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Pascal Galileo Cantor Monty Hall Liz Jackson Cosmic Skeptic and the Cast of Seinfeld Walk into a Bar

01 Thursday Apr 2021

Posted by Joe in Uncategorized

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epistimology, infinity, Pascal, philosophy

I am glad to find a new face in philosophy that likes to discuss Pascal’s wager and epistemology generally.   That she earned a doctorate from Notre Dame also makes me smile.  One of the papers that she published deals with an issue involving infinity and Pascal’s wager.  https://www.academia.edu/16612267/Salvaging_Pascals_Wager

She explains an issue by way of an analogy that is pretty helpful to understand it.  She says consider you are in a game show and if you choose door number 1 you have a 1% chance of getting an infinitely good reward.  If you choose door number 2 you have a 99% chance of getting the exact same infinitely good thing.  It would seem irrational to pick door number 1.  Since decision theory tends to favor the options that give us the highest chance of a good outcome.   

But infinities are crazy things.  And as it turns out the mathematicians can only really say that both options would be infinitely valuable because infinity multiplied by any positive number (even a small fraction) is infinity.   Well ok.  But we really should think about this a bit deeper to at least try to at understand where the mathematicians might be coming from and if this really makes sense.       And by “try to understand” I mean I am making absolutely no promises. 

First decision theory.  It is fairly straight forward.  For any given outcome for an option you multiply the potential gain by the chance of getting that gain for all the outcomes and then add them up.  This gives you the utility value of that option.  So if a ticket has a 30% chance of winning $100 dollars then we say the utility value of the ticket is $30. 

Ok now to infinity and beyond! But first infinity. 

Gregor Cantor has devised some proofs that suggest certain infinities that might seem bigger are the same size but also that some infinities seem to have “more” than others.    

 He had an ingenious proof that the shorter line segment has as many points as a longer line segment and indeed any line.  The trick is to simply bend the smaller line segment into a “c” and then for any sized line position it along the back of the c.  You can draw a line from any imagined point in the middle of the space of the c (which is just the shorter line bent) to the longer line.  That line will cross the “c” in a unique point for every unique point on the longer line. 

See the drawing I scribbled out below:

One of my undergrad philosophy papers actually showed how Galileo did something similar when he explained how a ball rolling down an inclined plane reached every speed of the ball falling straight down.  Anyway the concept is the same as Cantors.  Galileo just took the longer line and tilted it so that you could then draw a perpendicular line from the line showing the height of the ball with the inclined plane.   See the drawing I scribbled out above. 

This can also form various Zeno’s paradoxes.    How could the ball going straight down reach every speed of the ball going down the inclined plane?  If the ball is crossing more points along the longer inclined plane and at every point it is hitting a new speed wouldn’t this mean it must be hitting a more speeds?  And if it is hitting a new speed every increment of time and is rolling for longer wouldn’t it have hit more speeds than the ball that is falling for a shorter time?  Etc.  

The infinite is fun and frustrating at the same time.  I recommend AW Moore’s book “The Infinite” if you want to learn a bit more about how puzzling the infinite can be.   

Cantor also showed all counting numbers seem to be just as numerous as all even counting numbers.  How?  Well you can draw a correspondence to each counting number with an even number. The even number 2 corresponds with 1 and the even number 4 corresponds with 2 the even number 6 corresponds with 3 and on and on.  You can see there will always be even numbers to correspond with each counting number.  The same is true if we take numbers divisible by 100.  100 corresponds with 1 200 corresponds with 2 etc.    So it seems that half (or even one hundredth) of infinity is still infinity of the same amount as all the counting numbers! 

So the line proof shows that you can keep adding line segments which all have an infinite number of points but doing so will not actually increase the number of points. Comparing and drawing a correspondence to each even number with each counting number shows that halving or taking any other fraction of an infinite set of numbers will not actually decrease the infinity either. These concepts explain why multiplying infinity by any positive number does not actually yield a bigger number/infinity (and if the positive number is a fraction it won’t yield a smaller number/infinity). Thus as we see why the utility value of Homer Simpson’s God is no lower than the Christian God even if we admit it is less likely.

Not all infinities are equal though. He argued there are more real numbers than counting numbers. 

https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

Ok back to Pascal’s wager.  This notion that no matter how small the percentage chance of achieving the infinite is, it still yields infinite rewards seems to help Pascals Wager because it doesn’t matter how low you put the probability of God existing it will still be the winning choice.  But it also hurts because if there is even any chance that Homer Simpson’s God reigns then that small chance would also yield an infinite utility value.   And these utility values seem to be the same as per the above proof.    So if the “Homer Simpson God” that just gets more and more angry every time we go to Christian church because we are doing it wrong, has any positive chance of being the true state of affairs well that small chance multiplied by infinity equals infinity as well.

So even if we think the Homer Simpson God is less probable that doesn’t matter because the utility values end up the same.  Should this convince us that choosing the door that gives a 1 percent chance of eternal reward is just as rational as choosing the door that gives a 99 percent chance of the same reward?  I have a few concerns.  One is just how challenging any discussion of infinities can be for mere mortals.     So how sure are the mathematicians of every step here? I think I understand and agree with them on the math but still.

Studies show we react more to empathic suffering than to joy so I think it is worth asking a question of mathematicians who deal in this area.  If you choose option one you have a 1 percent chance of you and everyone you love suffering for an infinite amount of time but if you choose option 2 you have a 99 percent chance of you and everyone you love getting the same amount of infinite suffering.  How many do you think would really say its fine to flip a coin and choose either option?   

The infinite seems to be playing the same role when it hurts and it helps Pascal.  But I think there is a difference.  If for the sake of argument we assume Homer Simpson’s God is less probable than the Christian God it seems we need to take a few more steps of analysis to say it would be irrational to prefer one option over another.  I think those steps are much more controversial than the steps Pascal takes in saying a shot at infinite value will always exceed a shot a finite value. That is, the reasoning about the infinite that helps pascal seems much less controversial.  

First consider what helps Pascal. Why would we think an shot at infinite gain is always better than a shot at finite gain?  If you are better off suffering for a single day rather than two days and better two days then suffer for three etc. it seems infinite would be worse than any finite amount of time.  I mean on what day would I say ok keep the tooth ache going I am unwilling to pay any price to prevent the pain?  It would seem that we always want suffering to end and so the infinite suffering is worse.  We would all think yes we would prefer our suffering to end rather than continue and thus there is always some cost we would pay to end it for any given day.  Whatever finite cost we would pay to end it could thus be multiplied every day of eternity that we feel the pain and would add up to infinity.  How long are you going to pay for pills that help ease your pain?  As long as the pain lasts.  Therefore if it lasts infinitely long we would pay and infinite amount.  That is the analysis that works *for* Pascal’s argument and that seems to be consistent with everything we know about the world.  That seems the sort of intuition supported by math that I am comfortable betting on.

But the analysis that works against him is this notion that it doesn’t matter which door you would pick between the 1 percent or the 99 percent chance.     I don’t think it is irrational for me to say I think that is really a different case.    I’m not so sure anyone really has enough of a handle on the infinite to tell me that choosing either option or even flipping a coin is just as rational.   But let’s at least try to chart out why that might be.   

In a discussion with Dr. Jackson Cosmic Skeptic says it is like monty hall problem in that math shows our Intuitions are wrong.  

I think the Monty Hall problem can be enlightening here but I think it helps Dr. Jackson’s/Pascal’s case.    

The Monty Hall problem involves a scenario where someone is given 3 options/doors to choose from.  Behind one of the doors is a car and there is a goat behind each of the other 2 doors.  Now you want the car because it is more valuable than the goat.   You get to pick a door and let’s say you pick door number 3.  Now before that door is opened Monty Hall says “look I will open up door number 1” and he does and shows you it has a goat.  Now he asks if you want to change your choice.  You can now choose door number 2 instead of number 3.  Should you?  Yes.  It may seem counter-intuitive but you will have substantially better chances of getting the car if you choose door 2. 

How do we know this?  Well there are actually 2 ways.  The first is just to test it repeatedly through computer simulation or otherwise. 

The second way is to think it through further.  Consider that instead of three doors there are 1000 doors.  And you pick door number 58.  And then Monty Hall opens all the other doors except the door 58 (the one you originally chose) and door number 678.   Now are you going to change your vote?  Of course.  So we know not to trust our intuitions in the monty hall problem  due to testing and thinking it through more. This way of understanding the Monty Hall problem comes courtesy of Brian Blaise.

But perhaps most importantly I can understand how the testing and the conceptualizing are done to solve the monty hall problem.  If I just took someone’s word for it I might reasonably still have doubts.   

What about my certainty that picking option 1 where I have a 1 percent chance of getting an infinite reward is the same as option 2 where I have a 99 chance of getting the same infinite reward.   First can I conceptualize why my intuition to choose the 99% chance is equal to the 1 percent chance?  Not really.   In fact quite the opposite.    

It seems to me that there is a problem with how the “utility value” is being used here.  I understand that as soon as one person (call him “that guy”) who chooses the one percent option gets the infinite reward that whole column equals the 99% column.  After all even if 99 times that number get the same infinite reward it is just like adding line segments to the number of points on the longer line as compared with the shorter line.  Or it can be seen as taking every 100th number and matching it with the counting numbers.  I’m not disputing the math. 

But there still is this nagging concern about me having a much lower chance of being “that guy” that wins the infinite reward with the 1% chance and evens out the tables.  I don’t think the standard decision analysis deals with this concern to my satisfaction. 

See the thing is when we say the “utility value” of ticket that has a 30% chance of winning $100 is $30 that does not mean everyone gets $30.  On average about 70 people out of 100 will get nothing while the other 30 out of one hundred will get $100.   The same is true for this.  99% of the people will get nothing while one percent will get infinite rewards.  The utility value may end up equaling the other option where 99% get infinite rewards and 1 percent get nothing,  but I still want to be someone that gets the winnings.      

So as I try to conceptualize it I still think it is rational to want the 99% option.  I don’t think I am denying any math in saying so.    And I do think it would be irrational to choose the 1% route.  

I remember reading “the kluge.”  It is a fine book but I took issue with one thing the author said.  He said something like people would be irrational if they didn’t always follow this line of thinking:  If you could buy a lottery ticket for one dollar and that gave you Y% chance to win a lottery you should pay the same amount for a lottery ticket that gives you 1/50 Y%  chance to win 50 times that.  But I am not so sure I agree.  I think I would rationally prefer to pay 1 dollar for a lottery ticket that gave me 50 times the chance to win 1 billion dollars instead of 1 dollar for a ticket that gave me 1/50 the chance to win $50 billion.  I mean even if I could figure out what to do with the first $100 million I am not sure what I would do with the other $900 million for a billion dollar prize.  Let alone the other 49 billion.  How much lobster can I eat?   Now here my issue is that I value the first dollar more than the 1 billionth.  So it is not the same exactly.  But I do think it is similar.  I think utility value is a tool but the results can rationally be used differently by different people. 

Now what about testing this Dr. Jackson theory?  Perhaps we can!  Notice when we test the Monty Hall problem we don’t actually need to deliver goats and cars.  We run a computer simulation and just count how many would get the cars versus goats depending on their choice.  Since we don’t need the actual infinite prize perhaps this is as easy running the simulation.  And guess what we would find?   Those choosing the 99% chance have a much higher chance of winning the infinite reward than those choosing the one percent chance.  And I suspect that is pretty much all there is to it.  The fact that the prize for the population on the whole choosing the 1% option equals the prize on the whole for those choosing the 99% option doesn’t change the fact that only 1% will get the infinite prize in the 1% option and I like the 99% odds more.  

So imagine we are given Jackson’s choice.  And huge numbers of people choose option 2 and are happy with their infinite gift but of course 99% isn’t 100 percent so some don’t get the infinite reward.  But then people start to realize that it seems that more than 1 percent didn’t get the infinite reward!  I think most people would be like huh what do you mean?  Do you mean people chose option one with only the one percent chance?  Or people chose to flip a coin?  I suspect not many people who chose that option would raise their hand and say yep I chose option one. 

On the other hand if somehow I got this wrong and both options are the same somehow.  I have to admit those who chose option one would get infinity plus an envious amount of smugness. 

My own view as of now is that the aspect of infinity that helps Pascal (the notion that we would always pay a finite amount to end suffering or experience joy and that price would be infinite if we are dealing with an infinite suffering or joy) seems consistent with everything I know about the world.  But the view that choosing the 1 percent door or the 99 percent door are the same, seems contrary to what I know. 

This title had some mention of a bar and a cast of characters.  I talked about Galileo Cantor Pascal Monty Hall, Dr. Jackson and Cosmic Skeptic but what about the Seinfeld cast?  Well Ok when I was thinking about this last night I imagined the following scene. 

Monty Hall has this big game where you can win an infinite checking account!   Don’t worry both top republicans and democrats assured him everything would be fine and they could just keep printing the money.  So he decides to make a huge number of roulette wheels with 1000 numbered slots.  And people can choose any number between 1 and 1000.  And you have an option.   Option 1:  If the roulette ball lands on the number you pick you win but if it lands on any other number they lose (99.9% chance of losing) or they can choose option 2: if the roulette wheel lands on the number they pick they lose but if it lands on any other number they win (99.9% chance of winning).    

Everyone can play once and all the wheels are spun in the morning.  That night the bars are packed.  Huge numbers of people are celebrating their winnings!  But of course some people are going to lose so they are hitting the bar too.  But rumors start to spread that considerably more than 1 in one thousand people lost!  Hmm.  So yeah I am bussing tables because even though I picked option 2  (the 99.9% winning chance) I sometimes think I have one thousand times the bad luck of others so for once the roulette wheel landed on my number. 

But then I see George Costanza arguing with Seinfeld and Elaine.  I see Seinfeld looking at a very discouraged George and saying “you did what??” in disbelief.  And Elaine looking amazed at George with her mouth gaping.    Kramer walks in with a big smile and orders a round for the whole bar.  Costanza charges at him and yells “You!! You went with the 99.9% chance didn’t you!! You were the one who convinced me it didn’t matter!”  Kramer is initially taken aback but then says “you didn’t uh I mean didnt uh I mean did you uh…”  and George busts in and says “yes yes I went with option 1!”  The bar room falls silent.  Except George keeps on.  He yells “Some friends you are! you told me it didn’t matter!  *I* tried to say option two was clearly better but *you* guys just kept on saying it didn’t matter didn’t you?  Didn’t you!?”

Seinfeld Elaine and Kramer all look a bit sheepish but then Seinfeld says “yeah but we also said it was CRAZY. How could we know you would actually pick the crazy option?”  George then says “alright so you admit it was your fault!   So just buy me anything I want.”  After a pause “Come on you owe me that and you can certainly afford it.”  Seinfeld says “Well, you know, we signed an agreement not to just give money away since if everyone did that there would be no workers, you know, no one to make the cocktails.  I can’t break the agreement, they might take my infinity check book away.”  Kramer and Elaine seem to agree. 

Meanwhile I see Cosmic Skeptic bartending.  I was giving him a hard time because he chose to flip a coin and the flip landed on option one for him.   But for what he lacks in wisdom he tends to make up for in being quick witted.  So he sees Cantor getting sloshed in the corner with a nearly empty glass.  Of course, Cantor chose option two and won but his troubles aren’t always solved with money.  Cosmic Skeptic asks Cantor if he wants another drink and Cantor says yes.  So CS says “well you were the one who said even numbers are equal to the counting numbers.”  Cantor slurs “well actually I *proved* it.”   CS says “Yeah right, then you wouldn’t mind giving me a tip of ½ of your infinite checking account.   After all the rules say you can’t give the money away but this would be a tip.”  Cantor immediately smiles and agrees saying “sure just don’t tell anyone – you know someone has to make the cocktails.”  And sure enough CS ends up with just as much money as anyone else. 

A Problem with the Reliability of Moral Beliefs

24 Monday Feb 2014

Posted by Joe in Uncategorized

≈ 29 Comments

Tags

Atheism, EAAN, epistimology, evolution, Joyce, Linville, moral argument, morals, philosophy, religion, Street

Compared to some of my earlier blogs this one will presume quite a bit of philosophical understanding.  Even then since I am introducing a slightly new idea it will still be slow going.  But I am happy to answer questions anyone may have in understanding.  Also any editing advice is always appreciated.

Earlier I have referenced Richard Joyce, Sharon Street and Mark Linville as philosophers who have published arguments that if evolution (and naturalism) are true then any beliefs we have about real morality would be unreliable.

Here are some of their articles on the issue:

Sharon Street’s verision

A version by Richard Joyce

Here some of his other papers – many of which address this argument.

Linville gives much more than just the epistemic argument he also covers allot more ground.

This blog will attempt to advance that argument in light of a common objection.

By the way this argument not only tends to show why natural selection will not hone in on moral truths but also why science will have its efficacy limited as well.  Specifically it will explain why science can’t identify the actual rightness or wrongness.  After we determine what we deem right and wrong science will of course be very helpful in promoting or determining whether a set of facts fits that description.  But there will always remain a critical part of the analysis that science cannot help.

One of the common responses to the argument given by Joyce, Street, and Linnville is given in this blog (here he is responding to Street):

http://www.partiallyexaminedlife.com/2013/01/29/an-objection-to-sharon-streets-darwinian-dilemma/

In the end that author thinks there are 2 ways the naturalist can save moral beliefs he says:

“This is not to say that natural selection does not pose a challenge to moral realism. Street’s coincidence objection will kick in again unless the moral realist can either a) show there are at least some evaluative judgments which are not simply the result of more basic evaluative tendencies that have been shaped by evolutionary pressures (or better, are inconsistent with an evaluative judgment under reflective equilibrium that takes into account all tendencies but falls short by virtue of some form of moral reasoning that only the realist can supply); or b) show why tendencies that are clearly the result of evolutionary pressures so neatly line up with the results of a capacity for evaluative judgment that is supposed to be unrelated to such tendencies (what Street calls “tracking”). For (a) to be the true, it cannot be the case that our system of values cannot be as thoroughly “saturated” with the influence of natural selection as Street thinks it is. One option for (b) is to argue that adaptiveness and what is “good” are systematically related in such a way that selective pressures will tend to produce a tendency to true evaluative judgments. After all, what is adaptive is arguably a species of the good (although it’s possible that this line of thought leads us back to a constructivist account by relativizing the good to the constitutions or organisms).”

I personally do not think A accomplishes anything, but I won’t address that here.   In this paper I argue that approach B is necessarily doomed to failure.   Evolution, and incidentally science, cannot possibly track the truth of ultimate questions of real morality.

I’ll just throw a form of the argument on the table and then I will talk more about what it means:

P1)      The process of natural selection (and science) is blind (insensitive) to concepts/truths/facts that never have material or empirical manifestations or indicia.

P2)      Moral evil is a fact/concept/truth that has no material or empirical manifestations or indicia.

C1)      Therefore the process of natural selection (and science btw) is blind (insensitive) to moral evil.

First I will talk a bit about what I mean by these terms and where the argument is aimed, and then I will address the likelihood of these premises being true.

By “blind” or “insensitive” I mean the processes do not track the truth of the concept.  There can be no cause and effect relationship between that truth and the process of evolution (or science).

“Moral Evil” could be substituted for “moral wrongness” “moral goodness” “moral truths”.   Although the term “moral facts” is used by most philosophers in this area, it is to my mind, a poor word choice.    I think “wrongness” helps us focus in on what I am talking about better than the alternatives.  I use that term a bit and by wrongness I mean moral wrongness.

Let me explain more about what I mean by “material or empirical  manifestations or indicia”  Those who argue for the reliability of moral beliefs often make the very general claim roughly along the lines of:

Mechanisms that tend to produce true beliefs will generally be more adaptive than those producing false ones.   Therefore the mechanism(s) that produces our moral beliefs, likely tends to produce true beliefs.

The attempt is to sort of shift the burden to those who claim moral beliefs are an exception to the rule.  The validity of this move is suspect but my argument, more or less, accepts the challenge.    What is it about moral beliefs that would exempt it from the reliability we afford other forms of knowledge?

My position is that in every moral analysis there is going to be a critical determination, the truth of which has no material or empirical component.   Without such a component natural selection (and science) will be blind and insensitive to it, and therefore can’t possibly track it.

Let me give an example to help illustrate what I mean by material manifestation of wrongness.  Let’s say Leslie complained that her roommate Sophia used sticky traps to catch a mouse.   She thought this was not morally acceptable because sticky traps, unlike other traps, left the mouse to suffer longer.   Now let’s just assume Sophia thought her actions were morally acceptable.   Perhaps Sophia either didn’t place as much moral consequence on the mouse’s suffering or perhaps she thought the effectiveness or the inexpensiveness of the traps outweighed the suffering.  Hopefully all moral realists can agree Sophia’s use of the sticky trap was either morally acceptable or it was not.

Now it seems very clear to me that both parties can be fully informed and agree about  everything our five senses can tell us about this event and still disagree on whether it is morally acceptable.  That is Sophia can be well aware that the mouse will suffer longer. (and indeed Sophia might believe the added suffering from the sticky trap might be greater than what Leslie thinks)  Leslie can be well aware of the decrease in the efficiency, and the added cost, of other types of traps.  (and Leslie might even think sticky traps are relatively less expensive  and more efficient than Sophia thinks.)  They might both fully understand the neurology of mice and therefore understand how mice suffer in sticky traps as opposed to other traps etc.  Take any piece of information we can find out from our senses about this event and we can assume they both fully understand it and still disagree whether it was morally acceptable.   Because the actual “wrongness” of an action never has a material or empirical manifestation science will never be able to resolve this dispute.

It’s not like they can watch a recording of the events through a certain type of projector and the video will show with a red tint if Sophia was wrong and a green tint if what she did was morally acceptable.   Nor can we examine of the mouse’s liver or other organs to determine whether the killing was justified.   We can determine how it died and from there we might have certain beliefs about wrongness that lead us to believe it was killed through immoral means.  But we can’t see “the wrongness” itself.  Nor does “the wrongness” itself leave empirical indicia. [1]

I believe Sharon Street is on to something of the same point when she separates out moral beliefs from beliefs about a creatures “manifest surroundings”:

“What makes this point somewhat tricky is that on the face of it, it might seem that of course it promotes reproductive success to grasp any kind of truth over any kind of falsehood. Surely, one might think, an organism who is aware of the truth in a given area, whether evaluative or otherwise, will do better than one who isn’t. But this line of thought falls apart upon closer examination. First consider truths about a creature’s manifest surroundings—for example, that there is a fire raging in front of it, or a predator rushing toward it.  It is perfectly clear why it tends to promote reproductive success for a creature to grasp such truths: the fire might burn it to a crisp; the predator might eat it up.  But there are many other kinds of truths such that it will confer either no advantage or even a disadvantage for a given kind of creature to be able to grasp them. Take, for instance, truths about the presence or absence of electromagnetic wavelengths of the lowest frequencies. For most organisms, such truths are irrelevant to the undertakings of survival and reproduction;…”

It is my contention that moral truths never have a material manifestation and therefore evolutionary processes cannot possibly track them.

In his paper “Ethics and Observation” Gilbert Harman asked the question “you can observe someone do something but can you ever perceive the rightness or wrongness of what he does?”

I think this question is somewhat ambiguous because of the word  “perceive.”  We tend to say we “perceive” this is right or wrong but I think it’s quite clear that we don’t use any particular one of our five sense perceptions to do it.   So I think if he asked a question “you can observe someone do something but can you ever hear the rightness or wrongness of what he does?”   or “you can observe someone do something but can you ever taste the rightness or wrongness of what he does?” we could easily answer the questions in the negative.  The same would be true if he asked if we see, touch, or smell the rightness/wrongness.  We can’t do these things because there’s no “material/empirical manifestation” of rightness or wrongness. To the extent one  claims we can possibly “see” the wrongness I think he is exchanging “see” for “judge” the wrongness.  Wrongness is not a color.

Ok so at this point you might be wondering about other areas of knowledge.  How does the truth “manifest itself” in other areas of belief?

Sharon dealt with the more obvious case of evolution tracking the truth for our beliefs about our immediate material surroundings.

SCIENCE:

Dr. Harman gave a good example to illustrate the point dealing with science.   He says “let’s consider a physicist making an observation to test a scientific theory.  Seeing a vapor trail in a cloud chamber he thinks, ‘there goes a proton.’”

Well in this case, as in any case when we are trying to detect the very existence of a material thing, the truth of that material things existence will materially manifest itself in the existence of that material thing.  Here the proton itself is not observed but it’s material manifestation is observable by the vapor trail in the cloud chamber.  Thus although the proton itself may not directly manifest itself to our senses there is a material manifestation of the truth that there is a proton. One such “material manifestation/indicia” is the vapor trail.  So it would be at least possible that Natural selection could create mechanics that track the truth of protons existing.

MATH:

Next let’s look at math.  I think there is a sense that certain mathematical truths just appeared to be self-evident.  But setting aside self evidence, I think Richad Joyce and Dr. Harman also establish how mathematical truths have material manifestations.

Consider what Dr. Harman said in this regard:

“Perhaps ethics is to be compared, not with physics, but with mathematics.  Perhaps such moral principles as you want to keep your promises is confirmed or disconfirm them the same way (whatever it is) in which a mathematical principle as “5+7=12” is.   Observation does not seem to play the role and mathematics it plays in physics.  We do not and cannot perceive numbers, for example, since we cannot be in causal contact with them.  We do not even understand what it would be like to be in causal contact with the number 12, say.  Relations among numbers cannot have any more of an effect on our perceptual apparatus than moral facts can.

Observation, however is relevant to mathematics.  In explaining the observations that support a physical theory, scientists typically appeal to mathematical principles.  On the other hand, we never seem to need to appeal in this way to moral principles.  Since an observation is evidence for what best explains it, but since mathematics often figures in the explanation of scientific observations, there is indirect observational evidence for mathematics.  There does not seem to be observational evidence, even indirectly, for basic moral principles.  In explaining why certain observations have been made, we never seem to use purely moral assumptions.  In this respect then, ethics appears to differ not only from physics but also from mathematics.”

Joyce gives what I consider another example of mathematics having a material manifestation.  He states:

“Suppose you are being chased by three lions, you observe two quit the chase, and you conclude that it is now safe to slowdown.  The truth of “one plus one equals two” is a background assumption to any reasonable hypothesis of how this belief might have come to be innate.”  The Evolution of Morality Richard Joyce page 182.

Joyce’s example of running from lions demonstrates a ”material manifestation” of the mathematical truth that 3-2=1.  That mathematical truth manifests itself in that 3rd lion.   Mathematical truths would no doubt “manifest themselves” in trade as well. If you do not understand that seven is more than five when someone was, say, bartering food stuffs there would be a material manifestation in that you might lose lots of your food.

Due to these material manifestations we have reason to believe natural selection might be reliable in creating belief mechanisms regarding our manifest surroundings, science and math (logical truths have material manifestations in a similar way to math).    But moral judgments lack those material components and therefore any mechanism yielding moral truths would lack the reason we might find them reliable.

Now let me say the fact that people hold beliefs about morals often does have material manifestations  (eg., the creation of laws and posses) This is undoubtedly true. .   I don’t doubt our beliefs can have material manifestations.  They will have them whether they are true or false.  But how did those beliefs arise?  That is the question.    Since it seems clear the truth of those beliefs could not possibly be tracked by evolution then our beliefs are not reliable. (edit: I address this a bit more in my reply to Travis’s first comment on this blog.)

With that readers may have a few more questions about what I mean by “material manifestations” I would encourage people to go ahead and ask in the comment section.

At this point I would like to address whether the premises are true.

Is the first premise true?  Natural selection concerns itself with things that have physical /empirical impacts.  Only things with physical or empirical impacts, can effect whether things are killed or procreate.  I am not sure this will be much in dispute so I won’t dwell on it.   The same I think would be true with the idea that science concerns itself with empirical data.  If you can’t test it with empirical data then it’s probably not science.

I anticipate more reluctance to accept the second premise.

Moral naturalists might argue that the natural facts that they believe simply make up moral facts and they do indeed have physical and empirical manifestations and indicia.   For example facts that might make up a murder (i.e., a “wrongful” killing) might include the fact that the murderer knew firing his gun would likely kill the victim.  It would include the fact that the bullet from his gun did in fact go through the victim etc etc.  All of which could have various empirical indicia.  However we still need to make the determination that the set of facts I described belongs to the set of facts which are also moral facts.

We still need to differentiate the set of natural facts that happen also to be moral facts.  The “wrongness” made up of one set of natural facts leaves no additional physical or empirical indicia which we can see hear taste etc.   In fact the wrongness does not even exist outside the other natural properties so it couldn’t signal us to this set of facts as being ones upon which moral facts supervene.

As Street points out “The [Moral Naturalist] response, I will argue, ultimately just puts off a level the difficulties raised…..” “In trying to figure out which natural facts evaluative facts are identical with, we have no option but to rely on our existing fund of evaluative judgments…”

One person might say that the set of natural properties called set “n” equates to evil.  Another might disagree.  They might both fully acknowledge the empirical properties of the set yet still disagree on the whether the set properly has evil supervene on it.  In the end this problem is most difficult for the naturalist precisely because he argues there is no additional property of wrongness.  The wrongness is just the set of natural facts that make up the wrong action. (or sets of sets of wrong actions)  Accordingly, there can be no physical or empirical manifestation or indicia, that the wrongness leaves behind, that would help evolution select for the correct set(s) of facts that match up with moral facts.

Because moral naturalists posit no additional properties other than the natural properties that make up the set of a wrong action, there could be no additional material indicia that would result from the set of natural properties which would help natural selection distinguish the moral sets.

Again just to be clear when I talk about moral truths I mean only the wrongness or rightness of a particular action.  No doubt we have material indicia of the fact that the World Trade Center Towers were attacked.  However we have no material indicia of the very wrongness of that act.  There is no buzzing sound or red tint that we hear or see when we are witnessing an evil act.   We learn of the events and we judge them to be wrong.

What about non-naturalists?

Nevertheless some might argue that we can’t say for sure whether our moral beliefs cannot be traced to empirical evidence. (material manifestations)  They might say “Who knows? After all, a lot goes on in our brains when we see something.”   I think those who doubt the truth of premise 2 are simply misunderstanding the nature of moral truths.  I think the following thought experiment may help demonstrate this point.

Consider the possibility that they are right.  Let’s just pretend every time we perceive a wrong action the wrongness emits some, hitherto unknown, type of radiation. This radiation causes the “unease” we feel when we perceive an immoral act.  Every time we see an immoral act on television, or simply imagine one, our brain would apparently trigger the memories which bring about the same type of unease and belief again.

Okay it’s an outlandish idea but the point is not to suggest that this is plausible.  My point, is that if this were to occur it would not give additional justification to our moral beliefs.  It would just as likely debunk them.  We would just as likely understand that the reason we believe things are immoral is due to this physical trigger and not because it is really wrong.

The fact that we might reach this conclusion demonstrates that our conception of moral truth does not allow for material manifestations or indicia.  It is simply not part of the concept.   Since material manifestations and indicia are not part of moral truths, natural selection could not possibly track moral truth.


[1] I might say that evil does not occupy space or exist in any particular space.  Yes it exists when an occurrence happens but it is not a something that literally surrounds the occurrence.  It’s a property that seems to exist at no particular point of space at all.  When we consider a long embezzlement conspiracy would we think the evil was literally located all through the offices and everywhere the people perpetrating it conspired?  If they talked on the phone was evil in the phone wires?  I don’t really think so.   I’m not exactly sure if this is a proper way to express what I am saying but it might be a at least a start.

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