Skepticism And Atheism As Default

[mymistake]

 

I think atheism is a belief. The prior response to Human explains why I think that.

 

I don't expect to win anybody over to my point of view though.

 

 

 

You would be better off using the terms properly.  It would reduce confusion.

[florduh]

Essentially this is assuming that atheism should be universally acknowledged to be the default belief absent any contrary evidence.

 

Not believing in an assertion presented without sufficient evidence IS the default position. It is not an assertion in itself. You say that shape shifting reptilian overlords are secretly running the affairs of people on Earth, and I must ask for proof before I entertain this idea as probable. Applying this natural unbelief of an extraordinary claim unless accompanied by proof is accepted as normal and just common sense, but for some reason if it regards the claims of theists, then simple unbelief suddenly becomes a belief as well. I fail to see the distinction between claims that Gods, Reptilians, Fairies, Leprechauns and Xenu actually exist; all are incredulous assertions and all have no evidence to support such a claim. To simply reject such a claim for lack of merit does not imply an alternate belief system.

[mymistake]

[TheRedneckProfessor]

If a door-to-door vacuum cleaner salesmen told you his top-of-the-line deluxe model could also wash and wax your car, shine your shoes, and iron your laundry, would your default position be blind acceptance of his claim?  Or would you prefer he give you a demonstration?

 

And if you asked for said demonstration, would that be a belief system?  Or just a question?

[Thackerie]

Anyway, I guess I will give up, because it doesn't seem like anybody understands what I am talking about. Probably this isn't as interesting to others as it is to me. That's fine.

 

We do understand what you are talking about. You are wrong.

[mymistake]

 

Haha!

The religious dude's head looks like it becomes a baseball!

That is, his head becomes (is) what he believes.

That's very revealing, indeed.

 

 

 

I'm just trying to illustrate that skepticism is the normal and reasonable response.

 

"I don't believe you, prove it." should be our response to anything.  And we know baseballs exist in our world.  We have all seen baseballs.  Maybe we have owned a baseball.  We have all seen legitimate photos of baseballs.  There is plenty of video evidence of baseballs.

 

If I tell you that I own a time machine that is an extraordinary claim.  Time machines have only been seen in movies and works of fiction.  No time machine has been known to exist.  That puts an incredible burden on me to support my claim.  Nobody should take it seriously without a convincing demonstration, one that cannot be explained away by some other means.  Your assumption that my time machine claim is wrong isn't a belief system.  Not in the sense that you should have to support it or that both our ideas are on equal footing since neither one of us supports our idea.  Without a demonstration my claim is absurd and your claim is normal.

 

Now look at the house of cards known as the theology of any major religion.  Not only do they want you to blindly swallow their religion whole but they have fancy explanations for why there isn't a shred of evidence for any of it.  And you have to build your whole life around this world view.  Soft atheism - "I will wait until you can prove it" is a very normal response.

[Orbit]

Directionless--this might help you see what we are saying: 

[bornagainathiest]

This might also help you, Directionless.

 

http://www.ex-christian.net/topic/63715-thomas-the-skeptic-something-for-ironhorse/#.VAOa0fldVzM

[directionless]

o.k., everybody, I will take a look at some of those suggested links tomorrow to see if they change my opinion. At least they will give me a better understanding of the reasoning on that side.

[bornagainathiest]

Thanks for giving value to our input, Directionless.  

 

The link I provided leads to the thread, "Thomas the Skeptic - Something for Ironhorse".  Just about everything in that thread can be boiled down to these essential points.

 

1.  Thomas was skeptical (did not believe) that Jesus had risen from the dead.

 

2.  He would not take this on faith from the other disciples and followers of Jesus.

 

3.  He only believed when the concrete physical evidence (Jesus' wounds) were presented to him for him to examine.

 

4.  

After Jesus ascended into heaven no other Christian (except perhaps Paul) has had the opportunity to be skeptical as Thomas was, when it comes to deciding to believe in Jesus' resurrection.  Without Jesus being physically present so that his wounds can be seen, every Christian in the last 2,000 years has had no choice but to accept the resurrection of Jesus by faith.  No skeptical examination of any concrete evidence for his resurrection has been possible - because none is available. 

 

5.  

The written testimonies of eye-witnesses to his resurrection, as recorded in the Bible, are no better than the spoken words of Peter and John the other disciples, when they tried to persuade Thomas that Jesus had risen from the dead.  (See # 2, above.) Such evidence is not concrete evidence that can be examined first-hand.  It could not be accepted by a skeptics like Thomas then and it cannot be accepted by skeptics like us, now.  Such evidence is second-hand and can only be accepted by faith - which is the opposite of skepticism.

 

6. This is why no Christian since Biblical times has ever made a truly skeptical examination of the first-hand evidence for Jesus' resurrection. 

 

7.  So when Ironhorse claims to be both a skeptic and a believer, he of course, wrong.  He was never able to make a skeptical, evidence-based decision about Jesus' resurrection.  He simply accepted the scriptural claim that it did happen, purely on faith.  As we Ex-Christians all did.

 

8.  Therefore Directionless, Ironhorse is in clear and open denial of the scripture and the facts and he still refuses to accept, admit and acknowledge that he never was a skeptic about Jesus' resurrection.

 

Thanks,

 

BAA.

[directionless]

I am just starting to check those links, but as I was watching Orbit's link I realized that "belief" actually has at least three noun meanings.

 

For example, I could ask "do you have belief that I have enough belief in the belief of Christianity to go to heaven?"

 

Each of those noun forms of belief means something different:

- first instance means 100% confidence as in a binary choice between belief/disbelief

- second instance means a measure of confidence from 0% to 100%

- third instance means a statement like "the moon is made of cheese"

 

So to say "atheism is not a belief" can mean different things. I need to finish watching that video and reading some links to understand exactly what atheists mean, but maybe that is part my confusion.

 

Also, the video mentioned that many people want to label atheism as a belief to bring it down to the level of unprovable theistic beliefs. That is not what I am trying to do.

 

What I'm trying to do is to use the abstractions from decision theory to clarify my understanding of skepticism, default beliefs, etc. (http://en.wikipedia.org/wiki/Decision_theory).

 

Another problem I would like to point out is that theism is very difficult to define because deity is very difficult to define. Orbit's link mentioned that issue as justification for a loose definition of atheism. I would say the whole concept of atheism is worthless. Something like metaphysical naturalism would be a more useful label (http://en.wikipedia.org/wiki/Metaphysical_naturalism)

 

I'm taking a break, but I hope to finish reading those links this evening. Maybe they will clear up some of these new issues.

[Ravenstar]

" You say that shape shifting reptilian overlords are secretly running the affairs of people on Earth"

 

What! Wait!?  They aren't?!!!

 

 

[♦ ficino ♦]

 

4.  

After Jesus ascended into heaven no other Christian (except perhaps Paul) has had the opportunity to be skeptical as Thomas was, when it comes to deciding to believe in Jesus' resurrection.  Without Jesus being physically present so that his wounds can be seen, every Christian in the last 2,000 years has had no choice but to accept the resurrection of Jesus by faith.  No skeptical examination of any concrete evidence for his resurrection has been possible - because none is available. 

 

 

For what it's worth, various Catholic saints have claimed to have had direct contact with Jesus' wounds in visions or other sorts of experiences - or this was claimed of them.  I don't know whether that matters for the above discussion.

[bornagainathiest]

 

 

4.  

After Jesus ascended into heaven no other Christian (except perhaps Paul) has had the opportunity to be skeptical as Thomas was, when it comes to deciding to believe in Jesus' resurrection.  Without Jesus being physically present so that his wounds can be seen, every Christian in the last 2,000 years has had no choice but to accept the resurrection of Jesus by faith.  No skeptical examination of any concrete evidence for his resurrection has been possible - because none is available. 

 

 

For what it's worth, various Catholic saints have claimed to have had direct contact with Jesus' wounds in visions or other sorts of experiences - or this was claimed of them.  I don't know whether that matters for the above discussion.

 

 

Inadmissible, Ficino.

 

Their reports do not constitute first-hand concrete evidence.  

They ask us to accept by faith, that their experiences are of the same order as Thomas'.  But these reports are of exactly the same order as Peter and John's second-hand reports of the risen Jesus to Thomas, before Christ appeared to him in the flesh.

 

That's they key difference here, F.  

(Ok, I know you know this... I'm just explaining for Directionless' sake.)  Only an actual physical meeting with and examination of the wounds the risen Jesus constitutes first-hand concrete evidence.  That is the one and only standard that is acceptable to a skeptic.  And that is why every Christian who has not done exactly what Thomas did is not a skeptic.  Instead, what every Christian (bar a few) has done is to accept Jesus' resurrection by faith - not evidence.

 

That's not skepticism.  That's not being skeptical.  That's not thinking skeptically.

 

Thanks,

 

BAA

[bornagainathiest]

I am just starting to check those links, but as I was watching Orbit's link I realized that "belief" actually has at least three noun meanings.

 

For example, I could ask "do you have belief that I have enough belief in the belief of Christianity to go to heaven?"

 

Each of those noun forms of belief means something different:

- first instance means 100% confidence as in a binary choice between belief/disbelief

- second instance means a measure of confidence from 0% to 100%

- third instance means a statement like "the moon is made of cheese"

 

So to say "atheism is not a belief" can mean different things. I need to finish watching that video and reading some links to understand exactly what atheists mean, but maybe that is part my confusion.

 

Also, the video mentioned that many people want to label atheism as a belief to bring it down to the level of unprovable theistic beliefs. That is not what I am trying to do.

 

What I'm trying to do is to use the abstractions from decision theory to clarify my understanding of skepticism, default beliefs, etc. (http://en.wikipedia.org/wiki/Decision_theory).

 

Another problem I would like to point out is that theism is very difficult to define because deity is very difficult to define. Orbit's link mentioned that issue as justification for a loose definition of atheism. I would say the whole concept of atheism is worthless. Something like metaphysical naturalism would be a more useful label (http://en.wikipedia.org/wiki/Metaphysical_naturalism)

 

I'm taking a break, but I hope to finish reading those links this evening. Maybe they will clear up some of these new issues.

 

Take your time, Directionless.

 

We will be here to help if you need it.  

 

Thanks,

 

BAA

[sdelsolray]

 

 

 

4.  

After Jesus ascended into heaven no other Christian (except perhaps Paul) has had the opportunity to be skeptical as Thomas was, when it comes to deciding to believe in Jesus' resurrection.  Without Jesus being physically present so that his wounds can be seen, every Christian in the last 2,000 years has had no choice but to accept the resurrection of Jesus by faith.  No skeptical examination of any concrete evidence for his resurrection has been possible - because none is available. 

 

 

For what it's worth, various Catholic saints have claimed to have had direct contact with Jesus' wounds in visions or other sorts of experiences - or this was claimed of them.  I don't know whether that matters for the above discussion.

 

 

Inadmissible, Ficino.

 

Their reports do not constitute first-hand concrete evidence.  

They ask us to accept by faith, that their experiences are of the same order as Thomas'.  But these reports are of exactly the same order as Peter and John's second-hand reports of the risen Jesus to Thomas, before Christ appeared to him in the flesh.

 

That's they key difference here, F.  

(Ok, I know you know this... I'm just explaining for Directionless' sake.)  Only an actual physical meeting with and examination of the wounds the risen Jesus constitutes first-hand concrete evidence.  That is the one and only standard that is acceptable to a skeptic.  And that is why every Christian who has not done exactly what Thomas did is not a skeptic.  Instead, what every Christian (bar a few) has done is to accept Jesus' resurrection by faith - not evidence.

 

That's not skepticism.  That's not being skeptical.  That's not thinking skeptically.

 

Thanks,

 

BAA

 

Well, they are first-hand reports to themselves, and to them, apparently, their own "visions" act as concrete evidence, again to them.  Nevermind that their version of "concrete evidence" cannot be repeated, demonstrated to others or experienced by others.  Of course, these folks who have personal "visions" or "spiritual experiences" could simply be lying through their teeth, confused, mistaken or otherwise duped by their own confirmation biases.

 

I can think of a factual scenario that could even fool a skeptic, as fanciful as it might be:

 

Jesus had an identical twin brother, Harry, who looked just like Jesus (hair length, beard, clothing, everything).  Jesus was crucified on the cross with holes in his hand and feet.  He died.  Later, in an effort to play a practical joke, or seek money from chumps, or [fill in the blank], Harry shows up with holes in his hands and feet claiming to be his brother Jesus and claiming he has risen from the dead.  Skeptical Thomas, seeing this display, changes his mind and believes based on his perception of "concrete evidence", even though that evidence is false.  Of course, those in on the joke/con job do not change their beliefs because they know the evidence is false.

 

Accordingly, "concrete evidence", as interpreted by certain observers, can be misleading.

 

 

[Vigile]

"Well, they are first-hand reports to themselves, and to them"

 

By their own admission they didn't experience, they merely had a vision. Sheer faith is required to believe the vision divine and not just a medical or psychological issue.

[sdelsolray]

"Well, they are first-hand reports to themselves, and to them"

 

By their own admission they didn't experience, they merely had a vision. Sheer faith is required to believe the vision divine and not just a medical or psychological issue.

Agreed.  But mv point was they they believed their "vision" was concrete evidence, or, alternatively, they were mistaken, deluded or they were lying about it.

[♦ ficino ♦]

After I threw in my remark about stories of saints who encountered Jesus' wounds directly (St. Francis of Assisi, St. Theresa Neumann, et al.), it occurred to me that a difference is probably the lack of intersubjective verification in their cases.  The Gospel of John portrays the Thomas story as occurring in a crowd, so many could see Thomas touching Jesus' wounds.  St. Francis displayed the stigmata on his own body, but as far as I know, there were not witnesses who perceived Jesus' wounds simultaneously with Francis' perception of those wounds.  His visions were private, though people said they observed Francis' own body bleed in the five places.

 

------ Oh, sorry, Sdelsolray, you already made this point.

[directionless]

Directionless--this might help you see what we are saying: 

O.k. I watched the video.

 

good points:

- the definition of agnostic was interesting and accurate.

- the example of varying types of disbelief depending on the type of theism

 

bad points:

- The video begins by emphasizing that people can have varying degrees of confidence in a claim, therefore categorizing into true/false, belief/disbelief, etc. is not helpful. But later in the video they fall into the very same black and white thinking. IMO, it is much better to use probabilities. A strong atheist might give 0% to a particular theistic claim. A soft atheist might give 5%. A soft theist might give 80%. A strong theist might give 100%. Where do we draw the line between the soft atheist and the soft theist so that we can divide the world into atheist or theist? It is much better to use probabilities to reflect the varying degrees of confidence and avoid black and white category of atheist vs. theist.

- The default position seemed bogus to me. We can define the claim to be "there are no gods" (strong atheism) and lump the soft atheists, soft theists, and hard theists together into an opposing camp. Then we can say the default position is "lack of belief in strong atheism" and demand evidence from strong atheists. IMO, it is much better to say there is no objective default position.

 

So IMO skepticism is not sitting stubbornly in some mythical default position until evidence moves you to some other position. Skepticism is questioning and researching all possibilities without bias to refine the probabilities you assign them.

 

Finally these claims must have implications for decision making. There is no point in assigning a probability to Russel's Teapot, because that doesn't affect our decision making on anything that I can imagine. I think of the epistle of James where the author says that faith without works is meaningless. Claims that don't affect decision making are meaningless. We need to start from the decision making and then it will all become clearer IMO.

 

I think many of the arguments would be unnecessary if everybody could speak the same language.

[ExCBooster]

There's really two parts here, to my thinking: one part is to do with beliefs, claims, contradictory claims, and evidence. The second, is to do with logic, and how to distinguish contradictory claims.

 

As for the first, people are acculturated into a variety of beliefs, including religious ones. These are beliefs held without logical cause. It may not be valid or true, but they believe it. In a different time, in Europe, people believed that geese came from barnacles, or that maggots arose on their own from rotting meat, because they were acculturated - taught by their culture - to believe this. Not all of these beliefs are false, but they certainly can be. So, if you want to be able to tell true from false beliefs, you still need to test them, as we did with the geese and maggots. Dealing only with religious beliefs, it's pretty easy to observe that not everyone believes the same thing, and that this diversity comes from cultural background (CIA World Factbook online, under the "people and society" tab). Given that people generally believe what they are raised to believe, or what is common in their culture, religion is a culturally-transmitted belief. It's not logic, it's culture. The catch, of course, is that with so many contradictory religious claims, how is it possible to determine which are false, and which are true? It's not right to give unequal weight or special treatment to a belief, just because it's the one you were raised on, or acculturated to. Any monotheist, for example, is a much harder atheist than any sceptic, because, by definition, they reject, out of hand, the existence of ALL Gods but their own. This is still failing to hold one's acculturated beliefs to due scrutiny. Just because your culture taught you a belief, this doesn't make it true. If you reject, out of hand, other Gods, then why not your own God? To fail to even inquire is to give undue special treatment to a belief that could well be as false as goose barnacles.

 

The second part, then, is how to resolve this problem of contradictory beliefs, and that's where logic, and the default scepticism come in. In logic, for reasons we've already gone over, the default position IS to disbelieve any claim, until sufficient evidence and argument is produced FOR it. There's actually a LOT of things that any given person doesn't believe in, for exactly this reason. I could make some wild claim right now - that a pack of feral circus clowns held my car hostage on the way home from work (they gummed up the windshield with cream pies) and that's why I was late - and, if you DON'T default to disbelief, there's no way to dispense with ANY belief, argument, or claim, no matter how outrageous. It's one of the axioms of logic to default to disbelief, until proven true. Otherwise, there's an infinity of crazy things you have to investigate, one by one, and take seriously. On that note, why aren't you Zoroastrian, or one of the myriad other religions you could believe in, if you don't default to disbelief?

[Orbit]

 

Directionless--this might help you see what we are saying: 

O.k. I watched the video.

 

good points:

- the definition of agnostic was interesting and accurate.

- the example of varying types of disbelief depending on the type of theism

 

bad points:

- The video begins by emphasizing that people can have varying degrees of confidence in a claim, therefore categorizing into true/false, belief/disbelief, etc. is not helpful. But later in the video they fall into the very same black and white thinking. It is much better to use probabilities. A strong atheist might give 0% to a particular theistic claim. A soft atheist might give 5%. A soft theist might give 80%. A strong theist might give 100%. Where do we draw the line between the soft atheist and the soft theist so that we can divide the world into atheist or theist? It is much better to use probabilities to reflect the varying degrees of confidence and artificiality of atheist vs. theist

- The default position seemed bogus to me. We can define the claim to be "there are no gods" (strong atheism) and lump the soft atheists, soft theists, and hard theists together into an opposing camp. Then we can say the default position is unbelief in strong atheism and demand evidence from strong atheists. It is much better to say there is no objective default position.

 

So IMO skepticism is not sitting in some mythical default position until evidence moves you to some other position. Skepticism is questioning and researching all possibilities without bias to refine the probabilities you assign them.

 

The reason we make the distinction is because there is a difference between being sure there is no God (anti-theist

), and simply not having a belief in a god (atheist) because claims are unproven. But the main point is the definition of atheist is lack of belief.

[directionless]

Thanks for giving value to our input, Directionless.  

 

The link I provided leads to the thread, "Thomas the Skeptic - Something for Ironhorse".  Just about everything in that thread can be boiled down to these essential points.

 

1.  Thomas was skeptical (did not believe) that Jesus had risen from the dead.

 

2.  He would not take this on faith from the other disciples and followers of Jesus.

 

3.  He only believed when the concrete physical evidence (Jesus' wounds) were presented to him for him to examine.

 

4.  

After Jesus ascended into heaven no other Christian (except perhaps Paul) has had the opportunity to be skeptical as Thomas was, when it comes to deciding to believe in Jesus' resurrection.  Without Jesus being physically present so that his wounds can be seen, every Christian in the last 2,000 years has had no choice but to accept the resurrection of Jesus by faith.  No skeptical examination of any concrete evidence for his resurrection has been possible - because none is available. 

 

5.  

The written testimonies of eye-witnesses to his resurrection, as recorded in the Bible, are no better than the spoken words of Peter and John the other disciples, when they tried to persuade Thomas that Jesus had risen from the dead.  (See # 2, above.) Such evidence is not concrete evidence that can be examined first-hand.  It could not be accepted by a skeptics like Thomas then and it cannot be accepted by skeptics like us, now.  Such evidence is second-hand and can only be accepted by faith - which is the opposite of skepticism.

 

6. This is why no Christian since Biblical times has ever made a truly skeptical examination of the first-hand evidence for Jesus' resurrection. 

 

7.  So when Ironhorse claims to be both a skeptic and a believer, he of course, wrong.  He was never able to make a skeptical, evidence-based decision about Jesus' resurrection.  He simply accepted the scriptural claim that it did happen, purely on faith.  As we Ex-Christians all did.

 

8.  Therefore Directionless, Ironhorse is in clear and open denial of the scripture and the facts and he still refuses to accept, admit and acknowledge that he never was a skeptic about Jesus' resurrection.

 

Thanks,

 

BAA.

I agree that Thomas had better evidence for his belief than any later Christians (that I can think of) if we believe the gospel. Also the gospel portrays multiple witnesses, so hallucination is less likely.

 

I don't see it as black or white, skeptic or non-skeptic though. For example, maybe Thomas was fooled by a reptilian shape shifter, so his skepticism was inferior to IH who miraculously discussed theology over a cup of coffee with Jesus. Maybe IH has witnesses who photographed Jesus through his kitchen window during the discussion.

[directionless]

There's really two parts here, to my thinking: one part is to do with beliefs, claims, contradictory claims, and evidence. The second, is to do with logic, and how to distinguish contradictory claims.

 

As for the first, people are acculturated into a variety of beliefs, including religious ones. These are beliefs held without logical cause. It may not be valid or true, but they believe it. In a different time, in Europe, people believed that geese came from barnacles, or that maggots arose on their own from rotting meat, because they were acculturated - taught by their culture - to believe this. Not all of these beliefs are false, but they certainly can be. So, if you want to be able to tell true from false beliefs, you still need to test them, as we did with the geese and maggots. Dealing only with religious beliefs, it's pretty easy to observe that not everyone believes the same thing, and that this diversity comes from cultural background (CIA World Factbook online, under the "people and society" tab). Given that people generally believe what they are raised to believe, or what is common in their culture, religion is a culturally-transmitted belief. It's not logic, it's culture. The catch, of course, is that with so many contradictory religious claims, how is it possible to determine which are false, and which are true? It's not right to give unequal weight or special treatment to a belief, just because it's the one you were raised on, or acculturated to. Any monotheist, for example, is a much harder atheist than any sceptic, because, by definition, they reject, out of hand, the existence of ALL Gods but their own. This is still failing to hold one's acculturated beliefs to due scrutiny. Just because your culture taught you a belief, this doesn't make it true. If you reject, out of hand, other Gods, then why not your own God? To fail to even inquire is to give undue special treatment to a belief that could well be as false as goose barnacles.

 

The second part, then, is how to resolve this problem of contradictory beliefs, and that's where logic, and the default scepticism come in. In logic, for reasons we've already gone over, the default position IS to disbelieve any claim, until sufficient evidence and argument is produced FOR it. There's actually a LOT of things that any given person doesn't believe in, for exactly this reason. I could make some wild claim right now - that a pack of feral circus clowns held my car hostage on the way home from work (they gummed up the windshield with cream pies) and that's why I was late - and, if you DON'T default to disbelief, there's no way to dispense with ANY belief, argument, or claim, no matter how outrageous. It's one of the axioms of logic to default to disbelief, until proven true. Otherwise, there's an infinity of crazy things you have to investigate, one by one, and take seriously. On that note, why aren't you Zoroastrian, or one of the myriad other religions you could believe in, if you don't default to disbelief?

Why are the feral circus clowns a wild claim? Why is the default to disbelieve your claim until you give evidence?

What if I my claim is "your claim about circus clowns is false"? Do I need to give evidence for my claim or is the default to believe my claim and disbelieve yours?

 

What is a default claim, a reasonable claim, and a wild claim? The only way I know to define those is relative to each person's current understanding. A person who currently believes the world is flat would need evidence to believe the world is round because that might seem wild.

[Vigile]

 

A strong atheist might give 0% to a particular theistic claim. A soft atheist might give 5%. A soft theist might give 80%. A strong theist might give 100%. Where do we draw the line between the soft atheist and the soft theist so that we can divide the world into atheist or theist?

 

There's no need to assign probabilities here.  What could they possibly be based on outside of faith (which is nonsense)?  I'm a soft atheist because there is 0% proof or even indication there is a god by any definition I've encountered.  I highly doubt there is any chance (0 probability) there is a god by definition offered up by people who make the claim.

 

I'm not a hard atheist because in my mind it's silly to make a claim without evidence (absence of evidence is not evidence of absence). 

 

I'm not anywhere near a soft theist because I think it's silly to suppose god/s with absolutely no evidence.

 

The line, as you can see is quite easy to draw.  Math is getting in your way here as it's the wrong tool. 

 

Binary rules sometimes do apply in the real world.