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Cogito ergo sum

Here in the Philosophy forum we will talk about all the "why" questions. We'll have conversations about the way in which philosophy and theology and religion interact with each other. Metaphysics, ontology, origins, truth? They're all fair game so jump right in and have some fun! But remember...play nice!

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Infinity and Kalam

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  • #16
    Originally posted by mattbballman31 View Post
    Yep. I don't disagree with any of this. I said, "An infinite regress of equal, arbitrary, finite, non-zero events is an actual infinite." That's an actual infinite. I'm not talking about a dynamic, growing potentially infinite series of events extending into the past. It's being supposed to be actually infinite for reductio.
    This does not address the issue that our physical existence is possibly potentially infinite by definition.



    If the past is beginningless, the events of the past could be put into a one-to-one correspondence with the series of natural numbers.
    The artificial construct that 'the events of the past could be put into a one-to-one correspondence with the series of natural numbers.' is not reality.
    Simply as Aristotle proposed the nature of our existence is 'potentially infinite' as cited. No matter how far you attempt to go in the past you can always go further. This is true in space nor a hypothetical time reference.


    I'm not talking about science. I'm not talking about metaphysics.
    . . . but your trying put limits on the physical and/or time extent of our physical existence by metaphysical assumptions and that does not work.

    The problem remains this is an a priori assumption that our physical existence is finite, because actual infinities are metaphysically impossible, and not the fact that our physical existence is 'potentially infinite.'

    Again as Aristotle proposed is still relevant.

    Going all the way back to Aristotle there are two distinct 'infinities:' Actual Infinities and Potential Infinities.
    Aristotle's potential–actual distinction

    Source: https://www.google.com/search?q=potential+infinity+vs+actual+infinity&oq=potential+infinity&aqs=chrome.1.69i57j0l7.14758j0j15&sourceid=chrome&ie=UTF-8



    He distinguished between actual and potential infinity. Actual infinity is completed and definite, and consists of infinitely many elements. Potential infinity is never complete: elements can be always added, but never infinitely many.

    Also . . .

    According to Aristotle, actual infinities cannot exist because they are paradoxical. ... Aristotle argued that actual infinity as it is not applicable to geometry and the UNIVERSAL, is not relevant to mathematics, making potential infinity all that actually is important.

    © Copyright Original Source

    Last edited by shunyadragon; 09-16-2020, 08:10 AM.
    Glendower: I can call spirits from the vasty deep.
    Hotspur: Why, so can I, or so can any man;
    But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

    go with the flow the river knows . . .

    Frank

    I do not know, therefore everything is in pencil.

    Comment


    • #17
      Originally posted by mattbballman31 View Post
      Actual infinites are metaphysically impossible.

      An infinite regress of equal, arbitrary, finite, non-zero events is an actual infinite.

      There can't be a regress of this kind into the past.

      The past had a beginning.

      Something had to cause the beginning.

      Q.E.D. That's something that everyone would call 'God'.
      So god is not infinite? How do you differentiate and so claim that the one, i.e. god, the acts of god, can be infinite in extent, but the Cosmos, i.e. the actions therein, can not be?

      Comment


      • #18
        Originally posted by mattbballman31 View Post
        Hilbert's Hotel, Infinite Library cases, Tristram Shandy paradoxes, the impossibility of counting to/from infinity, Grim Reaper paradoxes, Benedarte's paradox of the gods, Benedarte's Peals Case, Al-Ghazali's Rotating Planets, Thompson's Lamp, Marble Shifter Case, etc . . .
        Okay, so actual infinities are not necessarily impossible, just counterintuitive. But a universe with a beginning is counterintuitive, too, so there isn't much to choose between one and the other.

        Comment


        • #19
          Originally posted by mattbballman31 View Post

          A spaceless, timeless, immaterial, personal, powerful, intelligent agent would constitute a set of properties of a substance whose definite description picks out that Being that only God could exemplify. That conjunction of properties could only be jointly exemplified by God.
          I understand why a first cause would need those properties in order to be God (but did you not forget necessarily existing, a key property?) But why would a first cause need all of those properties in order to be a first cause? For instance, why would a first cause need properties like personal or intelligent?

          Comment


          • #20
            Originally posted by crepuscule View Post

            I understand why a first cause would need those properties in order to be God (but did you not forget necessarily existing, a key property?) But why would a first cause need all of those properties in order to be a first cause? For instance, why would a first cause need properties like personal or intelligent?
            Actually all this argument for a 'first cause' is too mechanistic an approach to justify the existence of God. Actual infinities are useful in math, but are meaningless to propose whether our physical existence is finite or infinite. Regardlees our physical existence is potentially infinite whether it is or not.

            From the Baha'i perspective God and our Created physical existence as the reflection of the attributes of God are mutually infinite and eternal. I am not saying at this point this is an argument for the existence of God, but the present argument fails..
            Glendower: I can call spirits from the vasty deep.
            Hotspur: Why, so can I, or so can any man;
            But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

            go with the flow the river knows . . .

            Frank

            I do not know, therefore everything is in pencil.

            Comment


            • #21
              Originally posted by Stoic View Post

              Okay, why are actual infinities metaphysically meaningless?
              . . . because there are not any metaphysical conclusions that can be derived from a math concept, that is simply derived for the use of humans like all math. As Aristotle concluded our physical existence is potentially infinite. Important is 'potentially,' because there is no falsifiable hypothesis that could determine whether our physical is finite nor infinite.

              devloped for human use
              Glendower: I can call spirits from the vasty deep.
              Hotspur: Why, so can I, or so can any man;
              But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

              go with the flow the river knows . . .

              Frank

              I do not know, therefore everything is in pencil.

              Comment


              • #22
                Originally posted by shunyadragon View Post

                . . . because there are not any metaphysical conclusions that can be derived from a math concept, that is simply derived for the use of humans like all math. As Aristotle concluded our physical existence is potentially infinite. Important is 'potentially,' because there is no falsifiable hypothesis that could determine whether our physical is finite nor infinite.

                devloped for human use
                It seems like the impossibility of actual infinities would be metaphysically meaningful, in that it would entail a finite past.

                Comment


                • #23
                  Originally posted by Stoic View Post

                  It seems like the impossibility of actual infinities would be metaphysically meaningful, in that it would entail a finite past.
                  The actually infinity as defined is a closed set of infinity, and could only exist within a greater whole. Math has been a tool for practical reasons, science and technology, and nothing to do with metaphysics. Even if billions of actual infinities could exist in our physical existence it could still be potentially infinite.

                  Aristotle was the first to define infinities, and his conclusion was that actual infinities do not exist at all and potential infinities were the bottom line. I already described this in detail before.
                  Last edited by shunyadragon; 09-29-2020, 07:30 AM.
                  Glendower: I can call spirits from the vasty deep.
                  Hotspur: Why, so can I, or so can any man;
                  But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

                  go with the flow the river knows . . .

                  Frank

                  I do not know, therefore everything is in pencil.

                  Comment


                  • #24
                    Originally posted by Stoic View Post

                    I'm more concerned with claims that the extent of time and space cannot be an actual infinite.
                    I believe I have explained the problem the best I could .Actual infinity is a closed set of infinites, but cannot be objectively distinguished from potential infinity from the human perspective. Being 'Metaphysically Impossible' is sort of an odd oxymoron, that does not have any relevance as to whether our universe is infinite or not.

                    Source: https://math.vanderbilt.edu/schectex/courses/thereals/potential.html



                    Nearly all research-level mathematicians today (I would guess 99.99% of them) take for granted both "potential" and "completed" infinity, and most probably do not even know the distinction indicated by those two terms. Some of these mathematicians may be impatient with the few students who still have difficulty with completed infinities. But their impatience is not justified; they are forgetting what difficulty the mathematical community had in reaching its present perspective. Completed infinity has only been part of mainstream mathematics since the work of Georg Cantor (1845-1918), and his ideas initially were met with resistance, because they were not supported by what we see in the physical world around us. Before Cantor's time, mathematicians had struggled with the notion of infinity for many centuries, mostly without success. Indeed, the fact that the ancient Greeks turned to geometry rather than algebra can be attributed in part to the difficulty they had with infinite processes. For instance, the square root of two can be constructed geometrically in just a few steps, but to define it algebraically takes some understanding of an infinite procedure.

                    Infinity cannot be experienced in our everyday lives, but infinity might be a good "approximation" to some of the quantities that we read about in the news. There are 7 billion people in the world, and the annual national budget is several trillion dollars, and the national debt is many trillions of dollars; all of these numbers are much bigger than most of us -- even mathematicians -- have any real feeling about. And the number of atoms in the earth is much much bigger than trillions; I don't even know the name for that number. But still these numbers are finite.

                    Nor can we experience the infinitely small in our lives. In fact, the currently prevailing theories of quantum physics tell us that there is a lower limit, a smallest physical object.

                    © Copyright Original Source




                    Mechanistic math concepts cannot remotely define the limits of our physical existence. We cannot even falsify whether our physical existence is finite nor infinite from the human perspective. As a side note math functions perfectly well without using infinities.

                    Do you really think it is possible to metaphysically define the limits of our physical existence?

                    Glendower: I can call spirits from the vasty deep.
                    Hotspur: Why, so can I, or so can any man;
                    But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

                    go with the flow the river knows . . .

                    Frank

                    I do not know, therefore everything is in pencil.

                    Comment


                    • #25
                      Originally posted by crepuscule View Post

                      I understand why a first cause would need those properties in order to be God (but did you not forget necessarily existing, a key property?) But why would a first cause need all of those properties in order to be a first cause? For instance, why would a first cause need properties like personal or intelligent?
                      Suppose you got a rabbit in a box. Suppose you don't think there's anything in the box. I give you an argument for the existence of something in the box by showing you that there's something in the box that has the property of being a mammal. Now, that's not inconsistent with their being a rabbit in the box since a rabbit is a mammal. But then suppose I'm told, "Wait! Your argument doesn't show that the mammal has the property of being in the family Leporidae of the order Lagomorpha!" Right . . . The argument wasn't meant to do that. All the arguments in a cumulative case may all have conclusions that delineate all the properties of the rabbit in a box, but each argument ON ITS OWN can't be faulted for what ALL the arguments are trying to get at. And you don't get a different animal for every argument because of Ockham's Razor.
                      Many and painful are the researches sometimes necessary to be made, for settling points of [this] kind. Pertness and ignorance may ask a question in three lines, which it will cost learning and ingenuity thirty pages to answer. When this is done, the same question shall be triumphantly asked again the next year, as if nothing had ever been written upon the subject.
                      George Horne

                      Comment


                      • #26
                        Originally posted by shunyadragon View Post

                        This does not address the issue that our physical existence is possibly potentially infinite by definition.
                        I'm talking about a past temporal regress. If the intervals are arbitrary, non-zero, equal, and finite, and time isn't growing in the earlier-than direction, the past wouldn't be potentially infinite. You come to a final interval, a first interval. Causally before that isn't more intervals extending into the past.


                        The artificial construct that 'the events of the past could be put into a one-to-one correspondence with the series of natural numbers.' is not reality.
                        I have no idea what you're talking about. Denumerability in terms of countable infinities has to do with being able to conceptually correlate all the events of the past with the series of natural numbers. I have no idea what you mean by artificial construct. That's an established fact in set theory.

                        Simply as Aristotle proposed the nature of our existence is 'potentially infinite' as cited. No matter how far you attempt to go in the past you can always go further. This is true in space nor a hypothetical time reference.
                        The idea that no matter how far you go back, you can always go back further, is ambiguous. If the beginning point is just too far away, sure. If space is non-Euclidean, I don't care. Space could still be finite in extent even if the topology of space prevents from reaching an 'edge' or something. Same with time.


                        . . . but your trying put limits on the physical and/or time extent of our physical existence by metaphysical assumptions and that does not work.
                        That's just your claim, Shunya. If all you're going to do is claim things without backing them up, this will be another boring conversation. Give me an argument or something.

                        The problem remains this is an a priori assumption that our physical existence is finite, because actual infinities are metaphysically impossible, and not the fact that our physical existence is 'potentially infinite.'
                        No, it's not. It's the conclusion of a philosophical argument, the premises of which are backed up by more mini-arguments. I've addressed your point about potential infinities above. You have to specify the kinds of intervals you're talking about.

                        Again as Aristotle proposed is still relevant.

                        Going all the way back to Aristotle there are two distinct 'infinities:' Actual Infinities and Potential Infinities.
                        Aristotle's potentialactual distinction

                        [cite=https://www.google.com/search?q=potential+infinity+vs+actual+infinity&oq= potential+infinity&aqs=chrome.1.69i57j0l7.14758j0j 15&sourceid=chrome&ie=UTF-8]

                        He distinguished between actual and potential infinity. Actual infinity is completed and definite, and consists of infinitely many elements. Potential infinity is never complete: elements can be always added, but never infinitely many.
                        I'm aware of the distinction, Shunya. Potential infinities can't apply to the past once you specify the intervals you're talking about, and if time isn't growing in the earlier-than direction. It's just there. If it's there, the specified intervals are either actually infinite or finite. A potential infinite isn't a number; it's still finite, but it's indefinite since it's always growing. Cool. I cash that out as: another day happened today. That's consistent with their being a beginning to the series and the past being a potential infinite.




                        Many and painful are the researches sometimes necessary to be made, for settling points of [this] kind. Pertness and ignorance may ask a question in three lines, which it will cost learning and ingenuity thirty pages to answer. When this is done, the same question shall be triumphantly asked again the next year, as if nothing had ever been written upon the subject.
                        George Horne

                        Comment


                        • #27
                          Originally posted by Stoic View Post

                          Okay, so actual infinities are not necessarily impossible, just counterintuitive. But a universe with a beginning is counterintuitive, too, so there isn't much to choose between one and the other.
                          No, metaphysically impossible. Modal epistemology is a thing. Modal epistemologists use these types of thought-experiments all the time to inflate/deflate modal intuitions about what is or isn't metaphysically possible. Modal skepticism is also a thing. You can go down that route if you want, but that'll be a can of worms that'll lead us away from Kalam.
                          Many and painful are the researches sometimes necessary to be made, for settling points of [this] kind. Pertness and ignorance may ask a question in three lines, which it will cost learning and ingenuity thirty pages to answer. When this is done, the same question shall be triumphantly asked again the next year, as if nothing had ever been written upon the subject.
                          George Horne

                          Comment


                          • #28
                            Originally posted by mattbballman31 View Post
                            I'm talking about a past temporal regress. If the intervals are arbitrary, non-zero, equal, and finite, and time isn't growing in the earlier-than direction, the past wouldn't be potentially infinite. You come to a final interval, a first interval. Causally before that isn't more intervals extending into the past.
                            I know what you are talking about, but the existence of a potential post infinity would not be limited by any hypothetical past temporal regress, an actual infinity, which would be closed set of infinities by definition. The potential infinity of the past would be the same concept of simply as far as you go in the past or the future you could still go further than any limit one could conceive. This is very basic Aristotilian concepts of infinities. It is questionable that actual infinities actually exist.

                            I have no idea what you're talking about. Denumerability in terms of countable infinities has to do with being able to conceptually correlate all the events of the past with the series of natural numbers. I have no idea what you mean by artificial construct. That's an established fact in set theory.
                            It is a fact that putting numbers on time is a human artificial construct. There are no numbers on time in the present, future nor past except for the numeric designation human use for our convention.


                            The idea that no matter how far you go back, you can always go back further, is ambiguous. If the beginning point is just too far away, sure. If space is non-Euclidean, I don't care. Space could still be finite in extent even if the topology of space prevents from reaching an 'edge' or something. Same with time.
                            Not ambiguous simply the definition of potential infinities. Space and time is non--Euclidian whether you care or not. Space could be finite, but there is no way we could definitively determine whether space is finite nor infinite.


                            That's just your claim, Shunya. If all you're going to do is claim things without backing them up, this will be another boring conversation. Give me an argument or something.
                            Already presented the argument base don basic math, and what we know and do not know concerning whether our physical existence is finite or infinite.


                            No, it's not. It's the conclusion of a philosophical argument, the premises of which are backed up by more mini-arguments. I've addressed your point about potential infinities above. You have to specify the kinds of intervals you're talking about.
                            No, you did not address the issue of potential infinities. You just hand waved without a coherent explanation. Being a conclusion of a philosophical argument is terribly weak, because on has to accept the premises before the argument works, and the reality of math and our knowledge of time and space renders the premises false.



                            [quote] I'm aware of the distinction, Shunya. Potential infinities can't apply to the past once you specify the intervals you're talking about, and if time isn't growing in the earlier-than direction. It's just there. If it's there, the specified intervals are either actually infinite or finite. A potential infinite isn't a number; it's still finite, but it's indefinite since it's always growing. Cool. I cash that out as: another day happened today. That's consistent with their being a beginning to the series and the past being a potential infinite.

                            Your assertion that potential infinities cannot apply to past is just that an assertion without basis. The past and future time is just equally there without any natural intervals of time. Intervals of time remain a human convention and cannot put finite limits on time in the past nor the future.

                            Potential infinites are not finite by definition since Aristotle defined them. Time does not have numbers, and something can be potentially infinite regardless of it being number from the human perspective or not. Simply going back in time there would always be more regardless of how far back in time, nor perceive how far back in time you could go.


                            Last edited by shunyadragon; 12-02-2020, 08:36 AM.
                            Glendower: I can call spirits from the vasty deep.
                            Hotspur: Why, so can I, or so can any man;
                            But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

                            go with the flow the river knows . . .

                            Frank

                            I do not know, therefore everything is in pencil.

                            Comment


                            • #29
                              Originally posted by mattbballman31 View Post
                              No, metaphysically impossible. Modal epistemology is a thing. Modal epistemologists use these types of thought-experiments all the time to inflate/deflate modal intuitions about what is or isn't metaphysically possible. Modal skepticism is also a thing. You can go down that route if you want, but that'll be a can of worms that'll lead us away from Kalam.
                              I'd be interested in seeing the argument that actual infinities are metaphysically impossible. I'm guessing it would depend on one or more postulates that I would find questionable.

                              Comment


                              • #30
                                Originally posted by Stoic View Post

                                I'd be interested in seeing the argument that actual infinities are metaphysically impossible. I'm guessing it would depend on one or more postulates that I would find questionable.
                                Probably. It convinces some and not others. That's typically how it works in philosophy. How do you come to a conclusion about whether something is metaphysically impossible?
                                Many and painful are the researches sometimes necessary to be made, for settling points of [this] kind. Pertness and ignorance may ask a question in three lines, which it will cost learning and ingenuity thirty pages to answer. When this is done, the same question shall be triumphantly asked again the next year, as if nothing had ever been written upon the subject.
                                George Horne

                                Comment

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