What constitiutes 'proof'

From the thread about viewing the past:

I’m interested in the question of what exactly constitutes proof; I could assert that there is absolutely no proof that Winston Churchill ever existed.
Sure, you could show me photos and film footage, but can you prove that is him in the picture.
You can show me documents he signed, but hey, they could just be forgeries made by devout but misguided Winstonites.
You could dig up his mortal remains to show me, but heck, that could be anybody.
You could do DNA analysis against the remains vs his surviving relatives, but I have to take your word that they really are his relatives, not just the relatives of some anonymous stranger that you dug up, besides, it is well-known that DNA is all bunk.
You could introduce me to people that claim to have actually met him, but really, I have no desire to talk to people who insist in deluding themselves.
And so on.

So help me out here; at the moment, I’m of the opinion that statements like “absolutely no proof that Jesus ever existed” are merely the result of a careful exercise to exclude any available evidence or account.

I’d settle for non-Biblical contemporary records. The Romans were good about keeping track of rabble-rousers and executions. The only semi-contemporary Roman record I have seen is suspected by many historians to have been added many years later because it has nothing to do with the rest of the document.

Found it, earliest non-Biblical reference to Jesus was by Flavius Josephus in the second half of the first century of the CE, and it’s authenticity is highly questionable…


There are many different kinds of proof. But none of them are absolute. We know this because Goedel showed us that no system can be both complete and consistent, which means that we are always going to need axioms.

The strongest kind of “proof”, I would say, is mathematical. This is a proof by which having accepted a postulate, every step we take is logically rigorous. The conclusion is therefore an unarguable consequence of the premise. The only weakness, therefore, is the fact that it all has to start somewhere, so we need to accept some axioms (eg axiom of choice/Zorn’s Lemma) to build the theory up.

Scientific proof isn’t bad, but it’s far less rigorous because it is deductive rather than inductive. We accept that a zillion observations proves the case. There is, however, always the chink in the armour - maybe the sun will not come up tomorrow and the whole system will come crashing down around our ears.

There is, of course, a further chink in observational proof. We must rely on measuring devices - even if these are just our eyes and ears. Any image of a thing is not the thing, and the brain can be fooled into thinking something is there when actually it is not. Light, gravity, even our very existence could just be a mass hallucination. We assume not, for otherwise we could get nowhere. But the doubt must always be there.

Then there are situations in which we have less than the optimum number of observations anyway. The data so far agrees with the predictive model. Today. But will it tomorrow? We can only wait and see.

But mathematics and science are only two epistimological systems. There are other ways of evaluating knowledge - religion is one. Like science and maths, religion can never be both complete and consistent. It could be argued that unlike science and maths, which strive for consistency and accept a lack of completion, religion strives for completion and accepts a lack of consistency. This is still a valid approach. What consititutes a proof under the religious epistimological system I cannot guess.

But I could submit the epistimology “Every sentence that starts with a vowel is true”. This is then the (necessary) axiom of the epistomology (which of course is neither consistent nor complete). Under this epistomolgy proofs are very simple indeed. If a sentence begins with a vowel, it is proved true. As epistimologies go this one is useless. But you cannot prove that it is a definitively incorrect system of evaluation - Goedel showed us that. It seems to offer us nothing, so we reject it. But we are, in essence, using the science epistimology even to do this.

So what constitutes “proof”? Everything and nothing. After the layers of the onion have been peeled, there is nothing left to prove. Which is why you have to have belief, even if that belief is that what you see is what you get.


I must admit that I don’t completely understand Goedel’s proof, but I do think a slight qualification is in order. At most, he showed that any formal system of sufficient strength cannot be both complete and consistent.

A formal system could be both complete and consistent, provided it doesn’t have suffient strength.

(If anyone knows more about this than me, could you explain what the threshold is?)

Sufficient strength in this context means valid that statments within the system can refer to the system itself. As it turns out, any systems without this property are really pretty boring – any formal system that is actually useful (Arithmetic, predicate alculus, geometry, boolean algebra, etc. etc. etc.) are “sufficiently strong”.


We can choose to have incompleteness (the inability to prove certain true things), inconsistency (the ability to prove some untrue things), or a weak formal system (the inability to express anything as strong as arithmetic).

Inconsistency isn’t as much of a problem as some would make it. There are various logics (paraconsistent logics, for example) that reject either the law of non-contradiction or the law of the excluded middle (or both).

The law of non-contradiction says that A and (not A) cannot both be true (not more than one of them is true, though it allows both to be false). An equivalent is that a contradiction implies everything. It suggests that we should reject contradictions (what it actually says is: if we reject anything at all, we also must reject all contradictions).

The law of the excluded middle says that one of A and (not A) must be true (not less than one of them is true, though it allows both to be true). An equivalent is that nothing can imply a contradiction. It suggests that we should not accept contradictions (actually: we should not accept contradictions if we accept anything at all).

In two-valued logic, the two laws (and their conjunction) are all logically equivalent (they have the same truth values), though they don’t “mean” the same thing, and can be distinguished in non-standard logics. Since it’s not clear if the “real world” works like standard logics, philosophy will have to step in and help math make a guess about what to start with.

kg m²/s²

And in addition to apologising for missing out the other possibility to incompleteness and inconsistency I’d like to thank Newton Meter and greatZebu for explaining where my missing link lay.

I clean forgot about weak systems. I could try to wiggle out of it here by claiming that when we are talking about evaluating epistimological systems we are talking about something that is clearly strong, but we all know that I’d just be trying to cover my ass.


You have it backwards. Relying on a large number of examples, data points, or obeservations are inductive proofs. But the important thing is theories aren’t proved per se in science.

How is religion an epistemological system? How would one acquire knowledge through this sytem? How does one verify said knowledge?

How would a system without any consistency at all still a system? If 1 can be 3 some of the time, how can this sytem be reliable?

It appears that you have some confusion with regards to what epistemologu is.

This does not follow from your argument.

It seems that something that can be verified does not constitute a belief.

An epistimology is simply a method for examining and evaluating knowedge. Any code that allows us to do this qualifies. My “vowel” epistimology is certainly a method of identifying the truth of statements.

If you want to start arguing that religion is not an epistimological system then I’m afraid that I am going to have to suggest that it is you who does not understand what an epistimology is. But since I’m going in an hour and won’t be around for another five days, I think that I’ll leave it to the likes of Spiritus and Libertarian to clear up that little misconception. Sorry to cut and run.

Similarly, I don’t know where to begin with the idea that any system must be consistent. There are even branches of logic that don’t postulate consistency - ask Newton Meter about a few.

And whoever said that such a system must be “reliable”? Or even what “reliable” actually means? You can most certainly derive more than one truth from the religion epistimology for example.


Urban Ranger, it is a travesty to say that theories aren’t proved. That is one of many metaphysical premises which follow from Popper’s ideas about empiricism, and that a posteriori information cannot give us a priori truths. Clearly Kant, and offshoots of Kant, would disagree there, as well as most rationalists in general. I, for one, find the a priori / a posteriori distinction to be not quite so well-founded as some might consider, and as such, I am willing to view something like “proof” in an entirely different manner than, say, Hume or Popper.

Methinks your personal epistemology is tainting your understanding of, well, meta-epistemology. Spiritus Mundi once offered me the following epistemology: “All sentences which end in vowels are false.” (an offshoot statement of which kabbes has in his post above) Clearly, anything able of being expressed is able to be resolved in this system. If we want to cast this sentence into a religion we would simply say, “anything which is expressed in this religious tome is true.” Clearly a system of knowledge develops, and claims which are factual can, at least partially, be verified by the system. the fact that any particular element in question may not be able to be resolved in the system does not mean said system isn’t an epistemology. Also, if the system does not explicitly include a transitive property, the results of one which seem to contradict the results of another only seem to be so because you are making assumptions about what a system of knowledge should be able to do. Clearly a system of knowledge needs to do little more than sort statements into piles based on some (arbitrary) criteria.

We turn to epistemology to answer the question, “Can I say that I know this?” Why you feel religion is exempt from answering that question is something I would appreciate hearing.

I think the question, with reference to the OP and the thread from which it was extracted, is less what constitutes absolute super-duper accept-no-substitutes proof of a given proposition, than what constitutes acceptable validity for “historical” documents and the statements made therein.

The Gospels are quite clearly narratives which purport to set forth the life and teachings of a man, but they are not and three of four do not pretend to be objective accounts. Each is written with a particular slant, aimed at supporting a particular view of the subject person. Each contains a mass of material not supported by external evidence except for, at times, one or more of the other three.

However, we tend to give some credence to the historicity of things like Manetho’s fragmentary history of Pharaonic Egypt, the Icelandic sagas, etc., after critical reading to remove what appear to be obvious legendary accretions.

I am reminded of the Welsh royal genealogies, regarding which I have older books averring that they were made up of whole cloth, in an attempt to tie the princely houses at the time they were written down back to legendary earlier people. I say this is in “older” books because after they were published a pillar erected by Eliseg, one of the princes considered legendary, giving his immediate paternal ancestors as a part of his title, was excavated.

Socrates is considered one of the seminal figures in the history of Philosophy. Yet only two people have any record of him: Plato and Xenophon. And it is well known that Plato’s portrait of Socrates was slanted in a way calculated to support Plato’s own philosophical enthusiasms.

In short, to what extent can one give any credence to the narratives of the Gospels? Like Mangetout, I find people who allege that “it’s obvious Jesus never existed” are simply taking their own rejection of the claims made by historical orthodox Christianity about him to an extreme not warranted by the very existence of these four accounts.

Finally, contemplate the introduction to Luke:

In short, Luke is claiming to employ the best historiographic principles of the First Century to provide Theophilus with an accurate account of all the stuff about Jesus that he’s heard and doesn’t know what parts of to accept as accurate.

Doesn’t necessarily prove he’s telling the total truth and nothing but – but it indicates an intent to try to do so.

Haven’t time for a long post but I wanted to make one point.

I believe Urban Ranger is correct. Scientific theories are not really “proven.” This is not a “metaphysical premise.” Rather, it is simply a statement of one of the working principles of the scientific method. Scientific proof is not proof in the philosophical sense. Rather, it is a statistical process. We cannot say categorically that any scientific fact or theory is “true.” Without getting into exactly what a scientific theory represents, any such statement is always provisional. “Based on our observations, there is only a 5% (or one in ten-thousand or whatever) chance that X is false.” There is an entire, and somewhat controversial, branch of statistics which seeks to analyze how much data is required to “prove” a scientific proposition. The key point, however, is that no scientific proposition is ever proven absolutely. Rather, a scientific proposition is always subject to revision based on new data.

In a sense, you could make a better case that science is not an epistemological system than you could that religion is not an epistemological system. Indeed, mathematics is closer to religion in this sense than it is to science. Ultimately, science is not a system for determining “truth,” it is a method of predicting outcomes. Newtonian mechanics isn’t “true.” Nonetheless, it is scientific because it is adequately predictive for the vast majority of applications. Science is full of similar examples. Indeed, there are entire branches of science which are based on demonstrably “false” theories which are, nonetheless, perfectly scientific.