Basic Frege
I had to give a 5 min presentation on Gottlob Frege for my Analytic Philosophy class. I had a powerpoint, but I wrote out the entirety of what I said. Here it is.
Frege had several important ideas, and one of the more important ones was his championing of this view called “Logicism”. So what is Logicism? So Logicism is the view that math can be reduced to logical statements, thus making math a branch of logic. Just as there are branches in philosophy, like Ethics, Logic, Metaphysics, and those branches have sub branches, like in Ethics you can branch off into ethical theory, and applied ethics, so Frege wants to say that math is a branch of Logic. Which was a real trip at the time because it was something of a common opinion that math was a generalization of our experiences. And this view was held by philosophers like John Stuart Mill. So for example, when I have two dollars, and then I have another two dollars, I then learn that I have four dollars, and so I draw from my own personal experience that 2+2=4. In this sense, math is kind of subjective. But here comes Frege with a turbulence of rigor and clarity and is like, uh NO. Math is something more objective and rigid. It is not something that we work our way from the bottom up, like we do experientially, but rather we work down from our knowledge of arithmetic to understand what it is exactly that we are experiencing. And if that’s the case, then it should have certain axioms which are logical.
Now unfortunately for Frege, he had this Axiom called Basic Rule 5, which has a complicated formal statement, but can sort of be simplified by saying that a class can be a member of itself. So for example, there is the class of ducks, which contains all ducks, and there is a class of philosophers, which contains all philosophers. But what Frege’s Rule has said is that in some cases, some classes can be members of their own set. So for example, there is the class of all sentences, which would even include itself because it is also a sentence. Or there can be “The class of all sentences that begin with ‘the’” which would include itself as a member of its own set. That is what Frege’s rule 5 would allow. But then here comes this absolute chad of a British philosopher named Betrand Russell who was like, uh NO, and discovered that Frege’s Rule 5 leads to some self contradictions. Now, there is a formal way of putting it, but for simplicity sake, take this analogy. Suppose there is a barber, and this barbers rule is only that he shaves those people who do not shave themselves. So, if you do not shave yourself, you go to this barber to get shaved. If you do shave yourself, you do not go to this barber. That’s the rule. So, now we can ask, where does the barber himself go? If he shaves himself, then his rule is broken, the barber does shave someone who shaves himself. If he does not shave himself, then he must go to the barber who shaves him, which is himself, and so shaves himself, thus still breaking his own rule. So then we have a contradiction. And then Frege’s axiom fails and so does his whole project of logicism. But despite his epic failure, he still had a pretty cool way of quantifying things in logic that we still use today.
His contributions in the philosophy of language is also pretty significant, and comes from his work Sense and Reference, in which he distinguishes the two. And from that distinction comes many useful tools for doing philosophy. Now, I want to motivate the distinction by looking at a problem. So, here, I have two arguments. And these two arguments are supposed to be parallel. So the first argument is this. Premise 1. I love my girlfriend. This happens to be true. But I have this relation to this subject, my girlfriend. Premise two. My girlfriend is Lori. This also happens to be true. This is a statement of identity. My girlfriend is identical to this person named Lori. And 3, the conclusion, therefore, I love Lori. This seems pretty straight forward. I have this relation to X. X is identical to Y. So, I have this same relation to Y. This seems pretty valid. But now take the second argument. Premise 1a. Mary Jane loves Spider Man. This, according to the lore, seems true. And it parallels premise 1, which says I love my girlfriend. This is a relation to X. Premise 2a says Spider Man is Peter Parker. And according to the Marvel universe, this is also true, and just like premise 2, is a statement of identity. And then we have the conclusion, 3a, therefore, Mary Jane loves Peter Parker. Now, if you know Marvel, you know that this isn’t always true. In fact, this seems like an invalid inference. But how is that possible if it has the exact same structure as the first argument, and the first argument is valid. What is going on?
Well, according to Frege, they aren’t the same. But where is the difference? So, Frege says theres a difference between a sense, which is the way a word is presented or expressed, and the reference, or the object to which that thing refers to. Frege uses the example of Morning Star and Evening Star, but, if you don’t know astronomy or stars, it’s not the greatest example. It didn’t make sense to me for that reason so I’m going to change it lol So, if someone said “The President will debate” and “Donald Trump will debate” we understand that the term “the president” and “donald Trump” both refer to the same person and so are identical to that person. However, just because the referents are identical, it doesn’t follow that the senses are identical as well. We cannot say that the name “Donald Trump” IS the name “the President”. They have the same referent but that doesn’t make them identical words or utterances. Clearly they are not. So, with that distinction in mind, let's go back to the argument. Where is the disanalogy? Well, in the first argument, I know in my own mind that the sense of the word “girlfriend” and the word “Lori” are the same. And they both have the same reference. However, in the second argument, though Spider-Man and Peter Parker have the same referent, they do not, in the mind of Mary Jane, have the same sense. And that’s the difference. The identity statement, or how we are using “is” is different.
Frege had several important ideas, and one of the more important ones was his championing of this view called “Logicism”. So what is Logicism? So Logicism is the view that math can be reduced to logical statements, thus making math a branch of logic. Just as there are branches in philosophy, like Ethics, Logic, Metaphysics, and those branches have sub branches, like in Ethics you can branch off into ethical theory, and applied ethics, so Frege wants to say that math is a branch of Logic. Which was a real trip at the time because it was something of a common opinion that math was a generalization of our experiences. And this view was held by philosophers like John Stuart Mill. So for example, when I have two dollars, and then I have another two dollars, I then learn that I have four dollars, and so I draw from my own personal experience that 2+2=4. In this sense, math is kind of subjective. But here comes Frege with a turbulence of rigor and clarity and is like, uh NO. Math is something more objective and rigid. It is not something that we work our way from the bottom up, like we do experientially, but rather we work down from our knowledge of arithmetic to understand what it is exactly that we are experiencing. And if that’s the case, then it should have certain axioms which are logical.
Now unfortunately for Frege, he had this Axiom called Basic Rule 5, which has a complicated formal statement, but can sort of be simplified by saying that a class can be a member of itself. So for example, there is the class of ducks, which contains all ducks, and there is a class of philosophers, which contains all philosophers. But what Frege’s Rule has said is that in some cases, some classes can be members of their own set. So for example, there is the class of all sentences, which would even include itself because it is also a sentence. Or there can be “The class of all sentences that begin with ‘the’” which would include itself as a member of its own set. That is what Frege’s rule 5 would allow. But then here comes this absolute chad of a British philosopher named Betrand Russell who was like, uh NO, and discovered that Frege’s Rule 5 leads to some self contradictions. Now, there is a formal way of putting it, but for simplicity sake, take this analogy. Suppose there is a barber, and this barbers rule is only that he shaves those people who do not shave themselves. So, if you do not shave yourself, you go to this barber to get shaved. If you do shave yourself, you do not go to this barber. That’s the rule. So, now we can ask, where does the barber himself go? If he shaves himself, then his rule is broken, the barber does shave someone who shaves himself. If he does not shave himself, then he must go to the barber who shaves him, which is himself, and so shaves himself, thus still breaking his own rule. So then we have a contradiction. And then Frege’s axiom fails and so does his whole project of logicism. But despite his epic failure, he still had a pretty cool way of quantifying things in logic that we still use today.
His contributions in the philosophy of language is also pretty significant, and comes from his work Sense and Reference, in which he distinguishes the two. And from that distinction comes many useful tools for doing philosophy. Now, I want to motivate the distinction by looking at a problem. So, here, I have two arguments. And these two arguments are supposed to be parallel. So the first argument is this. Premise 1. I love my girlfriend. This happens to be true. But I have this relation to this subject, my girlfriend. Premise two. My girlfriend is Lori. This also happens to be true. This is a statement of identity. My girlfriend is identical to this person named Lori. And 3, the conclusion, therefore, I love Lori. This seems pretty straight forward. I have this relation to X. X is identical to Y. So, I have this same relation to Y. This seems pretty valid. But now take the second argument. Premise 1a. Mary Jane loves Spider Man. This, according to the lore, seems true. And it parallels premise 1, which says I love my girlfriend. This is a relation to X. Premise 2a says Spider Man is Peter Parker. And according to the Marvel universe, this is also true, and just like premise 2, is a statement of identity. And then we have the conclusion, 3a, therefore, Mary Jane loves Peter Parker. Now, if you know Marvel, you know that this isn’t always true. In fact, this seems like an invalid inference. But how is that possible if it has the exact same structure as the first argument, and the first argument is valid. What is going on?
Well, according to Frege, they aren’t the same. But where is the difference? So, Frege says theres a difference between a sense, which is the way a word is presented or expressed, and the reference, or the object to which that thing refers to. Frege uses the example of Morning Star and Evening Star, but, if you don’t know astronomy or stars, it’s not the greatest example. It didn’t make sense to me for that reason so I’m going to change it lol So, if someone said “The President will debate” and “Donald Trump will debate” we understand that the term “the president” and “donald Trump” both refer to the same person and so are identical to that person. However, just because the referents are identical, it doesn’t follow that the senses are identical as well. We cannot say that the name “Donald Trump” IS the name “the President”. They have the same referent but that doesn’t make them identical words or utterances. Clearly they are not. So, with that distinction in mind, let's go back to the argument. Where is the disanalogy? Well, in the first argument, I know in my own mind that the sense of the word “girlfriend” and the word “Lori” are the same. And they both have the same reference. However, in the second argument, though Spider-Man and Peter Parker have the same referent, they do not, in the mind of Mary Jane, have the same sense. And that’s the difference. The identity statement, or how we are using “is” is different.
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