Explaining Axioms?

[Sleeper]

I'm in a Facebook discussion with a Christian who thinks he has won some sort of battle by claiming that I can't "explain" axioms. Allow me to explain what he means by that:

He claims that I cannot explain things like "why" contradictory statements cannot be true, etc. I don't have any formal training in logic - is there something I'm missing here? I've tried to explain that it's an invalid question, but he's trying to get me to admit that I can't explain "why" these things are true.

Am I right in refusing to accept his phrasing? It just seems like an invalid, unnecessary  assertion that's dripping with agency attribution.

An example of his argument:

"Go ahead try to explain why you can't both be married and not-married at the same time? You're gonna end up saying something like 'you just can't' ... Explain why 2+2=4 or just admit that it can not be explained..."

[LikelyToBreak]

Good question!  My understanding of axioms, are that they are mathematically and logically provable assertions which start as a basis for proving something to be false or true.  Thus, we take two sticks and then another two sticks and then count the number of sticks altogether.  Done correctly, you will always end up with four sticks.  As far as the marriage question, it is because we define marriage in a certain way.  If we don't define things properly, then we have a communication breakdown.

For instance, in Japanese a taco is the English octopus.   If we don't define which taco we are discussing, then we can't make ourselves understood.  

Though, we also have to watch out on how certain words are defined.  Christians love to use one definition of a word to prove their point.  Commonly, they talk about how people have "faith" in science.  Yes, we do.  But, I think most atheists would agree it is a justifiable "faith" as opposed to simply having "faith" in something.  "Faith" that something is so, doesn't make it so.  But, having "faith" that something is the way it is, because of experiments and explanations of those experiments, is based on sound logic and observations, rather than just wanting something to be the way it is.

At any rate.  Even if you had an advanced degree in logic, the average Christian would not let you poke holes in his/her logical fallacies.  After all, here is a banana.  It is good, therefore there has to be a good God who sacrificed himself on the cross for us, so that those who believed in him would never perish but have everlasting life.  Now, explain how something can come from nothing, you baby eating, dog raping, lying, murderer!  

[aitm]

I'm in a Facebook discussion with a Christian who thinks he has won some sort of battle by claiming that I can't "explain" axioms.

because the almighty, benevolent, omnipotent, omniscient deity known as god could not write the holy words in a clearly understandable format for stone age goat herders to understand.

[Plu]

You can't explain axioms. That's their whole point. They're things that are agreed upon to be accepted for what they are, without the ability to prove them, because you need to start somewhere.

And because you can't prove them and must accept them, people need to be extremely critical of what they accept as an axiom, because you build your entire world view on them and if you managed to get one wrong (like, say, "there is a god and he loves me") then your entire world view will be built on a lie that's almost impossible to get out again, because you cannot prove or disprove an axiom. You can only show why an axiom is pointless or broken, but you can't prove it.

The reason you can never explain "why" something cannot be and not be at the same time is because the axiom of non-contradiction defines what it means to be in the first place. We can define things as things only because everyone (including dumbfucks arguing against it) realising that these axioms exist and are needed to make sense of the world.

It's flat out impossible to have a sensical worldview unless you accept a bunch of axioms, including "a thing is equal to itself" and "a thing cannot be something and not that something at the same time". If you want to laugh, ask him to point out a counter-example. The only valid way to debunk an axiom is by showing an example of where it doesn't apply.

[Brian37]

I ignore this type of crap.

First off, no human in our species history can be 100% consistent 100% of the time. You are falling for a "gotcha" tactic.

Mental masturbation will never replace universal scientific method. Humans will always have competing claims. So you skip the metaphor and philosophy and you take the claim, whatever it is on ANY subject, you set up tests and control groups based on established method.

The theists uses tactics like this to get you to admit "I don't know", then hit you with "AH HA, THEREFOR MY GOD EXISTS"

I'd suggest the next time some idiot pulls this ask them if they would buy their own argument if someone with a different pet god were using this same argument. Would they become a Muslim or Jew if they used the same argument?

Science does NOT claim to know everything, the entire reason of science is to figure out what is going on. What you witness is someone who is in denial that they buy a comic book who is looking for some way to seem relevant even though their myth is clearly BULLSHIT.

[GurrenLagann]

You're just dealing with a presuppositionalist, who use the WORST possible apologetic. It was recognized by Plato and Aristotle over 2300 years ago that certain axioms must be accepted by necessity. For example, you cannot deny the axioms known as the Law of Identity and Law of noncontradiction because any statement saying they're false must first assume as true and use the axioms and then proceed to deny them. In other words, those two axioms are self-attesting and necessary assumptions for language itself.

See how utterly insane it is to claim to have a worldview that "accounts" for those axioms? For them to even do, say, think or speak of their worldview and revelation, they inescapably assume these axioms.

All this person you're dealing with is doing is parroting nonsense he's heard Sye Bruggencate and Eric Hovind spout, two world-class idiots on anything, especially philosophy.

[GurrenLagann]

Really you should mostly ignore presuppositionalists. They always say they cannot be wrong about God's existence in the first place, so discussion with them is pointless. :(

[entropy]

You can't explain axioms. That's their whole point. They're things that are agreed upon to be accepted for what they are, without the ability to prove them, because you need to start somewhere.

And because you can't prove them and must accept them, people need to be extremely critical of what they accept as an axiom, because you build your entire world view on them and if you managed to get one wrong (like, say, "there is a god and he loves me") then your entire world view will be built on a lie that's almost impossible to get out again, because you cannot prove or disprove an axiom. You can only show why an axiom is pointless or broken, but you can't prove it.

The reason you can never explain "why" something cannot be and not be at the same time is because the axiom of non-contradiction defines what it means to be in the first place. We can define things as things only because everyone (including dumbfucks arguing against it) realising that these axioms exist and are needed to make sense of the world.

It's flat out impossible to have a sensical worldview unless you accept a bunch of axioms, including "a thing is equal to itself" and "a thing cannot be something and not that something at the same time". If you want to laugh, ask him to point out a counter-example. The only valid way to debunk an axiom is by showing an example of where it doesn't apply.

Right, the laws of non-contradiction and identity are axioms that are simply taken to be self evident and not in need of further explanatory justification. Anyone can be free to reject the assumption of those axioms, but good luck in having anything coherent to say without assuming them.

Assuming the axioms of non-contradiction and identity without further justification is not like assuming a deity exists without further justification. You can have a coherent view of things without assuming that a deity exists, but you cannot have a coherent view of anything without assuming the axioms of non-contradiction or identity.

[GurrenLagann]

^Agreed. But worse yet, to deny those 2 axioms you first have to assume them as true, i.e "The law of identity and noncontradiction are false" assumes that those laws are what they are, and are not what they are not, then proceeds to claim them false.

Lulz.

[Colanth]

Well ...

A thing can't be what it's not.  Anyone who can't accept that isn't worth arguing with, since it's pretty much a test of rationality, and arguing with an irrational person is, itself, irrational.

Since a thing can't be what it's not, a married person can't be unmarried.  A can not be not-A.

As far as why 2 + 2 = 4, that's the same reason as the sky is blue - it's true by definition.  (If we define something to be X, then things that have the properties of X are said to be "Xish" things.  That's just how we've all decided that natural language [languages spoken and understood by people] works.  It's also called "true by consensus" - we all agree to it.)

Of course you're "arguing" with either a troll or an idiot.  If the first, you may have fun, but you won't win, even if you're the world's greatest expert on formal logic.  If the second, why bother?

[Brian37]

You're just dealing with a presuppositionalist, who use the WORST possible apologetic. It was recognized by Plato and Aristotle over 2300 years ago that certain axioms must be accepted by necessity. For example, you cannot deny the axioms known as the Law of Identity and Law of noncontradiction because any statement saying they're false must first assume as true and use the axioms and then proceed to deny them. In other words, those two axioms are self-attesting and necessary assumptions for language itself.

See how utterly insane it is to claim to have a worldview that "accounts" for those axioms? For them to even do, say, think or speak of their worldview and revelation, they inescapably assume these axioms.

All this person you're dealing with is doing is parroting nonsense he's heard Sye Bruggencate and Eric Hovind spout, two world-class idiots on anything, especially philosophy.

You're just dealing with a presuppositionalist, who use the WORST possible apologetic.

No, they are both the same. "Presuppositionalist" is simply a newer name for "apologist".  Just like "Intelligent Design" is repackaging of "Creationism".

When you have facts you don't have to argue which is what "apology" means. When you have facts you can demonstrate.

Presupposition is nothing more than "lets pretend". And pretending existed long before that word did which is why humans make "apologies" for their bad arguments based on naked assertions.

[JonathanG]

I'm in a Facebook discussion

Bump.

with a Christian

Set.

who thinks he has won some sort of battle by claiming that I can't "explain" axioms

And spike.



A facebook discussion with a Christian on the existence of god.  It's like the perfect storm.


I know it's been said many times on this site alone, but most arguments with these types of people are of this form:

A) We don't know X
B) Therefore, God did it.

Let's assume for a moment that you aren't able to properly explain the axioms of logic.  That does not imply, first, that such an explanation does not exist, and second, that that somehow implies the existence of a god.  All it shows is that you are unable to properly explain the axioms of logic.

[Shol'va]

So I came on here looking for help as I was somewhat stumped when this very argument was presented to me.
I think thus far I muddled my way through it fairly well, you be the judge.
The challenge:

Axioms by definition are true for everyone beyond human ability to change. What could be the source other than something like god

To which I replied that firstly, given that I have seen several definitions of axioms, I relied on one I find particularly succint: a statement or proposition that is regarded as being established, self-evidently true and accepted.
So basically axioms are a human concept to enable us to interface with reality. So then I asked why must there be something transcendental for axioms to be true or exist?
Further, why particularly a supreme being? Why not a transcendental committee with no CEO?
If we want to nail particular axioms, then what logically follows should be along the lines of: the universe/reality exists, I exist, others exist.
From then on, the theist will try to inject the forth, the transcendental exist, or in the case of the presupper, that is the starting point.

Still pending a reply. What do you think so far?
I'm going to try to gracefully back out of it. I could sense some sort of SyeTen-ish trap encroaching. I have absolutely no desire to get into a neverending debate ... on Facebook.

[AllPurposeAtheist]

Axiom gets my clothes clean, brighter whites, more vivid colors and they always smell dryer fresh.. :)

[Shol'va]

WITNESS THE POWER OF AXIOM CLEAN !!!!