Infinite Regress Arguments

[@lkdonovan5775]

Very grateful for these videos, you're a pleasure to listen to Prof. Bonevac

[@yehoshuafuchs912]

I have only studied philosophy from ancient Jewish texts like the Maimonides, Rav Saadia Gaon’s Beliefs and Opinions, and the Book of Principles. (Two of which were originally written in Arabic, but I learn the Hebrew translations.)All written roughly 600-1000 years ago. And I found it very interesting to hear these concepts discussed in modern terms and language. Thank you.

[@PhiloofAlexandria]

I love Saadia Gaon!

[@carson6097]

Yes! More please!

[@esauponce9759]

Super helpful, professor! Thank you!

[@amoeba12221]

Huge thanks Sir!

[@alexdorand]

Beautifully explained

[@vitusschafftlein1282]

I have a question on the formal side of the argument. With the third premise, you are establishing the relational poperty of asymmetry (and, consequently, of irreflexivity). But are asymmetry and seriality sufficient for the argument to work? What about transitivity? Am I missing a relational property you establish in your argument? Greetings from Münster, Germany!

[@PhiloofAlexandria]

I phrased this in terms of infinite descending chains so that I could avoid transitivity and get acyclicity, asymmetry, and reflexivity as consequences. I didn't in the video define "infinite descending R-chain," but here's what I mean: x1, ..., xn, .... constitute an infinite descending R-chain iff Rx2x1, ..., Rx(n+1)xn, .... I was thinking about the Axiom of Foundations in ZF, which functions in the same way, even though set membership is not in general transitive.

[@vitusschafftlein1282]

@@PhiloofAlexandria Thanks for the fast reply! Now I understand why you were keeping the argument less formal (I assume you mean irreflexivity in your first sentence). I have two follow-up questions, if I may: 1) Is there a formula of predicate logic that matches acyclicity? 2) Am I right in assuming that you avoided transitivity for content-related (and not formal) reasons? I have learned so much watching your videos. Your channel is a philosophical treasure chest!

[@nullspark99]

Something seemed really familiar about the three premises you introduce, and then it dawned on me... These are basically the Peano axioms defining the natural numbers. You have a collection of things (the set N of all naturals), which is nonempty (contains 0), there there is a relation defined such that each element of N is related to another element of N (the successor function), and finally that there must be some element which no other element in N relates to (i.e. 0 is not the successor of any other natural number)

[@PhiloofAlexandria]

Excellent observation!

[@yehoshuafuchs912]

@@PhiloofAlexandria @Lilly Regarding numbers, Are you by any chance of aware of where I could find info as to why (philosophically) there are only 9 (or 10) numbers? Its a big topic and referenced in many places in Jewish philosophy and Kabbala but always after explaining a few pertinent examples they simple say something like, "...as it's explained by the philosophers, look there." The idea being that each number 1-9 (or 2-10, or 1-10) has a unique quality (odd, even, whole, etc...or points required for creating a line or plane, till a fully 3d space etc...) and once 10 (or 11) comes around it is simply a repeat of one (or as the first whole with one of it's parts) but as a unified group. I apologize that I cannot use the proper jargon as my studies are done in ancient Hebrew. Thank you in advance for your time and help.

[@notspaso6644]

​@@yehoshuafuchs912 Hi, I know that quite some time has passed but I thought I might give you an answer from the point of view of a maths graduate. The choice for having "only ten numbers" (better said, only ten distinct digits for expressing numbers) comes presumably from the fact that we have ten fingers and we are naturally inclined to count on our fingers. This might sound bizarre, but there's not much else to it. The Babylonians used a base 60 system, so they had 60 symbols for the basic building blocks of their numbers, and then they would construct any number in a similar fashion as we do in base 10. There's no secret meaning or completeness of properties in the first 10 natural numbers, as an example 23 is the first prime with a next prime gap of 6, which is a property distinct from any you may find to hold for numbers 0 through 9. One may wish to seek a deeper reason, but that has little to do with philosophical research, in all respect of your interests. Kind regards

[@carsonianthegreat4672]

This is Thomas Aquinas’ (from Aristotle) distinction between essentially ordered and accidentally ordered causation, correct? Accidentally/Linearly ordered series can be infinite, but Essentially/Hierarchically ordered series cannot

[@iruleandyoudont9]

why?

[@MrDuvinci]

Is it logical to imply that having elements in a domain implies immediate finiteness?

[@lsd7879]

Thank you!

[@hennessyhd7879]

what a legend. even his cat likes his way of teaching philosophy

[@robertstevens1287]

It's a very interesting idea, a domain of unique objects each susceptive of the same binary relation! I can't think of any examples right now, but ...I like your shirt!

[@CMVMic]

What about cyclical causality?

[@makermaker11]

I know what you mean Lets take a set and assume it was eternal; a,b and c are elements of A A = {a,b,c} Now lets also assume that they are in a loop a causes b and b causes c and c causes a Now when we look at this loop we realise that there is a contradiction because a has basically caused itself. Note: a,b and c MUST have no common dependencies Example: You might say oh the eater cycle seems to be. But the thing is that they all are dependant on water itself and water itself has not caused itself into existence it was always there so basically, if you don't have a common dependency then the loop is impossible Another Note: Everything including Matter depends on energy, time and space

[@frankhansen2992]

the turtle rest inside itself

[@rhoharane]

The slow zoom is really distracting. But the cut to a zoomed view of the board where it was relevant is appreciated!

[@PhiloofAlexandria]

rhoharane Thanks-I’m still learning how best to edit these!

[@sollux13]

@@PhiloofAlexandria The "Enter Emmit" part was a nice touch, made me giggle. Love your videos, thanks for sharing your knowledge with us!

[@simon6932]

Thank you for clearing that up! It's often used as a trump card by religious speakers without people realizing that they are making several assumptions.

[@carnivorous_vegan]

@@dikdik1313 How are you going to comment on a philosophy playlist designed for charitable and sincere interpretation of ideas yet be so disrespectful ?

[@YAWTon]

​@@carnivorous_veganI cannot see why you think that Simon'# comment was disrespectful...

[@avimei]

Thank you so much for clearing this for me. Now I can believe in a pantheon of gods

[@waldwassermann]

Truth is one... it is just that it is not good to be alone. Blessings.

[@peterrosqvist2480]

I think that first relation is God, what is outside the domain. I think this is also why to name God is to reduce God to something God is not. Just like the Tao that can be spoken is not the eternal Tao.

[@waldwassermann]

Truth is one; it is just that it is not good to be alone.

[@timothytrudelle9245]

In the begining there was God, and the rest is his-story.

[@jxmbusab]

"Doesn't make any sense" doesn't seem a particularly rigorous way of dispensing with descending infinite regress. "There can't be an infinite regress of causes because that makes my brain hurt" isn't persuasive.

[@PhiloofAlexandria]

True-that’s partly my point. The thesis has a strong intuitive basis, but it’s hard to think of conclusive arguments either way.

[@matswessling6600]

@@PhiloofAlexandria"its hard to think of conclusing arguments"... then you dont have any argument. Then why pretend?

[@grantdm]

Isn't this Aquinas's argument for the existence of God; the first object that exists outside of our causal domain must be God. To put it in a modern way, whatever existed before the big bang -- before space and time itself -- must be God! Of course skeptics will retort that nothing requires that the first object to be God, which is fine, but if you can accept broader definitions of God, then yes God exists per Aquinas.

[@PhiloofAlexandria]

Exactly! I think it's the core of Aquinas's first three ways.

[@carsonianthegreat4672]

Daniel Bonevac, isn’t it more just the first two ways? The third way is more about contingency rather than series of causes

[@iruleandyoudont9]

@@PhiloofAlexandria but I don't understand how this doesn't beg the question when it's a premise that the chain "cannot go on forever."

[@dark6.6E-34]

@@iruleandyoudont9 It doesn't beg the question because it isn't trying to prove if infinite regress is possible or not. But rather takes it as an axiom to prove the necessity of an uncaused cause

[@iruleandyoudont9]

@@dark6.6E-34 if the thing in question is a causal chain, and you're considering whether or not there must be a first cause, it seems you could easily establish a true dichotomy: "Either there is a first cause or there is not a first cause." it seems the latter horn of this dichtomy implies an infinite regress (assuming there exist any causes at all). so if you eliminate infinite regress via axiom in a premise in your argument, you're begging the question, because such a premise assumes the other horn of the dichotomy, which is that there is a first cause.

[@shahfaisal8771]

It's about to understand a loop a loop which has two infinity infinite back and infinite front and has no beginning if the univers has no beginning than its a loop because a loop has no beginning and if that's true we were be stuck at that loop and never get out of it we will never reach at the present because of no beginning thus we were be still waiting

[@brianbridges8124]

but an infinite god solves this problem?

[@gabrielduran291]

Isn't it a false analogy to compare infinite turtles vs infinite causes? Not all causal relations are active or actual but instead potential. For example, once we light a match, the match causes a flame, but once the flame goes out we no longer say that this particular match stick causes a flame but that this particular match stick caused a flame. In other words the two objects no longer stand in a direct actual immediate relation to each other but the causal relation is now theoretical or in the history of our memories and can potentially happen again with other objects of the same kind. Whereas the resting turtles seem to all be there at once infinitely many which seems like an absurdity.

[@sigigle]

I agree with this, I don't see why there can't be a causal loop. It wouldn't be turtles all the way down and all the way up forever. It's not a vertical, stacking metaphor, like others I've heard like cups pouring water into cups (implying the last cup couldn't possibly be filling the first, due to this vertical, gravity based, stacking metaphor). It would be more like turtles holding hands in a circle doing a Mexican wave. I can't see what's wrong with that.

[@FarwanIrfan]

Then what about the actions of God? Since God always could create one thing after another, then this premise requires that an infinite regress is at the very least possibble isnt it?

[@ScientificGentlemen]

You are my Jordan Peterson ha!

[@cnault3244]

Numbers are infinite. Starting at zero, the numbers increase ( progress) infinitely. Starting at zero, there are negative numbers that decrease( regress) infinitely.

[@cnault3244]

@SmashRockCroc It is worth noting that infinity is not a physical thing Like numbers, it is a concept. For this reason, the very notion of an "an actual infinity moot. It is not possible to show someone a number, all you can show them is an agreed upon symbol for the number. eg: for the concept of the number four you can use the symbols 4 or IV You also cannot show someone an actual infinity.

[@cnault3244]

@SmashRockCroc "I don’t think think that there being a conceptual infinity proves an actually existing infinity if that’s what you’re going for." I am saying that the phrase "an actual infinity" is a meaningless phrase because the word infinity refers to a concept, not a physical thing. Just as you cannot be shown a number 3 because numbers are concepts ( all you can be shown is a symbol to represent a number 3 or 3 pebbles to represent a number 3), you cannot be shown an infinity.

[@cnault3244]

@SmashRockCroc Like the term infinity, an infinite regress is a concept.

[@cnault3244]

@SmashRockCroc "Yes, a theoretical concept, just like how wormholes and the possible ways our universe ends are theoretical concepts" Not really. Wormholes are a theoretical concept. Black holes were a theoretical concept until we found evidence for them. Numbers are NOT a theoretical concept. They are strictly a mental concept, and as we have learned they are a useful tool. They are not a mental concept of a physical thing, you cannot show someone a number... all you can show them is something to symbolize or represent the number.

[@ashley_brown6106]

Numbers are not real entities. No infinite regression of actual things or events or causes can exist. The logical impossibility of the infinite regression has been proven long ago.

[@carsonianthegreat4672]

This reads a lot like Aquinas’ 2nd Way argument.

[@shahfaisal8771]

Or its a loop that if u get back infinitely back at the loop u will still has no BIGINIGING and still had an infinity so we get back at infinite past we will still had an infinite past and vise versa at the future if try to go infinitely at future u will still had an future of infinite

[@Keepedia99]

But we do have numbers all the way up to infinity

[@andreiparaschiv9915]

Applying the argument that prof. Bonevac explained: Let there be a set of numbers (say, natural numbers) and the relationship of having a successor (2 follows 1 etc) Premises: 1) There is at least one number 2) Every number has a successor 3) This cannot go on forever; a number cannot be its own successor; no loops Conclusion: there must be some "number" outside numbers, which succeeds another number but does not have a successor. You can accept the conclusion (and what is that number? Infinity maybe? No, because infinity is not the successor of some particular number.) Or you can deny at least one premise. Denying 3.1, we can say that the series of natural numbers CAN go on forever. This is quite intuitive to us. In order to deny 2), you gotta give an example of a finite number that has no successor; kinda counterintuitive, right? Or you can deny 1), and claim that there is actually no such thing as a number. But then you gotta explain what we mean by saying "one", "one hundred" etc. There certainly SEEMS to be such thing as a number. Honestly, my best guess is that numbers CAN actually go on forever, just like the stacked turtles.

[@iruleandyoudont9]

@@andreiparaschiv9915 yeah why are we stipulating "this cannot go on forever"?

[@andreiparaschiv9915]

@@iruleandyoudont9 I'm not sure myself, but it seems that throughout history philosophers had a huge problem with the concept of infinity. Look at Zenon's paradoxes, where he concludes that motion is an illusion because it can be broken down into an infinity of very tiny parts. Centuries later came Newton who invented calculus, basically telling Zenon "yeah man, there is nothing wrong with that. It's just how math works."

[@iruleandyoudont9]

@@andreiparaschiv9915 right, I'm fairly familiar with that. I just don't understand how this sort of reasoning still seems to be so prevalent today. I've never heard an argument against infinite regress that didn't beg the question

[@andreiparaschiv9915]

@@iruleandyoudont9 well, it's not an argument against infinite regression. it's an argument for/against something, by means of infinite regression. it's just a method.

[@ScientificGentlemen]

This also brings to mind Aristotle's Unmoved Mover.

[@timhorton2486]

Yeah, it’s very often used by theists to make their various cosmological arguments for god more convincing.

[@ScientificGentlemen]

@@timhorton2486 I have a theory I might call "Infinite Progress", meaning that in the infinite unfolding universe(s) there will eventually be beings so advanced they will be able to time travel and therefore create eternity. For any and all beings forever. That includes us now. Maybe it's a stretch, but it kind of makes sense from a sheer probability stand point.

[@timhorton2486]

Nice Shapes If time travel is even possible via the laws of their universe, and assuming that somehow they wouldn’t age.

[@ScientificGentlemen]

@@timhorton2486 Yeah, I'd imagine they would have time travel in their universe, and have beaten the effects of aging. There might be a universe out there now that has that going on. Check out Asimov's The Last Question.

[@timhorton2486]

Nice Shapes If it is possible to actually leave one’s own universe at all, then I don’t think you would even need time travel anyway. The aging thing is a hurdle that seems insurmountable considering the laws of physics, but if it was possible then the only thing a significantly advanced civilization would need is the ability to “jump” universes.

[@Nekronity]

15:30

[@log6778]

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[@SamuelJFord]

Thank you for these videos! You are very engaging. Is this essentially the same as Godel's incompleteness theorems?

[@souzajustin19d]

Oh my God!, literately lol.