the rebuttal that doesn’t need a logic textbook
After extensive debate with Mr. Frog, I find the theorem absolutely useless.
To understand my first problem requires understanding the difference between states and visible colors. If an emerald is seen before the date and gives the visible characteristic of green light, Mr. Frog makes the conclusion that since both definitions enclose this occurrence that we then can induce that the emerald is both green AND grue. This is just not so. If the state of being green and the state of being grue both display the visible characteristic of being green, then it is impossible to know which one the emerald is, if it is either of them at all.
This does not change what the proof “proves”, only the method. Mr. Frog claims the true definition of grue is not based on an inner state, but objects become defined as grue automatically if they are seen before the date as displaying the color green.
In that case I define everyone I meet who has red hair to be named Jackass. If I meet someone who is really named Tony, I will tell them sorry, but I defined their name to be Jackass, so they have to be named Tony AND Jackass, because that is my definition. In reality the individuals name is Tony, but through an irrational definition I can now claim he is defined as a Jackass.
Now say there actually is an individual whose name is Jackass, and his hair actually is red. Put him in a room with another guy that has red hair, and then walk me in. I know that there does exist an individual or multiple individuals whose names are Jackass, and that they all have red hair. I look at these two red haired individuals, and since someone named Jackass has red hair, then these red heads are named Jackass.
This logic doesn’t work. If I am human, and Bill Gates is human, I can’t prove to anyone that I’m Bill Gates with just that information. Now if I happened to be a little squirrelly guy who was the head of the largest computer software manufacturer on earth and I was famous for unscrupulous business practices, then I might be able to convince someone I was Bill Gates. They would be convinced only if presented with information that they believed.
My final problem is Mr. Frogs conclusion. Apparently Goodman makes this conclusion too, and that disturbs me.
This contradiction is Goodman's proof for showing that induction is totally useless.
In the induction write-up by Webster 1913, it is defined partly as “The act or process of reasoning from a part to a whole, from particulars to generals.” Gleaning something large from something small.
You show up to my house knowing you’ll be meeting my two best friends for the first time. I tell you only about one of them, named Josh. He is 5’9”, wears a baseball cap, always a Steelers hooded sweatshirt, shorts, sandals and has his eyebrow pierced. He has glasses, and never smiles. If you show up and see someone who matches these characteristics, you don’t know that it’s Josh, but chances are it is. You might induce that since most people wouldn’t dress exactly alike on the same day, that the odds of two friends wearing matching outfits when they are hanging out are fairly low. This isn’t wrong, induction isn’t useless, but it’s not perfection.
But Goodman proves that induction is “useless”. I’m glad he did, because now I know that although it was helpful for me to wear shoes in the past that doesn’t mean it always will be. Who knows, shoes could stop being useful tomorrow, so not wearing shoes is just as viable an option as wearing them. Come to think of it, these clothes I have on can go. Just because people historically think nakedness is a taboo in America doesn’t mean it will be tomorrow! Because I know induction is useless then that means that the past has no bearing on the future.
As humans we have five senses, which constitute a limited set of data. If we cannot induce generalities from a limited set of data, then we are crippled. If induction is useless, than so are our senses. If our senses are useless, I’m going to go find a knife, because life then is pointless.
Induction is not perfect, but induction is not useless. Induction is by definition an imperfect tool, and Goodman’s proof says nothing of importance.