coolguy8472 This is just like saying if 1,000,000 people each try to eat a fully grown elephant in 2 seconds the probability of someone doing so is greater than if 5 people try. Wrong! The probably is always 0.

When it comes to the lottery the chance of winning, or guessing that someone will win, is the same for everyone. Guesswork doesn’t change this, it only a\narrows the margin down that SOMEONE will guess correctly.

Witnessed experiences (illusionary of otherwise) are not in the same ball park. — I like sushi

There are piecewise functions involved to weed out these absurdities I'm sure. Like if someone said a trillion people confirmed something verses a trillion and 1 people confirmed something, which is more likely to be true. Well there aren't even that many people on Earth.

Regarding your absurdity example, it's conceivable that there exists a person with super powers that can devour an elephant in 2 seconds. We see feats like that performed in fictional writings. The likelihood is some low number like 10^-999999999999999999999999999. But more probable than square circles I would estimate.

It's my best guess. Because the claim that claims more eyewitnesses has more persuasive power to some people. Double and triple hearsay is a persuasive enough topic for courts to at least discuss the issue before rejecting the idea of it being valid persuasive evidence.

Sorry this seems so easy, maybe I'm not thinking about it hard enough. Okay pick any 3 things call them Thing A, Thing B, and Thing C and assume they're all different with no similarities with each other. A, B, and C all share the property that they can be classified as things. Therefore it's not the case that they're all different with no similarities with each other.

Even if it's not worth living everyone going to die soon enough anyway. Might as well get what you can out of life while you still have it.

I tried to research the problem a bit, it's considered double hearsay in court and generally not admissible as evidence.

Person 1 Claim: "I won the lottery, my friend saw the ticket and can confirm"
Person 2 Claim: "I won the lottery, 10 people saw the ticket and can confirm"

My guess is that that in a lottery where the odds are 1 in a billion:
P(Person 1 won the lottery given they claimed "I won the lottery, my friend saw the ticket and can confirm") = 1%
P(Person 2 won the lottery given they claimed "I won the lottery, my friend saw the ticket and can confirm") = 1.01%

It depends on the setting, odds of invalid tickets, odds of being mistaken, odds that they were joking, etc... I didn't specify what would be random variables.

In terms of christian apologetics, making an unconfirmable claim that many people witnessed a miracle versus not making that claim I would say probably slightly increases the likelihood of the claim being true but the probability amount that increases from them making that claim is so minuscule it's really not worth mentioning as evidence that the claim is true. But people cite it as an argument that miracles occurred and seems to have persuasive power to some so that leads me to think double and tripple hearsay carry some slight amount of weight.

You are trying to make an actual infinity (past eternity) into a potential infinity. That's not possible, past eternity actually happened; implying whatever number we choose will be smaller than the number of moments elapsed; but there is no number with the quality it is bigger than all the others (there is no largest number X because X+1>X). Hence the nonsensical conclusion that the number of moments elapsed is not a number. — Devans99

I get what you're saying but it's special pleading that it's not possible to traverse an infinite amount of time. When you try to prove eternal time is a contradiction by first assuming an infinite amount of time exists before now, we can prove that traversing any amount of time is possible with a proof by induction.

1) an infinite amount of time can exist before now
2) it is possible to traverse 1 second of time
3) if it's possible to traverse x seconds of time then it's possible to traverse x+1 seconds of time
4) therefore it's possible to traverse any number of seconds of time

That means that you can name me any number and it's possible for that second to exist. That is why the number of seconds before now that can possibly exist is "greater than any number". Since you cannot show me a single moment of time that cannot exist in an eternal universe there is no contradiction here. Because we're granting an infinite amount of time before now in 1), that allows for all moments before now to be traversed.

Another way to approach this problem is use another system of math like hyper reals. Maybe using real numbers to explain the universe is invalid and something else like hyperreals would work better. The archimedean property of real numbers says infinity and infintecimal numbers cannot exist but other number systems allow for their existence.

Did you get what I've been saying though?

1. The number of events in an infinite regress is greater than any number.
2. Which is a contradiction; can’t be a number and greater than any number*.

*(Infinity is a concept not a number, proof: Infinity, if a number, would be a number X which is greater than all other numbers. But X+1>X).

When you say "The number of events in an infinite regress is greater than any number". I would accept that as true when describing the event as having no upper bound but does not mean the number of events equals a number called infinity. That's why point 1 is not a contradiction.

It would be like me proving infinite integers smaller than 0 don't exist this way:
1) The total number of integers smaller than 0 is greater than any number.
2) Which is a contradiction; can't be a number greater than any number*.

*(Infinity is a concept not a number, proof: Infinity, if a number, would be a number X which is greater than all other numbers. But X+1>X)

Not trying to do that. I can word it a different way like how do you prove an unknown property doesn't exist between this letter ==> "a" <== and this letter without commiting an argument from ignorance fallacy?

Infinity is a description of a set of numbers. Any finite number is a number. If you count from 1, you'll never get to large because "large" is not a number. Using "infinity" as a number like that to disprove some claim doesn't work for that reason.

Yes, you have to come to the conclusion the age of some moments is greater than any number which is a contradiction. You cannot have past eternity without actual infinity. — Devans99

You can have no upper limit to the amount of time before now while at the same time having any number of age of any moment in history. So a million years ago exists, 10^434343 years ago exists, but "infinity" years ago does not exist because it's a malformed value. But any finite number of years ago exists.

What I am doing is starting from the non-existent start point and adding infinity moments to it to get to a non-existent end point in the present. — Devans99

If the starting point is non-existent in your scenario then it serves no purpose to use it within that hypothetical reality to arrive at a contradiction.

In a universe with eternal time before now there would be no such thing as a moment an infinite amount of time before now because it's not possible to traverse an infinite amount of time. There would be a moment a million years ago, a billion years ago, or any other number of years ago. But not a moment "infinity" years ago. While at the same time having an infinite amount of time before now.

It sounds like you're projecting backward to a starting moment from "now" and then saying you cannot reach "now" from the starting moment because it never would have reached "now" from the starting moment. But premise 1, defines that no starting moment exists. It's a red herring because moments that exist an infinite amount of time ago do not exist anyway even if the univerrse were eternal in the way I framed it in the previous paragraph.

But I would argue that it does not matter how much time you allow; if the objects do not have temporal starts, they do not exist. To see what I mean, try imagining a brick without any identifiable spacial start point. It would not exist. Works exactly the same for time as it does for space. As I've pointed out before (https://thephilosophyforum.com/discussion/5242/infinite-being), infinite existence is impossible for beings so it should be impossible for anything else also. — Devans99

when you break it down though we're getting this as the logical argument:

1) infinite time with no starting point
2) cannot get to now without a starting point
3) therefore 1) is false

Not really getting any substance there except a bias against the idea of an infinite regress being the fact. There's no contradiction with infinite falling dominoes if we grant the premise of infinite dominoes, infinite time, and no prime mover. Without the contradiction it's not a false statement.

You are saying you can't perform mathematical operations on infinity? IE it's not a number. — Devans99

Not in conventional real number math. It's meant to be a description saying that no upper bound exists. Asking what 1 + "no upper bound exists" makes about as much sense as asking 1 + rainbow.

The point is that the rationals are larger than the naturals. For every natural, there is an infinity of rationals. That's a simple proof that bijection gives the wrong answers. — Devans99

That's 2 different definitions of equals you're using. Because whole numbers are a subset of rational numbers then there's more rational numbers than whole numbers.

|natural numbers| = |rational numbers| means they have the same cardinality but that's as far as it goes.

Definition 1: |A| = |B|

Two sets A and B have the same cardinality if there exists a bijection from A to B, that is, a function from A to B that is both injective and surjective. Such sets are said to be equipotent, equipollent, or equinumerous. This relationship can also be denoted A ≈ B or A ~ B.

For example, the set E = {0, 2, 4, 6, ...} of non-negative even numbers has the same cardinality as the set N = {0, 1, 2, 3, ...} of natural numbers, since the function f(n) = 2n is a bijection from N to E.

Outside of sets I wouldn't use equals in that manner to make predictions about the world.

I wanted to get some opinions from people who are more knowledgeable than I am in logic. Regarding the Law of identity "a is a" is it wrong to argue that a is not a because one a is on the left side of the copula and the other a is on the right side, and having different properties they are clearly not identical. I was actually going to use this in an argument but it sounds too cute so I thought I'd ask people who knew the subject better if this is a valid point, Is there some technical reason why it doesnt work and in general what your thoughts were. Has Aristotelian logic been subjected to the same critiques as Euclid's geometry. In other words is there a non Aristotelian logic to be derived by a critical examination of it's axioms? — jlrinc

More generally is it incorrect to point out that some unknown property may exist between "a" and "a" that makes them different? Would claiming no property exists because it cannot be proven otherwise not be committing an argument from ignorance fallacy?

* A more detailed proof by contradiction:

1. Assume a particle does not have a (temporal) start point
2. If the particle does not have a start, then it cannot have a ‘next to start’ (because that would qualify as a start)
3. So particle does not have a next to start (by Modus Ponens on [1] and [2]).
4. And so on for next to, next to start, all the way to time start+∞ (IE now)
5. Implies particle does not have a (temporal) end
6. Implies particle never existed — Devans99

"time start+∞" in your point number 4 contradicts point number 1. You're identifying a start point when you've already said none existed. The proof itself assumes that the truth about reality itself has to conform with what makes sense in our organic brains. Maybe something came from nothing because that's just how it is even if it qualifies as a logical contradiction. It could be one of those "too bad, it is what it is" things.

I've given thoughts about this myself

Or think of it this way. Each event in an infinite regress has a predecessor so each event makes sense on its own, but the series as a whole has no start so the series as a whole can't exist logically. — Devans99

If we assume an eternal universe we are assuming that there exists an unlimited amount of time before now. I don't see a logical contradiction in the idea of "no start to a series" when we grant an unlimited amount of time before now. If we agree that 1 day ago is possible and that any day before some day is possible is also possible then all finite amount of days before now are possible.

Typically any attempt I've seen against an eternal universe goes along the line of presuming an infinite number of something exists then asserting infinite is impossible without actually pointing out a logical contradiction giving the assumption they already made.

The definition of the first transfinite number is the cardinality of the set of natural numbers. No way is that a number. It's a conception of a mad man.

I should point out that there is only one kind of infinity; by definition it is the largest thing, so it's not possible to have two of the largest things; one of them would not be infinity. If you want to take a look at what sort of nonsense the opposite assumption produces, then bijection is the term to google. You will find that the procedure produces plainly laughable results such as the set of natural numbers being the same size as the set of rational numbers (the 2nd is clearly infinitely larger than the first).

What are we to make of the rules for working with transfinite cardinals:

∞+1=∞.

If you buy the first point about a single type of infinity, then the above expression immediately leads to 1=0. Even if you don't, there is something deeply wrong with it. In english, it's saying that 'there exists something, that when you change it, it does not change'. What sort of object behaves like that? No objects behalf like that, so does it deserve to be enshrined at the heart of a supposedly logical discipline (maths)? — Devans99

Infinity means without limit that doesn't exist as a value in conventional math. It's not part of a set of natural numbers therefore not appropriate to treat it as a number in conventional math like "∞+1=∞". The reason why the number of elements in the set of natural numbers "equals" that of rational numbers is because they defined "equals" when it comes to cardinality to mean possible to completely map from one to the other. In that case it's possible to map all natural numbers to all rational numbers without missing any rational numbers.

Every whole number maps to every fraction like this:

A naked claim is more likely than one with added details (such as alleged additional witnesses) because every detail is also an additional claim. — Echarmion

In the P("I own a car") > P("I own a red car") sense yeah.

More detail can increase the likelihood too like:

P("I own a red car given that I own something that's red, it makes noise, and has lights on it") > P("I own a red car")

But the original scenario is different than that example because we're dealing with claims and not "givens". But I'm thinking often times we can see that a statement is more likely to be true when it's claimed versus when it's not claimed if we can determine that it's more likely to not be fabricated. Maybe an example of that would be if I forgot what day of the week it was and asked someone then they told me "Wednesday", then that should raise the probability of it being "Wednesday" from 1 in 7 to something pretty close to 100% even though all that's changed is the introduction of someone else claiming it's Wednesday.

Oh, the scenario was supposed to be just a claim? Well in that case the answer is that a statement alleging more witnesses is less likely to be true, by virtue of alleging extra facts. For a reasonable number of witnesses, the probability of the statements is roughly identical and only depends on the likelihood the person is lying in the first place. — Echarmion

I would have thought the more witnesses with consistent answers adds credibility. Assuming honesty and the existence of the witnesses in order for them to be mistaken every witness has to be wrong. The likelihood of all witnesses being wrong approaches 0 with the more witnesses you have.

We can see this in real life all the time when rumors and accusations spread. Like if someone just claims they were assaulted versus someone claims they were assaulted with many eye witnesses according to them. Or if someone makes a claim about the government versus someone a claim about the government that was corroborated by many anonymous sources according to them. Do people correctly apply more likelihood of the event being true when introducing more facts like that? Whether the person expects to be fact checked, how disprovable the facts are, and how intelligent the person is all pay a factor too.

as already said, lots of variables involved

Even with the frequentist data, however, there would still be a number of problems to overcome. That's because there are so many different variables that can come into play. Making a probability claim on this sort of frequentist data implies that we're parsing the witnesses as ideal--no sort of bias, no sort of hidden agenda, no perceptual problems, ideally intelligent and rational, etc., and it also implies that we're assuming they have a more or less ideal access to information. Otherwise there would be no way to establish that the correlation is implicational, and that's what you'd be looking for here. — Terrapin Station

Because we don't know a lot of the facts it makes it difficult to make a probability judgement. But maybe there's some kind of ambient probability like a weighted average of people who would tell a big lie that has more to attack versus a small lie that's harder to verify.

Not in the least. The sole arbiter is the issuing authority of the lottery, whether a country or a state or a church group. No number of non-arbiters, no matter how large, can confirm a win. If a thousand people see your winning ticket, the lottery authority can always claim machine error. Here is a real life case. https://www.npr.org/sections/thetwo-way/2017/12/28/574070736/how-the-glitch-stole-christmas-s-c-lottery-says-error-caused-winning-tickets — fishfry

Unless of course the ticket is fake or otherwise invalid. No amount of witnesses will modify that probability. — Echarmion

Yeah I've considered that when determining "P(Person 1 won the lottery | Person 1 is being truthful) < P(Person 2 won the lottery | Person 2 is being truthful)". I would agree P(Person 1 did not win the lottery | Person 1 is being truthful and the ticket is invalid or fake) >= P(Person 2 did not win the lottery | Person 2 is being truthful and the ticket is invalid or fake). But I was thinking there's more scenarios of individual people thinking they won the lottery and are just mistaken due to human error within P(Person 1 won the lottery | Person 1 is being truthful). In cases of human error I consider more people making the same verification a way to minimize that.

But it's harder to find 10 people willing to lie for you than it's to find 2, so even if they were willing to forge more evidence, the evidence still increases the probability of them being truthful. You can always construct reasons to not consider any single piece of evidence convincing, but it's still evidence and you still need to take it into account. — Echarmion

Except we don't know if the 10 people exists when considering the probability. They could just being saying there are 10 people that can verify and are making it up. That's the part I'm tripped up on the most: determining the likelihood that someone is being untruthful then the probability that they would make a claim like "1 other person can verify" versus "10 other people can verify" if their goal is to be as convincing as possible.

It should be true given certain basic assumptions about symbols and logic.

Most importantly the law of identity needs to be true or "X=X". What's on the left of "=" is considered the same value as what's on the right of "=". To prove they're the same we would need to be concerned with their value and not their appearances. "2+2" and "4" may look different but if they have the same value that means they're the same.

Then there's the number symbols
1 = o
2 = oo
3 = ooo
4 = oooo

Then the "+" symbol is an operation that combines the group of objects together.

So 2+2 or "oo+oo" does the equivalent of removing the "+" and pushing the 2 groups together to get "oooo".

The "oooo" looks like what's defined to be the symbol "4". Using that law of identity again 2+2=4 for that reason.

In a situation where Person 1 and Person 2 are being truthful it seems to me that Person 2 is more likely to be an actual lottery winner because of corroborating evidence for the same reason why 10 eye witnesses in the trial describing the same thing is stronger evidence than just a single eye witness.

Stated differently for that reason I can buy that P(Person 1 won the lottery | Person 1 is being truthful) < P(Person 2 won the lottery | Person 2 is being truthful). That part make the case that claiming more people observed it helps the probability of the claim.

But there are multiple scenarios to consider besides that one I put in bold

P(Person 1 won the lottery | Person 1 is being truthful) + P(Person 1 won the lottery | Person 1 is not being truthful) + P(Person 1 did not win the lottery | Person 1 is being truthful) + P(Person 1 did not win the lottery | Person 1 is not being truthful) = 1

P(Person 2 won the lottery | Person 2 is being truthful) + P(Person 2 won the lottery | Person 2 is not being truthful) + P(Person 2 did not win the lottery | Person 2 is being truthful) + P(Person 2 did not win the lottery | Person 2 is not being truthful) = 1

conversely someone is more likely to have actually won the lottery and not be mistaken if more people look at the ticket can confirm it.

Stated differently for that reason I can buy that P(Person 2 did not win the lottery | Person 2 is being truthful) < P(Person 1 did not win the lottery | Person 1 is being truthful).

P(Person 1 won the lottery | Person 1 is not being truthful) and P(Person 2 won the lottery | Person 2 is not being truthful) seem negligible or about the same low value.

The main thing it looks like that determines how P(Person 1 won the lottery) compares with P(Person 2 won the lottery) is how P(Person 1 did not win the lottery | Person 1 is not being truthful) compares with P(Person 2 did not win the lottery | Person 2 is not being truthful). But it seems to me that if someone were trying to be dishonest, they would choose to be as convincing as possible making P(Person 2 did not win the lottery | Person 2 is not being truthful) > P(Person 1 did not win the lottery | Person 1 is not being truthful) for the same reason why someone who bluffs in poker might bet more if it's their goal to deceive others.

If Person 2 is more likely to lie big when they are lying and Person 2 is also more likely to have more impressive evidence when being honest, I don't know if that helps if it just leads back to determining whether likelihood of comparative probabilities of Person 1 and Person 2 being honest versus deceptive.