As I discussed in my video originally introducing Calculemus, conditionals are a problem when trying to logically represent natural language. To recap quick, let’s take a look at this silly claim:
“Chocolate is gross because it’s made of wheat.”
If we were to represent this as an argument against chocolate being delicious, we might do it as follows:
A: Chocolate is made of wheat.
B: Chocolate is not delicious
S2: A -> B
In all likelihood, we find ourselves wanting to disagree with not just one but both premises of this argument. “Firstly, chocolate is not made of wheat; and secondly, it wouldn’t matter if it was, because many delicious things are made of wheat!” However, S2 is only true when A is true and B is false (when Chocolate is delicious and made of wheat). The moment we disagree with S1 we are forced to agree to the seemingly ridiculous S2. Not a very fair representation of what we are actually thinking. The trouble is that we were imagining an indicative conditional, not a material conditional. An indicative conditional is not something that can be represented trivially in logic, because it deals with philosophical ideas about causality. Questions about cause can be difficult to answer if not entirely subjective. Did the existence of gunpowder cause the invention of guns? Does 1+1 = 2 cause 1+2 = 3? Do rivers cause disease?
Fortunately, when saying “if” in everyday life, even though we are using indicative conditionals, we’re not usually discussing such weird examples, and we find that we don’t have much trouble understanding each other. In the case of the indicative conditional “If it’s made of wheat, it’s gross!” we understand the gist of what’s being said, even if the corner-cases are still a bit fuzzy (we might not know whether the speaker means it’s impossible to make good food with wheat, or simply that most food made with wheat isn’t good; but details like that probably aren’t key to our debate, and can be clarified later if necessary).
In logic, we use logical operators as connectors to relate the meaning of sentences or literals like A and B. Those sentences can be packed with all kinds of meaning and language or culture-specific subtleties that are not part of logic. An indicative conditional has more meaning packed into it than can be practically represented by logic. So why not stuff all that fuzzy, language-y, culture-y meaning into a literal? Here’s what I mean:
A: Chocolate is made of wheat
B: Chocolate is not delicious
C: If something is made of wheat, it’s not delicious.
S3: C -> (A -> B)
C1: A -> B
Now we can agree with S1 and still disagree with S2, which clearly demonstrates what we really mean. But what’s going on in S3? Here we make a material conditional claim that should be extremely uncontroversial. We are simply saying that if the indicative conditional is true, then it’s counterpart material conditional is also true. We can’t know much about the formal implications of an indicative conditional, but I think at minimum we can know that much. And since this implication is itself a material conditional, we know there’s only one way it could be false: If (A -> B) is false and C is true. Let’s think about that.
If A -> B is false, that means B is true and A is false. That is to say:
“If something is made of wheat, it’s not delicious” – TRUE
“Chocolate is made of wheat” – TRUE
“Chocolate is not delicious” – FALSE
It’s hard to imagine when the three statements above could all have these three values in the same universe, unless someone thinks of indicative conditionals in a very very strange way.
It’s for this reason that I’ve changed my design philosophy very slightly with Calculemus. I’ve included one of those “indicative therefore material” propositions in the background everytime someone makes an argument, and every user automatically agrees with it. This allows the “literal” part of the indicative to appear in its place. In our above example, S1 and S2 would appear to comprise the argument while S3 would hide out in the background. Originally, I wanted Calculemus to be more like a logic calculator, and completely devoid of any original philosophy, no matter how unassuming. This made it very tedious to use. and the “if”s could be incredibly confusing. Instead of being such a purist, I’ve decided instead to add this one tiny scrap of assumption and make the program immensely more usable. Logical operators are gone, and valid arguments are constructed automatically from a simple list of full-sentence premises. Of course if someone thinks this is problematic, you’re always welcome to argue about that topic with me the old-fashioned way.
A response to Kuan’s 3 videos, which were a response to my last video blog post.
As my mind becomes exhausted and my thoughts succumb to chill
‘Tis not inquiry can warm me, but exacting of my will
‘Tis not noble new endeavors or improvement of the self
That I pray relax my neurons and restore my mood and health
Into long fingered gloves of lightning do my causal tendrils slip
Bullets, blades and balls of fire soon fly from each fingertip
Such godliness is barred to we who crawl along the ground
So in defiance do we finger-puppet colored light and sound
Tis a power, tis a tool, tis an armor we adorn
With which we roam impossibility where other selves are born
Won’t you let me stay much longer, one more block, one more bite
One more city, one more kingdom, one more fate deciding fight
Oh I know that in good time, my feet must reunite with ground
For I cannot eat or drink of only colored light and sound.
The above is a poem about my love of video games.
Today I was in a G+ hangout with Dan from Camels with Hammers and several other folks. Had conversations about moral philosophy, religious language, secularist communities, and the relationship between knowledge, belief, and morality. Fun stuff. I don’t think I articulate my meaning as well when I’m not privileged to the luxury of excessive editing and re-recoding, but I sure do enjoy the ability to join a hangout for an hour that I can just link to. Don’t even need to upload it myself! Woo future!
Made a few arguments in my last video against utilitarianism that I have since recanted, so I revisit my protest in this video.
The Lonely Cabin
“It wasn’t really as interesting of an experience as you thought,” I said as I turned the pages of my notebook. I was of course talking to myself, but there was no one else around to be “you” so I had to fill in. I’s are very lonely without you’s, after all. I already knew what the next page said. I had written it after all. My notebook was full of stray notes I would jot down when I liked a particular thought and didn’t want to lose it. The notes I read now were written a bit more neatly than usual because I had anticipated reminiscing over them once the hypnosis had worn off, as it had an hour or so ago.
Self-hypnosis had been the most wonderful thing I’d learned since learning itself. Learning to learn had been a very difficult business which first required learning to time-travel, which in kind, required learning to time-travel.
“It was a bit too much,” I continued in disappointment. “I still never really believed it. I mean, I did, I put one foot in front of the other and all. Went to school, went to work, but… leastwise I was hardly surprised to be waking up in this cabin again. Even before my memories had returned to me.”
I made myself believe all sorts of uncanny things with hypnosis. I once believed I was a triangle, shortening and extending my legs in every strange way I could think, on a lifelong endeavor to project my center slightly into the third dimension. With only my corners in contact with my home plane, I would tiptoe over the Y-axis and explore forgotten lands, long lost to reckless and unsustainable subtraction. This wasn’t nearly so hard to swallow as I had suspected it would be.
Even so, my most recent experiment had been entirely too bizarre. There were “others” for starters. Creatures that were like myself, but were not myself, and I was “one of” them. Supposedly they had their own thoughts, but only they could hear them and I never could. Even though I had never once heard the thought of another being, I felt positively committed to the belief that they had them. This was because I had a body and a voice and a language, and they had bodies and voices and languages too, so they apparently must have everything that I had. I had encountered precisely zero people who I knew for certain to posess or lack thoughts, and precisely one person who I knew for certain to posess them. It wasn’t much of a sample size, but I sure was certain about the findings.
Next was movement. Things were always moving to places that nobody had told them to. Apparently they were just following the rules. One of the rules was about sticking to big things. One of the rules was about constantly falling through time with no bottom in sight.
There was a tremendous amount of argument over whether or not anyone had actually made the rules or if they were just there for no reason. More curiously everyone who thought the rules were made on purpose were fairly unanimously certain that the rule-maker was a really fantastic guy, even though his rules so frequently made stuff move to places nobody wanted it. Bacteria into wells and bullets into stomachs and what have you.
One thing everyone did seem to agree about was that dying one of the worst things ever.Somehow they managed to cope with living in a world where one of the worst things ever was garaunteed to happen to everybody. Still stranger that they all agreed about it being so terrible, considering some of the people thought dying was the end of existing while others thought it was passage to a really lavish and exclusive party. There was also a lot of variance on what was OK to kill and what wasn’t for what reasons. Counterintutively, it seemed the people and creatures least believed to be headed for a party after death were the most permissible to kill.
It was a strange and elaborate dream. An impossible world populated by impossible creatures full of impossible ideas. I had thought I might awaken from it with broadened perspectives, a whole new range of possibilities in view. In the end, it turns out there are things too wild to ever truly believe, even in total immersion. I closed my notebook. I crawled into my bed in the corner, and with that, the bed, the notebook, the cabin, and everything that has ever existed went to sleep.
Yesterday I was cooking, and I went to briefly set a stoneware bowl on the burner next to the pot I was cooking noodles in. I was struck with a moment of uncertainty as a stoneware bowl really shouldn’t go a burner generally speaking, but it should be fine if it’s not hot. I hadn’t recalled turning that burner on, but in a moment of just-in-case paranoia, I tapped my wrist against the burner just to assure myself it was cold, and it was.
Now WHY did I do this. I started to wonder immediately after I did it.
Scenario1: It was not hot, no problem.
Scenario2: You burned yourself instead of slightly warming a stoneware bowl, you moron.
It seemed for a moment like a patently irrational decision. On further contemplation though, I would defend my actions as sensible. This is because Scenario 1 ignores the displeasure of a mental state of uncertainty. It is not truly “no problem.” It is a minor problem.
Let’s say I represent my dislike of the feeling of uncertainty as 2BU (bad units), and my dislike of having my wrist burned as 100BU, and I estimate the likelihood of the burner actually being on at about 1/100.
A 1/100 risk of experiencing 100BU seems to sensibly be treated as a 100% chance of 1BU. If I do the wrist test, I take just such a risk, but if I don’t, I have 100% chance of experiencing 2BU, so provided I can defend my dislike of uncertainty, the decision would come down clearly on the side of putting my wrist at risk.
Can I defend disliking uncertainty that much? Shouldn’t uncertainty about the chance of harming the bottom of a replaceable and affordable bowl be pretty insignificant? The discomfort of uncertainty need not be mere calculation from the possibilities in question. For example, I can be irritated by not knowing if a thing is red or blue while having no vested interest or utility for the answer. Knowing is an experience, like eating ice cream or burning a wrist. There’s nothing inconsistent or irrational about assigning an arbitrary value to it.
And for anyone thinking I should’ve just hovered my hand over the burner, that would’ve taken more time, and been a bother that I rank at around 1.5 to 2 BU, so it’s out of the question.
Well what the hell do you think about when you’re cooking?
This is a video showcasing my argument-mapper and logic calculator, Calculemus, on it’s very first release to the web at www.internetargument.org. This project has a long ways to go, but I hope this release and this video give people an peek at what I’m shooting for in the long run. This is not currently, but will eventually be, an open source project. Let me know what you think!
Some devil’s advocacy for a Christian apologist. – update: Theo has since taken his video down. The gist, as I understood it, was that WLC claims to believe in God foremost on account of personal “spiritual” experience, and Theo equated this to faith rather than reason.