txaq007's Inescapable Error

[chezlaw]

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Assume for the sake of argument that the Goldbach conjecture is true. If it is true, then it is also certain.

Mathematical truths are not contingent truths such that they can be true, but then turn out to be false later on (if they turn out to be false, then they were never true). They are necessarily true (i.e. true in every possible world). Thus when David proclaims that every mathematical certainty can be proved he

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The discussion is about the certainty of beliefs. Yes something can be neccesarily true i.e. true in all worlds and unprovable but that's not what we are talking about.

chez

[txag007]

The Bible says to pray about all things and to pray constantly. I often pray for wisdom about certain decisions, calmness is certain situations, etc. I pray for protection for friends and family.

I don't have the dramatic testimony about coming to Christ that many other Christians do. I was raised in a Christian home and accepted Christ at a relatively early age. In recent years, however, I began to study the evidence for and against Christianity because I wanted to know whether what I believed was accurate. It is.

I can't deny that there is a psychological factor involved with coming to Christ. When you accept Christ, it is more than just accepting a new belief system. The Holy Spirit enters your life and fills an emotional void. I think it is something that cannot be adequately explained to those who have never experienced it.

As far as God not being necessary for the content of my last post to be true, couple the experience of accepting Chirst with the available evidence for Christianity. Look at the evidence for God's existence in the first place. Look at the evidence for the creation of the universe. Look at the evidence that the Bible is true. Look at the evidence that the resurrection actually occurred. Too many coincidences are involved for the proof not to be considered reasonable. That's how I would explain to a non-believer that it's likely my experiences are actually from God. After one has accepted Christ in his life, it becomes more certain that He is God.

[Kripke]

Ok I see. However, that was not what David seemed to be talking about. In fact I do not think that was what he meant.

And, if we are talking about certainty of belief, then I conjecture that there are many mathematical truths which we do not need proof of in order to have certainty.

I assume almost everyone knows that the proposition "2 + 2 = 4" is true and that they have certainty in their belief. However must people are unable to prove this (i.e. do a formal proof), since almost noone is acquainted with the Peano axioms of arithmetic.

If it is the epistemological point of view that is in focus here, then David's is also wrong.

- Kripke

[chezlaw]

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I assume almost everyone knows that the proposition "2 + 2 = 4" is true and that they have certainty in their belief. However must people are unable to prove this (i.e. do a formal proof), since almost noone is acquainted with the Peano axioms of arithmetic.


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Geeting closer but I think you are exploiting a looseness in the language rather than addresing the point in context.

Someone may have a dream that the Riemann hypothesis is true, so powerful it convinces them beyond doubt. They may turn out to be right so they would be certain and correct without proof but its nothing to do with mathematical certainty which requires proof.

Lets wait for DS to clear up what he meant before proceeding further.

chez

[Cooker]

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Almost 100% of the smartest men on earth maintained this planet was flat and the center of our solar system at one time.



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Just for those curious, it is indeed a myth that people believed the world was flat until Columbus. Hero of Alexandria calculated the radius of Earth to astonishing accuracy well before the birth of Christ using differences in shadows at 2 locations. Most intelligent people of his day and beyond that time believed Earth was round. I doubt there is a time in recorded human history where Earth was genuinely believed to be flat by most intellingent people. I think if you researched it, you would find that the belief that Earth is the center of the solar system is not as prevalent among intelligent people even in the distant past as well, but I haven't looked into this much.

Still, your logic has flaws. David's proposition is that given a statement and its negative, if a majority of intelligent people believe the statement to be true then it is more likely to be true than the negative and similarly if more intelligent people believe the negative. This does not mean that throughout history all statements believed true by a majority of intelligent people at that time must be true for this proposition to be true or useful.

Also, since we have more evidence collected and better access to that evidence, it is reasonable to assume modern day intelligent people fair better in this respect than people from the past.

[Piers]

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Correspondingly, I can KNOW God with out being able to JUSTIFY that claim of knowledge to others.

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What ‘you’ are saying is largely OK. The point you are not mentioning is that the feeling of certainty is an emotion. You become certain of something due to some trigger in you brain switching, the trigger need have no correlation with rational thought.

Certainty is a trick the mind plays on you on order to ease decision-making.

I am completely certain that Jesus Christ was not resurrected. I would never let the possibility that Jesus Christ might have been resurrected affect any action I might take. However rationally I accept that there is a non-zero chance that he might have been resurrected. I see no contradiction here. You can call me close minded, but then you are agreeing that being closed minded is part of the way human thinking works.

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He is claiming 100% certainty. While at the same time admitting there is not 100% proof. While at the same time claiming that he is not close minded.

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txaq007, just admit your close minded, and we can all go home. Don’t worry you’ve in good company.

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I am not well versed in mathematical proofs, so I am wondering from others on the site if there are indeed mathematical certainties that cannot be proved.

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I think it would be normal to define a mathematical certainty as something that can be proved mathematically; so no unless you cheat.

However the use of certainty as regards mathematical proof, and the use of certainty in describing human feelings are too different definitions of the word. If you treat them as one you just confuse yourself, I present this thread as evidence.

[Timer]

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"You can "be convinced" by taking an objective look at the evidence."

Then why do you think that over 90% of the people who have IQs above 130 and know math, physics, chemistry, biology, logic, and probability, well, and who have taken an objective look, are not convinced?

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I challenge this 90% figure. I'd say it's off by quite a bit. Show me some proof that I'm wrong, however, and I'll reconsider the evidence.

[chezlaw]

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I think it would be normal to define a mathematical certainty as something that can be proved mathematically; so no unless you cheat.


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If that's what DS had in mind by mathematical certainty then its going to be really hard for anyone to argue his wrong in claiming there are no mathematical certainties that cannot be proved [img]/images/graemlins/smile.gif[/img]

chez

[Piers]

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I think it would be normal to define a mathematical certainty as something that can be proved mathematically; so no unless you cheat.


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If that's what DS had in mind by mathematical certainty then its going to be really hard for anyone to argue his wrong in claiming there are no mathematical certainties that cannot be proved
chez

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The only smallish problem is that maths cannot be proved to be consistent and so every theorem could be provable along with its negation, but we don't worry about that
[img]/images/graemlins/smile.gif[/img]

[Kripke]

"Geeting closer but I think you are exploiting a looseness in the language rather than addresing the point in context."

I really don't think so. In retrospect and on second thought, I actually find the phrasing 'mathematical certainty' to be most surely a non-epistemic term.

Clearly, if someone asks 'is that a mathematical certainty?' they are not asking whether someone can be entirely sure of that - rather they are asking whether it could turn out to be false?

- Kripke