• Metaphysician Undercover
    4.1k
    A definition can't enable or disable the proof of a point of any interest, as any proof that uses the defined term can be converted to one that doesn't by simply replacing every instance of the defined term by that which it is defined to mean. For instance, if I have a proof about bachelors, and I have defined bachelor to mean 'Live, adult, male human that has never married', I can change the proof to one that does not use the defined term, simply by replacing the term by those italicised words, wherever it occurs.andrewk

    That's irrelevant, because all those other words would need to be defined as well, according to your stated principles of reasoning, which requires definitions. So these words could just be defined in a way which suited the purpose as well.

    The purpose of a definition is to enable one to write shorter, more intuitive proofs. Semantically, introducing or removing a definition cannot change the provability of anything.

    A useful definition is one that shortens a proof or attempted proof in a way that makes it easier to find a way through the logical maze.
    andrewk


    This seems to contradict what you were saying earlier, that reasoning requires exact, objective definitions. Your objection against Aristotelianism was that it didn't provide clear definitions which are required for proof. Now it appears like you are saying that definitions are not required for proof, they just make the proof easier.

    Myself, I would rather read hundreds of pages of examples of usage of the terminology to make sure that I grasp a firm understanding of the meaning, rather than a few words of definition. The former ensures that I have a clear understanding of the things being proven, the latter only ensures that I can associate some words with some other words.
  • Metaphysician Undercover
    4.1k

    I am wondering, are we part of the virtual reality, or are we real? If we are real, then I am real, and you are real, so you cannot be part of my virtual reality, you are real. If we are not real, then what difference does it make, even to ask your question?
  • Myttenar
    61

    The point is the logical process one can attend.
    Questioning reality is the foundation of philosophy...
  • Andrew M
    419
    I'd be interested to hear what other Aristotelians think about the importance of arguing over definitions.andrewk

    If substantive, yes, if merely about word symbols, no.

    For an Aristotelian, a definition signifies what it is to be something. For example (per the Oxford dictionary), an apple is a round fruit of a tree of the rose family, which typically has thin green or red skin and crisp flesh.

    Note that this is not merely defining the word "apple". It is describing something in the world, namely, those objects we call "apples". The definition serves to distinguish those objects from other objects, such as pears (a different kind of fruit) and rocks (not a kind of fruit at all), and so can be considered a valid definition.
  • Myttenar
    61
    well I can't speak for you but since I am conscious of myself I can deduce that I exist at very least.
  • andrewk
    1.4k
    This seems to contradict what you were saying earlier, that reasoning requires exact, objective definitions.Metaphysician Undercover
    What is required is that any defined terms used in the proof have exact, objective definitions. However it is not mandatory to use any defined terms. One can write a proof without any defined terms, in which case no definitions are needed.

    There can be a grey area in that axioms that refer to a particular item in the Domain of Discourse may in some circumstances be considered as in a sense constituting a 'definition' of that item. For instance, the axioms that refer to the item '0' in Peano Arithmetic might be interpreted as constituting a definition of '0'. But there are various complexities about that, which I think it would not be fruitful to delve into now, as I don't think they relate to the topic under discussion.
  • Meta
    185
    @andrewk
    @Metaphysician Undercover

    On one hand it is reasonalbe to expect a "proof" to be logical, which requires complex concepts to be well-defined. On the other hand one can argue that metaphysics is more general than logic because it adresses everything while logic investigates only a fraction of reality. (Concepts like "everything" have different meaning in logic and in meaphysics.)

    I think your debate clearly shows the continental-analytic disagreement and won't be resolved anytime soon.
  • Agustino
    11.1k
    From a quantum mechanical viewpoint, nothing always happens. The most we can say is that the probability of it not happening is negligible. But we can still work with that.

    Is the following a fair rendition of your concept of 'is directed towards'.

    We say that an object of category C1 (e.g. a match) is 'directed towards' phenomena of category C2 (e.g. ignition) if there exists a set of conditions S that include at least one condition relating to an object of class C1, such that our current scientific theories predict that, whenever conditions S are satisfied, an event of class C2 will occur with probability p, where p is very close to 1 [we would need to specify an exact value to complete the definition. Let's say 0.99999].
    andrewk
    It doesn't matter. This doesn't save you in any way. We're still back to the same square. Take radioactive decay which is probabilistic by nature.

    Is an atom of whatever - say Uranium - going to decay with a specific probability of x%? Sure. This means that that specific atom (or type of atom) is directed towards decaying into the following components (X, Y, Z) with this, and only this probability.

    Whatever causes there are out there, they have to be directed towards producing whatever their range of effects happen to be (even if those effects are probabilistic), otherwise, why is it that they always produce only that range of effects and not just any effect imaginable?
  • andrewk
    1.4k
    This doesn't save you in any way.Agustino
    Goodness me, do I need saving? From what? My original sin perhaps? Oh dear. Or am I to be punished by a posse of Aristotelians, for having the unmitigated temerity to decline to adopt their worldview?

    I'm afraid I don't understand the assertions and questions in your post. Perhaps they mean something to Aristotelians.
  • Metaphysician Undercover
    4.1k
    What is required is that any defined terms used in the proof have exact, objective definitions. However it is not mandatory to use any defined terms. One can write a proof without any defined terms, in which case no definitions are needed.andrewk

    OK, I think I understand, if a definition is used, it must be unambiguous. An ambiguous definition would not qualify as a proof because the conclusion may be the result of equivocation or misunderstanding. But a proof can be made without any definitions.

    In the case of making a proof without definition, the meaning of the terms must be properly demonstrated in order to avoid ambiguity. This is the case in Aristotelian metaphysics. The meaning of the important terms is demonstrated by numerous examples through many pages of text. This requires attentive study and dedication from the student. You called that a leap of faith, but "faith" here would imply that the student believes that the effort is worthwhile. That is the nature of ostensive demonstration, it requires effort to learn, and one must have faith in the authority of the teacher. It is only discovered after the practise, whether the effort was worthwhile or not.

    You seemed to be saying earlier in the thread, that this type of argumentation, through a demonstrating of the meaning of terms rather than a clear definition, does not constitute a proof. Now I see that you believe that it may constitute a proof. And whether or not it actually constitutes a proof is not a judgement which you can make until after you've put in the effort to understand the terms.
  • andrewk
    1.4k
    I would not use the word 'ostensive' to describe learning a meaning by reading long texts. Ostension is pointing to a dog and saying 'dog', jumping and saying 'jump' or making a sad face and saying 'sad'.

    But even my sort of ostension is prone to error. It's possible that I've got the wrong idea of what other people mean by 'dog' and our success in communicating about dogs thus far has been a happy coincidence of the fact that the animals we were talking about lay in the intersection between my understanding of dog and yours.

    My understanding of language use is mostly WIttgensteinian, so I see my use of 'dog' or 'potential' as elements of a language game that often, but not always, works in everyday life. But it all falls apart as soon as we move away from everyday life into metaphysics.

    I don't know what Aristotle would have made of Wittgenstein but my guess is that he'd have been appalled, since describing categories of objects as simply moves in a language game is like the antithesis of believing that a category has an essence.

    It sounds like becoming an Aristotelian involves a process of initiation into a new language game, that involves a lot of reading. I am not inclined to do that because, while that language game may be fun (Feser certainly seems to enjoy it), it doesn't seem to lead anywhere.

    As a wise member of the previous forum once said:

    "Fancy piles of words cannot oblige the universe to be thus and so'

    (or something like that).
  • Metaphysician Undercover
    4.1k
    I would not use the word 'ostensive' to describe learning a meaning by reading long texts. Ostension is pointing to a dog and saying 'dog', jumping and saying 'jump' or making a sad face and saying 'sad'.andrewk

    No, "ostensive" means learning by direct demonstration, and that's what giving examples is, just like drawing triangles is demonstrating the meaning of "triangle". The difference we are discussing here is the difference between giving the meaning of a word by definition, and giving the meaning of a word by demonstration. You seem to be of the opinion that definition is the preferred method for presenting the meaning of a word. My claim is that demonstration gives one a better understanding of what the word means.

    But even my sort of ostension is prone to error. It's possible that I've got the wrong idea of what other people mean by 'dog' and our success in communicating about dogs thus far has been a happy coincidence of the fact that the animals we were talking about lay in the intersection between my understanding of dog and yours.andrewk

    Yes, that's what I said about this type of learning, it is a matter of "faith", in the sense that one must have faith that the teaching authority is truly an authority. And the problem, as I explained, is that you cannot make the appropriate judgement on this until after you have learned what the teacher is teaching, until after it's been taught to you. You may have an opinion, that the supposed authority is truly an authority, or not, prior to the procedure, but just like going to a movie, you don't know for sure whether you will like it until after you see it.

    My understanding of language use is mostly WIttgensteinian, so I see my use of 'dog' or 'potential' as elements of a language game that often, but not always, works in everyday life. But it all falls apart as soon as we move away from everyday life into metaphysics.andrewk

    That's odd, I find the very opposite is the case. I found that everyday use of words was very odd, with the way that many words are used being strangely inconsistent and ambiguous. I am one who has always had difficulty communicating. Communication does not come easy for me, so my word use is deliberate. When I studied metaphysics I found that word usage suddenly started to make sense to me. Word usage was always a puzzle to me, and in ancient philosophy such as Plato and Aristotle, with all the demonstrations, I found that the pieces of the puzzle started to fit together. So I see everyday word use as very fragmented, but metaphysics makes sense of that fragmentation.

    It sounds like becoming an Aristotelian involves a process of initiation into a new language game, that involves a lot of reading. I am not inclined to do that because, while that language game may be fun (Feser certainly seems to enjoy it), it doesn't seem to lead anywhere.

    As a wise member of the previous forum once said:

    "Fancy piles of words cannot oblige the universe to be thus and so'

    (or something like that).
    andrewk

    I can speak from experience, and tell you that all the reading does lead somewhere, it leads to an understanding. "The way the universe is" is not what is at issue here, what is at issue is understanding. Anyone can make statements defining "the way the universe is", but what's important is understanding. And we all desire to understand, that's human nature. But this is where you're very clearly lacking faith. You do not believe that the alleged authority is really an authority, you have no faith in that proposition, so you dismiss the endeavor as a waste of time.
  • andrewk
    1.4k
    You do not believe that the alleged authority is really an authority, you have no faith in that proposition, so you dismiss the endeavor as a waste of time.Metaphysician Undercover
    I do not, and would not dismiss it in that way without qualification.

    I am confident that reading Aristotle would be a waste of my time. It sounds like you have found it an enriching experience, so it was not a waste of your time, nor of that of any other enthusiastic Aristotelian. If his writings on metaphysics bring joy to some people, and they do not induce them to harm others, then that is a good thing (IMHO).
  • Wayfarer
    6.2k
    I am confident that reading Aristotle would be a waste of my time. It sounds like you have found it an enriching experience, so it was not a waste of your time, nor of that of any other enthusiastic Aristotelian.andrewk

    The (possibly unintended) irony of that observation, is that the idea of a philosophy as 'something that works for you' is a sentiment that no Aristotelian philosopher could ever entertain.
  • Wayfarer
    6.2k
    I should add something to the above. I would much rather live in a world governed by the attitude that Andrew expresses - ‘live and let live, what works for you’. It is vastly preferable to one in which there is a single truth to which all must adhere. But even so, I am also obliged to believe that there is a truth to which I must conform, and not simply choose.
  • darthbarracuda
    2.8k
    If we value liberty and freedom, and see them as good, is it reasonable to assume that God, if he exists, also values liberty and freedom, and therefore can be expected to remain hidden and allow his creatures to believe what they want to believe and live as they wish to live?
  • Metaphysician Undercover
    4.1k
    If his writings on metaphysics bring joy to some people, and they do not induce them to harm others, then that is a good thing (IMHO).andrewk

    I don't think "joy'" is the best word to use here. As I explained, what it brings is understanding. And because we desire to understand, then satisfying that desire with actual understanding brings joy. So "joy" is not incorrect. But "joy" has a very broad, ambiguous meaning, when the more specific word "understanding" is proper according to what I explained. To argue in a way which replaces more specific, well defined terms, with the more general, ill-defined terms is counter-productive. That's the way you are going.

    It's like if we were discussing the nature of moral virtue, and we realized that being virtuous is a pleasure, so we switch "virtue" with "pleasure", and you say, if it brings you pleasure, and doesn't induce harm to others, then virtue is a good thing. This would completely miss the essence of virtue, which is concerned with doing good, replacing it with pleasure that doesn't harm others.

    So you have removed the virtue from my description, the particular good, which is referred to with "understanding", and replaced it with "joy that doesn't involve harm to others", implying that anything which brings joy is equally good so long as it doesn't cause harm to others. Then understanding is of no more value than masturbation.
  • Wayfarer
    6.2k
    Well said. Indeed I think it was exactly that kind of understanding that was behind the original formulations of liberalism.
  • andrewk
    1.4k
    'Better to be Socrates dissatisfied than a pig satisfied', eh? I am more sympathetic to Bentham's view (to which I expect Mill was responding): 'Push-pin is as good as poetry' (even though personally I would prefer poetry).
  • Metaphysician Undercover
    4.1k

    I think we're loosing objectivity here. Do you agree that understanding is inherently subjective, meaning that it is always a subject which understands? And do you agree that the judgement of whether or not an argument constitutes a proof is dependent on that argument being understood?
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