Frege’s Challenging Questions

  1. Gottlob Frege was a German logician, mathematician, and philosopher who played a crucial role in the emergence of modern logic and analytic philosophy. His work has influenced computer programming and mathematical set theory. He had some interesting things to say about language, and noticed some inconsistencies in way people thought about language and logic.

In Ueber Sinn Und Bedeututng Frege makes this assertion:

  “Equality gives rise to challenging questions which are not altogether easy to answer.”

In order to understand what he means by this phrase we must flesh out two things. Firstly, we must understand what he means by “equality”, and secondly investigate the kinds of challenging questions which are not easy to answer.

When Frege uses the term “equality” the reader must understand that he is referring to certain ways people use language. Specifically, “equality” refers to the relationship that different words have in reference to the same object. For example, Frege brings up two different phrases which refer to the same object. He points out that the phrases “morning star” and “evening star” are two separate phrases that refer to the same object in the sky commonly called Venus. And in terms of equality they share a relationship since “morning star and “evening star” both equal the object Venus. It’s understandable how one can infer that “morning star and “evening star” share a relationship of equality since they both point to the same object. After all since they point to the same object, logically one would think that the phrases are identical (or to use Frege’s term equal). But Frege notices a complication in this reasoning.

Frege makes a keen observation in terms of people equating two separate phrases to one another. They aren’t necessarily saying that these phrases are actually the same. To use Frege’s Venus example, “the morning star” and “the evening star” do refer to the same object. But the phrases themselves are different when considering humanities relationship to the object and other contextual factors. In order to flesh this idea out further I will use an example of my own to convey the complication Frege is addressing.

Let’s say two people are looking at a person with a hat. One person is to the left and another person is on the right of the hat wearer. Now let’s say that this hat has two colors on it (red and blue ). The person on the left can only see the blue and the person on the right only sees the red.  When these two people attempt to refer to the hat they could say something to the effect of  “look at the “red” or “blue” hat”. If they were to go back to people who’d never seen the hat they’d use the colors they saw as ways to refer to the hat. So if one was given the description “blue” and they saw the red side of the hat they wouldn’t realize that the hat was the object being referred to. The only way the person would realize that is if they knew that the hat was BOTH red and blue. But the person is given a particular phrase to describe the object so we can’t fault them for not realizing that “blue hat” and “red hat” are equal in terms of referring to the hat. After all “blue hat” and “red hat” without the context of the duality of the hat wearer are to be understood differently. Complications like this are what Frege intends to point out.

Now the aforementioned example may seem highly unlikely. But you’d be surprised in the ways this complication pops up in the real world. Let’s take a case from the 21st century. On February 26th 2015 a picture began to circulate on the internet creating quite a stir on social media. The photo in question is known commonly as “the dress”, and it drew strong reactions. The reason being is that the object in question (the dress) appeared to convey two separate colors to observers. One set of individuals claimed it was “yellow” and another set said it was “blue”. But how could this be? To be

“The Dress”

frank, there is no large consensus in terms of an explanation. But logically the object in question possess 2 color impressions at the same time. That would mean you could see both the blue and the yellow, but human cognition only allows for one. So logically it’s either yellow,  blue, or neither. But despite the logical inconsistency people could talk and point to the dress while at the same time holding their own interpretation of “the dress”. So in this weird case “yellow dress” and “blue dress” mean the same thing when referring to “the dress”. But when they are alone and not referring to anything they absolutely can’t mean the same thing.  Frege recognized this phenomena over a hundred years ago, and perhaps forces us to investigate human cognition itself when it comes to conundrums such as this.

A Brief Critique of Locke: Deconstruction and Reconstruction

words in their primary or immediate signification stand for nothing but the ideas in the mind of him that uses them (p. 146).”

The quote above is taken out of the work called An Essay Concerning Human Understanding by John Locke. Specifically, the quote is from Book III which talks about how humans come to understand words and communicate ideas to one another. From the quote above the reader can get a general idea of John Locke’s theory on words. We can reason that Locke thinks words are equal to ideas when he says “Words in the their primary…. signification stand for nothing BUT ideas in the mind…”. Additionally, he goes on to explain that humans are endowed with various thoughts that are supposed to benefit other people. But there’s a catch, these thoughts are all locked up within the individual. Despite this dilemma, words allow these ideas to become unlocked from the individual. According to Locke the unlocking process is what allows society to flourish (Chapter ii sec1. Pg 146 Locke). From that readers are compelled to conceptualize language as a phenomenon which instructs and provides knowledge in order for society to flourish. Furthermore, sharing ideas would be living in accordance with human nature, since he also believes that humans are inherently designed to be sociable (Chap I sec 1 pg 145). Since for Locke ideas are used to be sociable, that means words have utility as well. He argues there are two use values when it comes to recording words: 1. it aids memory 2. It brings ideas out in the open where others can see them (Chapter ii sec 2 pg 146). But words would become too idiosyncratic if people conceived of their own “markings” to translate their ideas. So words that flourish are a “mark” which are universally recognized. Locke explains this notion by saying:

nobody can apply a word, as a mark, immediately to anything else. For that would involve making the word be a sign of his own conceptions, …applying the word as a mark of a thing involves applying it intending it to stand for that thing, which means applying it with an accompanying thought about the word’s significance.”

So if you want an idea to universally stand for a certain mark that means one must find a mark within the world which can generally signify the idea you are trying to convey. This process is what facilitates proper communication with others. So, for example,  if “x” signified the idea “car” in a certain society, then another mark such as “y” (y= not car) would be inappropriate to use for car since “y” isn’t generally understood to mean car. Though Locke has interesting reasons to justify his views on words and ideas, that doesn’t exempt his arguments from criticism.

One objection to Locke’s reasoning would be one that challenges the claim that recording words aid personal memory. While yes, generally this may seem true, readers should analyze the full extent of this claim. Let’s consider a brief example. Imagine an individual who has trouble with long term memory but is proficient at remembering locations. Now let’s say this person is attending a speech and wants to remember the way the orator was talking, and so writes down “Remember the address”. Later on in the week the person finds the paper and reads what he had written. According to Locke the words written down on the paper should aid our forgetful person in remembering the infliction of the orator. But problems arise considering the fact the person is proficient at remembering locations. So he reads it and thinks “Right, it was 5th street”. On the surface this seems like it aided his memory but his initial intention was to remember the infliction of the orators voice, and not the location. After all the person is already good at remembering locations and didn’t necessarily need the words to remind him where the speech was. This could be mitigated by recording his voice (since address (location) and address (speech style) can have different pronunciations). But this would be problematic if the person voice recorded words like “councilor/counselor” or “bank”. Because these words sound the same, the forgetful individual might still find trouble in remembering what they meant.

Another detail we must pay attention to in Locke’s reasoning is the concept that when we write symbols to denote ideas we are doing this to share ideas with others. This once again is generally true. And we get a qualifier on why sometimes it may not be true, since popular symbols must be used to signify ideas (“x”= car example above). So Locke successfully explains why sometimes people don’t understand words that explain ideas. The symbols are too idiosyncratic. But he fails to go deeper on what makes these symbols generally understood in the first place. It’s not as if when human’s with linguistic capacity look at objects they immediately have word impressions of that object. Quite plainly, when you look at a dog in the real world, the brains initial impression doesn’t initially stimulate the cognitive impression of “dog!”. And if you were to pan over to a chair your brain doesn’t exclaim “chair!”. It just understands these objects as such. The word and the object here don’t seem to be directly linked to one another in terms of recognizing objects in our consciousness. But nonetheless these names exist and we have formulated them, so in that sense Locke is correct in saying words are ideas. But it’s wrong to say the inverse, that ideas are words. Mainly because objects in themselves don’t contain the property “word”. But rather, this cognitive property assignment comes from humans. He acknowledges the arbitrary nature of word denotation but still believes that the impressions of objects warrant an automatic denotation. But this isn’t an accurate conceptions of human cognitive thinking. We don’t get impressions from objects in the world and immediately think “this object is that”, rather the brain seems to conduct a process of pattern recognition. The brain’s process seems to fall under reasoning like this “this object is this object, which generally falls under this set of symbols/sound in the world”. This distinction, though small, opens up the scope of Locke’s inquiry into the human mind. Here, we can begin to understand the creatures we are. We aren’t creatures who cognitively just process objects and translate them to ideas, but rather we do that and then inquire about its relationship in the world. This process happens quickly, and most humans master this skill by around the age of 3. That’s how we are able to come closer to understanding each others intentions. Animals are generally good at understanding intentions. Humans obviously fall in that category too, but we are different in that we are able to connect patterns with certain sounds and symbols. Let’s imagine, I invite you over for dinner but I don’t speak your language. Now, I could be standing at a table with some spaghetti on a plate and I can point to it and say “fleeblah” and then have another family member come to it and say “fleeblah”, and a person who has never even heard “fleeblah” uttered can reason the sound “fleeblah” has something to do with that spaghetti. Now if I go even further and open up my phone and google many pictures of spaghetti. And then point and say “fleeblah” that person is inclined to understand that when I utter “fleeblah” I am intending to put the idea spaghetti into their head. This recognition of intention should warrant our attention when we speak about human cognition and language. It seems as if when humans utter/ write words we are intending to put ideas into other people’s cognition. This turns Locke’s assertion that words are used to bring ideas out in the social world, into a question of “what do humans intend with words when they try to bring ideas out in the social world?”. A question which may be tackled in a future post.