Is this a true statement? Anyone who passed kindergarten should be able to tell us that yes, two plus two does equal four. You can use basic addition to show this, or you could put two apples on a table, put another two apples next to them, and then notice that you see four apples on the table. Either way you choose, you are ultimately using some sort of metric. There is some bar that “two plus two equals four” passes which allows you to call it a true statement. Let’s call that bar “the rules of mathematics.”
In the vast majority of circumstances, when someone asks “is 2 + 2 = 4 a true statement,” they are interested in precisely this metric. What they want to know is “does 2 + 2 = 4 obey the rules of mathematics?” So in this common context, the word “true” literally means “obeys the rules of mathematics.” For all intents and purposes, “2 + 2 = 4 is a true statement” is the same as “2 + 2 = 4 obeys the rules of mathematics.” We can literally substitute the notion of truth with the notion of obeying the rules of mathematics. (Incidentally, this is a really good way to identify word play. Replace the suspicious words with what they’re supposed to mean and you can usually spot the errors).
Now comes Bob the philosopher, who thinks he sees a problem. Bob says we still don’t really know whether 2 + 2 = 4 is a true statement. Sure it obeys the rules of mathematics, but what if those rules are wrong? How do we know that the rules of mathematics always lead to true statements?
If any of you have your word play detectors out, you might be hearing a loud beeping noise right about now.
When we ask “is 2 + 2 a true statement?” the vast majority of the time we mean “does 2 + 2 follow the rules of mathematics?” So when Bob comes by and asks if the rules of mathematics really lead to true statements, are we supposed to interpret this as “do the rules of mathematics really lead to statements that follow the rules of mathematics?”
If so, my response is a resounding duh.
It’s quite obvious that this is not what Bob the philosopher wishes to ask when he asks whether the rules of mathematics really lead to true statements. It’s clear from the way philosophers present these sorts of questions that they aren’t trying to ask something so completely trivial.
But remember the rules of not being a douche. If you are going to change the definition of a word, then you need to tell your audience. And you can’t just say “hey guys, I’m going to change things up a bit.” You have to specify how you’re changing things. If Bob wants to change the definition of “true” so his question isn’t completely trivial, it’s his job to tell us what his new definition is. If he doesn’t (and the philosophers almost never do), then whenever Bob says true, and it’s clear he’s not trying to use the old definition, the only thing I have to replace it with is “unspecified property X”
Many people have taken questions like Bob’s and tried to answer them by (effectively) projecting a new definition onto Bob’s terminology. But as soon as someone points out that the rules of mathematics are logically valid, Bob just asks how we know that the rules of logic lead to truth, which means that he’s once again shifted the definition of “true.” And of course Bob can keep pulling this crap all day long. As soon as you’ve teased out the new “true” and met that metric, Bob will just shift the definition again and say “but how do we now that metric gives us true statements?” And on and on and on.
What you have to realize here is that with every iteration of this process, the definition of the word true changes. It’s called moving the goalposts. People miss this fallacy, and mistakenly conclude that this silly little exercise tells us that we can never really demonstrate something to be true. But that’s crap. Don’t get hung up on the fact that Bob is using the word “true.” Just because he’s using a word doesn’t mean he automatically gets to apply all of its connotations. Replace the suspicious word with what it’s supposed to mean. As far as Bob has bothered to supply, “true” means “unspecified property X.” So the real conclusion, the meaning, rather than the word play, is that we can never really demonstrate that something has unspecified property X.
Of course we can’t demonstrate that 2 + 2 = 4 has unspecified property X. But this has nothing to do with our intellectual capabilities. It’s just that X is unspecified! Saying this reflects some inherent limit to human knowledge is like saying “No one can vtneqeafi” reflects some inherent limit to human athletic ability. Bob has disguised this fact by using the word “true,” but you have to look past that. Look past the word and realize that Bob has left it without meaning. It reads t-r-u-e, but it may as well read v-t-n-e-q-e-a-f-i for all the good it does us.
So the next time you hear someone ask if you can ever really know something, call them out. Don’t try to guess what they mean by really know, that lets them move the goalposts. Instead, insist that they tell you what they mean. After all, they’re the ones who are clearly deviating from the criteria we use in our everyday lives. So it’s their job to tell us what the heck they’re talking about.