• andrewk
    1.4k
    do you agree that the judgement of whether or not an argument constitutes a proof is dependent on that argument being understood?Metaphysician Undercover
    It depends on what one means by 'understood'. There are proofs that I have followed step by step, and validated each step, yet I am still unable to visualise the big picture, as to why the proof works. There is a formal understanding but not an intuitive one and it is the latter that is ultimately most important to me. So I would say that there are proofs that I have verified to be valid even though I do not really understand them. But in such cases I have suffiicient understanding to recognise that my failure to fully understand the proof is a deficiency in my cognitive capabilities rather than a deficiency in the proof.

    I suppose that's a 'No' then. One can judge that something is a proof without understanding it.

    Perhaps a helpful parallel is a chess game. One can look at the moves in a Fischer vs Spassky game and verify that Fischer did indeed do a sequence of legal moves that resulted in Spassky being in an unwinnable position. But that is not the same as understanding the strategy by which Fischer achieved that.
  • Aaron R
    178
    In my view, part of the essential nature of a lion is that it lives in the world that we inhabit, whereas a unicorn is a merely a fictional creature represented in books and pictures. So for someone to mistakenly talk about lions as if they were fictional entities would be for them to entirely misconceive the essential nature of lions.Andrew M

    If the essence of being a lion included its existence, then lions could never cease to exist. What you are arguing implies that lions have always existed and will always exist just in virtue of what they essentially are.
  • Metaphysician Undercover
    4.1k
    I suppose that's a 'No' then. One can judge that something is a proof without understanding it.andrewk

    How can you be sure that such a proof is actually a proof then, without any understanding? You claim that you can verify the proof to be valid, without understanding it, and I question whether this is really true. Understanding come in degrees, and any such verification, I believe would require some degree of understanding. So I disagree with your distinction between a formal understanding and an intuitive understanding. I think that within any system of logic, there are different depths of understanding, different degrees to which one understands.


    For example, if I multiply two numbers, 7 and 8, I get 56. I can verify this by taking 56 and dividing it by 8, to see if I get 7. Such a demonstration requires some understanding, an understanding of the relationship between multiplication and division. I could also proceed to take eight groups of seven, put them together, and count them all up. This demonstrates an understanding of the procedure of multiplication. We can propose that someone could learn multiplication by memorizing times tables or something like that, so that this person could multiply without understanding anything. This would be just an association by recognition. But how would that person "prove" that what they are doing is multiplying, without some understanding of what it means to multiply. So I think that any type of verification, i.e. a judgement that a so-called proof is actually a proof, requires some degree of understanding. The depth of understanding demonstrated by the verification relates to the quality of that judgement.

    Perhaps a helpful parallel is a chess game. One can look at the moves in a Fischer vs Spassky game and verify that Fischer did indeed do a sequence of legal moves that resulted in Spassky being in an unwinnable position. But that is not the same as understanding the strategy by which Fischer achieved that.andrewk

    That's a similar example to mine. To determine "legal moves", and "unwinnable position" requires some understanding of the game, a rather shallow understanding. To be able to produce strategies within the game is to have a deeper understanding. I do not agree to your distinction of formal and intuitive understanding, because I think that there are just degrees of depth to this type of understanding, which is specifically understanding the rules of the game.

    However, in the case of a competitive game, there is a matter of anticipating the moves of the competitor, and that requires a completely different type of understanding which is unrelated to understanding the rules of the game. We could assume that there are some type of (intuitive?) rules here, which are rules for application. Understanding application is a completely different type of understanding from understanding the rules of the game We could say that there are similar "rules" for application of logic and mathematics as well. This would be such as what qualifies as "8", what qualifies as "7", how do we judge an object as fulfilling the conditions of the definition. Understanding the rules for application is a completely different matter from understanding the rules of the logical system.

    But I don't think that there are any such rules, in reality, there is only some sort of intuition. We can't have rules for the application of rules, or we'd need rules for the application of those rules, ad infinitum. So these are definitely two distinct types of understanding. One is concerned with relating rules to each other, and this you call a formal understanding. The other relates rules to other things, opponents in games, and physical objects in science. Of the latter type of understanding, the intuitive one that relates rules to things, do you not agree that there is a better and a worse intuition? So judging by statistics or something like that, the person who wins the game more often could be said to have a better understanding of how to apply the rules.
  • andrewk
    1.4k
    Of the latter type of understanding, the intuitive one that relates rules to things, do you not agree that there is a better and a worse intuition?Metaphysician Undercover
    I would partially agree, but I expect it would not be the sort of agreement you would wish.

    First, the agreement is partial because I would see the set of intuitions about relationships of rules to phenomena ('things') as a partially ordered set. In such a set, for some pairs of intuitions we can say one is better than the other, but for other pairs we cannot.

    But we also need a definition of 'better'. The one I would instinctively reach for is 'more useful'. One intuition is 'better' than another under my interpretation if it enables more accurate predictions.

    Based on past posts, I have the feeling that you would reject using 'usefulness' as a benchmark for quality of an intuition. But that then begs the question of what definition of 'better' you would like to use in its place. Again I might guess that you would prefer a definition that had something to do with 'truth'. Personally, I would reject such a definition, as I do not believe in Absolute Truth.

    Now my understanding is that Aristoteleans form a proper subset of those who believe in Absolute Truth. So there should be no difficulty finding a non-Aristotelean that believes in Absolute Truth, who thus could continue down that line of discussion, by accepting 'truth' as a measure of the quality of an understanding. But I am not such a person.
  • Metaphysician Undercover
    4.1k
    But we also need a definition of 'better'. The one I would instinctively reach for is 'more useful'. One intuition is 'better' than another under my interpretation if it enables more accurate predictions.andrewk

    Yes, surprisingly enough, I agree with this, but of course, there is a catch. As Aristotle distinguishes two types of knowledge in his Nichomachean Ethics, practical and theoretical, accordingly there are two distinct types of intuition. What I have described, and we seem to agree upon is practical intuition. At the other end of the spectrum is theoretical intuition

    Consider practical intuition, as what is called for when we are apply theory to the physical world in practise. The farmer with good practical intuition will choose the best time to plant the crop. Theories of calendar date, soil moisture, weather forecasts, etc., all must be considered with the appropriate weight, to bring about the best result. In the case of theoretical intuition, this is inverted, such that knowledge gained from the world of practise is applied toward producing theories.

    In theories, words are defined. Often in the form of hypotheses, the definitions need to be confirmed. Good intuition, in the sense of theoretical intuition, refers to the person who can foresee hypotheses which will be confirmed, and will produce theories which have a high probability of being verified. So for example, people like Isaac newton, and Albert Einstein had good theoretical intuition. Einstein for instance defined simultaneity in a particular way, giving examples to demonstrate exactly what he meant, and he had good theoretical intuition to stipulate that the speed of light is constant.

    Based on past posts, I have the feeling that you would reject using 'usefulness' as a benchmark for quality of an intuition. But that then begs the question of what definition of 'better' you would like to use in its place. Again I might guess that you would prefer a definition that had something to do with 'truth'. Personally, I would reject such a definition, as I do not believe in Absolute Truth.

    Now my understanding is that Aristoteleans form a proper subset of those who believe in Absolute Truth. So there should be no difficulty finding a non-Aristotelean that believes in Absolute Truth, who thus could continue down that line of discussion, by accepting 'truth' as a measure of the quality of an understanding. But I am not such a person.
    andrewk

    With respect to "Absolute Truth" then, practical intuition is not at all concerned with truth in any absolute sense. The theories are in place, and they are applied to the best of one's ability, to get the best results, This is a matter of predicting outcomes according to what is necessary for the particular circumstances. In the case of theoretical intuition though, we may consider the possibility of absolute truth. The individual who is crafting the theory must be guided by certain principles. The theory must be the most practical as is possible, the best means the most practical. That is an ideal which the theoretician follows. It could be argued that this ideal, the "most practical", is equivalent with "absolute truth".
  • Andrew M
    419
    If the essence of being a lion included its existence, then lions could never cease to exist. What you are arguing implies that lions have always existed and will always exist just in virtue of what they essentially are.Aaron R

    My view is that only existents have essential natures. Why would that imply an eternal existence?

    I notice that this specific issue seems to mark a point of departure for Aquinas from Aristotle. From the SEP entry on Existence:

    Aristotle seems to have seen nothing more to existence than essence; there is not a space between an articulation of what a thing is and that thing's existing. Saint Thomas Aquinas, on the other hand, famously distinguished a thing's essence from its existence.
  • Aaron R
    178
    My view is that only existents have essential natures.Andrew M

    Right, but I don't believe that this is what is being called into question. What is in question is whether there is a real distinction between essence and existence within each existing thing.

    Why would that imply an eternal existence?Andrew M

    Denying the real distinction between essence and existence within a being implies necessary existence. If the "what-ness" of something includes existence, then it exists simply in virtue of what it is. Such a being could not fail to exist insofar as it is what it is.

    I notice that this specific issue seems to mark a point of departure for Aquinas from Aristotle.Andrew M

    Yes and no. Aristotle recognized the distinction between what a thing is and that a thing is: in fact, his entire scientific methodology (posterior analytics) is founded upon the distinction. It's true that Aristotle never explicitly elaborated a theory of existence apart from essence, but the beginnings of such a theory are implied by much of what he wrote. One could argue that the failure to elaborate such a theory is a gaping hole at the heart of Aristotle's overall system. After all, if form is act with respect to the potency of matter, then form must be the principle by which any individual substance is. Yet, for Aristotle, form has no being in and of itself. But how can something that has no being in itself be the principle by which anything is? It doesn't add up.
  • Andrew M
    419
    Right, but I don't believe that this is what is being called into question.Aaron R

    I think it is. In "On Being and Essence" Aquinas says, "I can understand what a man is or what a phoenix is and nevertheless not know whether either has existence in reality."

    Aquinas is saying that a phoenix has an essence (or, put differently, that there is a phoenix essence - "what a thing is") even though phoenixes don't exist. That becomes the basis for his distinction between existence and essence.

    This would have been foreign to Aristotle, who held that valid (formal) distinctions can only be made on the basis of existents (particulars).

    If only particulars have form (and an essential nature) then there is no implication of necessary existence. It is not the form that exists (or not), it is the particular.
  • Aaron R
    178
    Aquinas is saying that a phoenix has an essence (or, put differently, that there is a phoenix essence - "what a thing is") even though phoenixes don't exist. That becomes the basis for his distinction between existence and essence.Andrew M

    Indeed, that is one of the arguments that is often given. I was trying to steer us away from that particular line of thought because it takes us pretty deep into epistemology. In scholastic terms, phoenixes do not have "subjective" existence - that is, they are not mind-independent subjects of existence. However, they do exist "objectively" - that is, mind-dependently. Qua objects of thought, phoenixes have a form all their own. Indeed, it is via such forms that we classify imaginary creatures into "this" or "that" type. When I imagine a particular phoenix, I am objectively instantiating the form "phoenix".

    This would have been foreign to Aristotle, who held that valid (formal) distinctions can only be made on the basis of existents (particulars).Andrew M

    Yes, all formal distinctions trace their ultimate genesis in subjective reality as appropriated by the senses. A more metaphorical way to put it is to say that all distinctions are woven from the raw materials provided by the senses. That doesn't imply that every formal distinction is a real distinction, and I believe that Aristotle recognized that distinction to some extent.

    It is not the form that exists (or not), it is the particular.Andrew M

    If a particular's form (essential nature) does not exist in its own right, then a particular's existence cannot be identical with its form (essential nature) and there must be a real distinction between a particular's essential nature and its existence. This is exactly what Aquinas is arguing for.
  • Mitchell
    134
    I have several problems with Feser's argument.
    1. His Principle of (Aristotelian) Causality: Every change is a change from potentiality to actuality brought about by something with the actuality in question.
    2. His Principle of (Hierarchical) Sustaining Causality
    3. His claim that the existence of anything is the result of the actualizing of the potential to exist by something already actualized as existent.
    4. His claim that anything that already existing cannot continue to exist with out something sustaining that existence, continually actualizing the (so-called) potential for existing.
    5. His claim that while there may be an infinite chain of (temporally extended) initiating causes, there can not be an infinite chain of simultaneous sustaining causes.

    What I would like to know is whether there are any good arguments against these theses, especially #1 and #3. #3 seems to treat existence as a property that something may have as either potentially or actually, similar to the potential for hotness. And that just as something that is actually hot "activates" the potential for hotness in another object, so to something that exists activates the potential for existence in another.
  • Mitchell
    134
    Addendum:
    The problem I have is with Feser's (Aristotle's and Aquinas's) view of causality. I'd like to think that it is not just a disagreement about the meaning of the term 'cause', but rather about what account we can give of the causal relation, viz., what makes the proposition ^A causes B^ to be true?
  • Metaphysician Undercover
    4.1k
    3. His claim that the existence of anything is the result of the actualizing of the potential to exist by something already actualized as existent.


    ...

    #3 seems to treat existence as a property that something may have as either potentially or actually, similar to the potential for hotness. And that just as something that is actually hot "activates" the potential for hotness in another object, so to something that exists activates the potential for existence in another.
    Mitchell

    What is meant by #3 is that the existence of things are contingent, and that they are temporal, meaning that they have a beginning and ending in time. So for example. let's say that a particular thing came into existence at some time. Prior to that time, this particular thing did not exist. But in order for that thing to have come into existence, the potential for it to exist must have been there at that time. The potential for the thing does not necessitate the thing's existence though, because when there is the potential for something, it may or may not come into existence. So we need to assume something actual which necessitates (actualizes) the thing's existence, to account for the fact that it actually did come into existence.
  • Andrew M
    419
    Indeed, that is one of the arguments that is often given. I was trying to steer us away from that particular line of thought because it takes us pretty deep into epistemology. In scholastic terms, phoenixes do not have "subjective" existence - that is, they are not mind-independent subjects of existence. However, they do exist "objectively" - that is, mind-dependently. Qua objects of thought, phoenixes have a form all their own. Indeed, it is via such forms that we classify imaginary creatures into "this" or "that" type. When I imagine a particular phoenix, I am objectively instantiating the form "phoenix".
    [...]
    Yes, all formal distinctions trace their ultimate genesis in subjective reality as appropriated by the senses. A more metaphorical way to put it is to say that all distinctions are woven from the raw materials provided by the senses. That doesn't imply that every formal distinction is a real distinction, and I believe that Aristotle recognized that distinction to some extent.
    Aaron R

    The crucial distinction that Aristotle recognized here was between perception and imagination. Mythological writings and pictures exist (and can be perceived) and so we can classify the various ideas people had about phoenixes (e.g., Ezekiel the Dramatist said the phoenix had striking yellow eyes and Lactantius said that its eyes were blue like sapphires). That is, what we're actually investigating are people's (sometimes contradictory) ideas about mythical creatures, not the nature of mythical creatures.

    "Mind-dependent objects" is really a metaphor that derives its meaning from the concrete (natural) particulars that can be investigated. But a metaphor doesn't imply anything about the literal notions of existence and nature as applied to concrete particulars.

    If a particular's form (essential nature) does not exist in its own right, then a particular's existence cannot be identical with its form (essential nature) and there must be a real distinction between a particular's essential nature and its existence. This is exactly what Aquinas is arguing for.Aaron R

    A particular's existence is itself a formal notion (a universal). We distinguish in language between existence and form, but there is no such distinction in the particular. There isn't an apple that has form but does not exist, nor an apple that exists but lacks form.
  • JupiterJess
    90
    Are you going to make a thread for the second proof soon? I think I have more to contribute to that. I've nearly finished the book, and it has some interesting ideas.
  • darthbarracuda
    2.8k
    Go ahead and make one, if you want to discuss it.
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