referent. As such, the term "true" or "false" must have its own referent, the relationship. Here the content (something) attempted is "truth" but "truth" as such presupposes antecedent relationship which it cannot itself supply. So in a sense, only the content is meaningless, or better, missing. The string of words says nothing about "This sentence" although it promises to. So what about "is true"... do we treat it as inapplicable, nonsensical, or missing entirely? "This sentence is furry." Here "is furry" is inapplicable to words. But is the sentence meaningful? Certainly the referent is clear. But the content is categorically inapplicable, words can never possess furriness or non-furriness. Is this simply an error of degree akin to "this sentence has 2 words in it" or is it an error of a different kind? In some sense this is cleaner than "This sentence is true" because it does not mislead one (quite as much) to presume something... namely that the sentence can be evaluated as true or false... since most sentences can be evaluated as true or false, it sucks us in... whereas since we know sentences cannot be valuated on furriness "This sentence is furry" can easily be dismissed as nonsensical. In what sense can something be nonsensical but meaningful? Alternatively should we adjudge based on higher principles that all sentences which are not true are simply FALSE, and any attempt to distinguish between meaningful, non-meaningful, sensible or nonsensical is somehow artificial? This reminds me in a very indirect way the impotence of the zero... What I like about dropping the idea of meaningful versus meaningless falsehoods, is that it wipes away all the confusions about the so called indeterminate cases. It also seems to take care of fiction. Everything that does not qualify as TRUE is simply FALSE. Now if we ground truth in objectivity, then the referent, the something, and the relationship all each have to be identified with words in a meaningful and rational manner. The words must identify valid concepts and their valid relationships in a logically cogent manner. "This sentence is true" cannot be objectively true, it is nonsensical, meaningfulness is beside the point? Do I have anything to say anymore? Is my OP in any sense useful? I'm not sure...
  3. I am no expert, but I seem to recall the kinds of "truths" missing from a consistent system, making them "incomplete" are the sorts of things which have no meaning... self referential and/or are self-contradictory... at the very least, and I am no expert, I have not been heard of any meaningful truth being missing from a consistent system... Whether or not this is a real problem is also something I am not sure about... but the claims as to the ramifications, import, or profundity of the work is in many cases overblown... especially when it is used to attack knowledge as a whole, which I believe to be a gross misapplication out of context. The reasoning is as follows: If Gödel's system applies to systems of math... then since reality and thought are also math (Platonic Idealism) then the universe and/or man's knowledge is also complete but inconsistent or consistent but incomplete.
  4. Ah yes... "The vampire ate the demon's soul." Is FALSE... (and on some level quite insane).. but IN the context of imagination... not necessarily meaningless. If "statements" can be about non-reality or unreality... how do we keep them grounded IN reality? In what sense are ungrounded statements ... meaningful? IF we can do this and have "meaningful" literary FICTION.. what is to stop one from engaging in "meaningful" ethical, political, mathematical, philosophical, or scientific.... fiction? In such contexts, what is the concept "meaningful"? It should not be conflated with "useful", "rewarding", or "valuable"... Are we really reading into each and every statement of fiction, IF SUCH WERE REAL... "the vampire ate the demon's soul". Yes I will need to rethink 2, possibly the combination of all 3.
  5. Ah yes. How about the following: K) This sentence has eight words and is true. L) This sentence has eighteen words and the first part of this sentence prior to the "and" is true.
  6. Interesting read at TOS: https://www.theobjectivestandard.com/2019/07/regarding-carl-barney-and-scientology/
  7. Still playing around with this. Does anyone have any thoughts about the following: 1. A string of words is a statement if and only if it has meaning. 2. A string of words has meaning if and only if it states something about a referent in reality. 3. Only those strings of words which are statements, are either true or false, the truth or falsity of which only arises as a consequence of the relationship between the something it says and its referent. Corollaries: A. A string of words which is neither true nor false, is meaningless, and cannot be deemed a sentence. B. A statement's truth can also be a referent in reality if and only if the string of words making up the statement can first be evaluated as true or false given the something it states about its referent in reality. Result: P- "Sentence A is true" is either true or false. (if A is not a sentence P is a lie... false) Q-"This sentence is true." is a meaningless string of words. It states nothing about any referent in reality, and hence there is no relationship between what it says and reality which in the first instance could cause it to be true or false, from which one could then evaluate whether the string of words is true or false.
  8. Here is the interesting part. Since the fundamentals of math grows out of concepts which ultimately come from percepts, absolute disconnection is difficult to achieve. As for entire branches of math... I do not know. The problem is not that math can get VERY abstract, VERY far from the concretes of reality which are connected to them, but that those who are DOING the math dispense with that connection entirely. Embracing either the idea that it is a game of the mind disconnected from reality or a revelation of a Platonic Ideal Reality risks the creation of mathematical concepts which do become disconnected in the same way floating abstractions can become disconnected. Imagine, like some freshman philosophy students, you embrace the idea that what you do need not conform to anything, nothing in reality, none of the axioms, and you can simply create systems out of nothing and with no rules except what you give it. WE know such creations do not fall within what is VALIDLY to respectively be called knowledge or the love and study of it (philosophy) nor mathematics. Attempting to "Invent" a "number system" (system of symbols) which represent contradiction as part of a formal system would constitute such an insanity... I'm not sure it was ever done... but a mentality that thinks of it as "fair game" is NOT hinged to reality. I believe there is a strong case to be made philosophically against various mathematical constructs and even well accepted "profound" conclusions. Symbolic logic and nonsensical implication (truth tables) and Gödel's theorem are the types of things that require better Objective explication and understanding.
  9. I have an MSc. in physics and not quite a minor (with my BSc. w hon in physics) in Math... I have to say that the VAST majority of professors and students in Math and Physics have a severely Rationalistic, Platonic, and Idealistic (as in Idealism) slant. Very few have a good grounding in valid philosophy, and are quite happy to embrace logical fallacies, engage in compartmentalization, and come with a desire to find incomprehensibility, like a strange desire not to understand, but to embrace the impossible. I would put the ratio at 80%-20%... and I would say only with my exposure to Objectivism have I been able to put myself in the more objective out of that 20%. It is unfortunate but it is not surprising. Like people who go into philosophy with the best intentions, certain mentalities are drawn into "high math" and "high physics"... the most common baggage is a rejection of "low reality", the "concrete", the "practical", money and business (life?) and an embrace of the "ideal", the abstract, the Academy... it is hard for me to convey ... one has to live it to really understand the culture, the philosophical undercurrent. Roger Penrose's "Three world" theory is something most Physicists and Mathematicians would not bat an eye at. Rather than mental contents "in here" versus the world "out there", Penrose imagines a relationship between three "worlds": the "Platonic Mathematical World", the "mental world", and the "physical world". It might be understandable that the false dichotomy between consciousness and existence is exaggerated (minds are not supernatural but consciousness is a unique functioning/attribute/property of reality) but a separate world of Ideas for math... only comes from studying numbers to a point that they take on an existence all to themselves... reification by sheer repetition. Here is an article which talks about this: https://astudentforever.wordpress.com/2015/03/13/roger-penroses-three-worlds-and-three-deep-mysteries-theory/ and another one https://scientificgems.wordpress.com/2013/05/18/three-worlds/
  10. This I think is a species of a more general principle. ALL mental content is ultimately “about” living in the real world. Of course we can think about thoughts and imagine and abstract from abstractions and go play with mental contents off in the far lands of the mentality, but we do so with reference to its ultimate connection with reality... finally in our ability to use our mental capacity to gain knowledge of and act in the world. Some small bit of mental content might not have a direct and concrete referent in reality, but every sane concept has to be at least indirectly connected to reality. Even imagination is often connected to, taken from, or relatable to parts of reality. A concept whose referent is wholly disconnected from all of reality would be the product of insanity. Math although highly abstract at times is ultimately about quantities and measurement of aspects of reality not an untethered game tossed upon a sea of floating abstractions. This might remind one of Rand’s reframing and reinforcing the term morality for man living life in reality rather than a nonexistent soul’s duty to a nonexistent God. In the same way and for the same reason Math as a value for man is about the world.
  11. Well now... that was fast... and without even a glowing review from me. Have you read any of the following by Tara Smith? Ayn Rand's Normative Ethics: the Virtuous Egoist Viable Values: A Study of Life as the Root and Reward of Morality They are as good, if not better, than anything from anyone who has written on Objectivism. IMHO she is an extraordinary thinker and communicator.
  12. Merlin For a more in-depth treatment of Math being about the world (nothing to do with Tew) see Robert E. Knapp’s book. https://mathematicsisabouttheworld.com/ I’m slowly making my way through it. In the first chapter I find his style awkward and repetitive (this might change in later chapters) but the substance so far, once distilled, is illuminating. I can’t wait to get to the chapter on group theory.
  13. You claim to have a superior logical system to mine or at least you “fear” my logic is wrong... well here is your opportunity, teach me, teach us all. Please do, I’m asking you. You say: For the first lesson, explain how “finding an example of a contradiction” proves the premise “all contradictions are impossible” is false. Don’t worry about my inferior logic; please show us using your logic and keep it simple and clear so we can all follow and understand.
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