The Directionality of Argumentation and Meaningful Propositions: Theoretical Exploration
The directionality of argumentation is another phenomenon other than the “elucidation problem” that we can see in the act of drawing conclusions. While we have discussed the “elucidation problem” in one of my previous essays, the directionality of argumentation still remains to be discussed. Here, I wish to discuss at length what it is and how it affects our way of thinking without us explicitly being aware of it. Even though the main topic will be the directionality of argumentation, we will still touch briefly on the “elucidation problem”, because as we will see later, these two problems are connected in parts.
The Directionality of Argumentation
The directionality of argumentation is something that is so obvious for some that it is my opinion that someone must have come across this problem in one way or another before. However, even though it is always there in front of our eyes to see whenever we draw a conclusion or even when we try to make a chain of propositions, I personally am not aware of anyone having actually brought it up to clarity. Therefore, if someone has indeed brought this up in one form or another, it is not my intention to claim their discovery as mine. It is simply a coincidence that I also stumble on the same thing as them, just like someone accidentally stumbles upon a biological species previously found by someone else without any prior knowledge of the first discoverer’s works.
What is the directionality of argumentation? Simply put, in a chain of propositions, the directionality of argumentation is about which premise in a chain of propositions serves as the foundation of that chain. While this at first seems rather simple, especially in formal logic, where the chain of propositions is rather clear, the directionality of argumentation becomes more complicated when we start including meaningful sentences into the picture. This is because while in formal logic, the foundation can simply be determined based on the logical operations that make up the chain of propositions, this is not always the case when it comes to meaningful propositions. As we will see later, when it comes to meaningful propositions, sometimes what should be done according to formal logic is taken only in form, while in practice, the meaning of the sentence forming that chain might at times hold the true power behind the whole logical operation. However, we first have to discuss how it is done in formal logic before discussing how meaning affects the entire operation of this problem.
Formal Logical Operation
In a formal logical operation, where conclusions are usually drawn from logical operations only, it is usually easy to discern which one serves as the foundation for the chain of propositions and which one follows from it. For example, at times, the foundation of the whole chain is usually the first premise in a chain, for example, if we have the chain Q →B →C →D, then if we want to obtain (D), then we first have to obtain (Q), therefore (Q) is the foundation for the whole chain of argument because only based on it can we get (B), and out of it (C ), then finally to (D). Therefore, we can see that here, (Q) is what I will call the “primary”, while (B), the “secondary”. Now even though it is true that if (Q) is false, it doesn’t necessarily mean that we won’t obtain (B), it doesn’t mean that the directionality of argumentation is superfluous. If (Q) is false, (B) doesn’t have to be false as well simply because there are premises other than (Q) that (B) can base itself on. In this case, we’re simply changing (Q) to (X), for example, but still then having the chain X→B →C →D. However, this is not our main point at the moment, as discussing it now will simply divert us from the main problem that we want to clarify right now.
In the chain Q →B →C →D, does that mean that since (C ) comes out of (B), it is the “tertiary”? In a sense, yes. But since doing that would only needlessly make new terms that actually serve the same purposes, it will be easier for us to break the chain apart to Q →B, then to B →C, then finally to C →D. Note that this division only serves the purpose of making the operation easier to be dissected, not because of some inherent logical rule. If we break the chain Q →B →C →D into those three smaller chains, then we will be able to limit our terms to “primary” and “secondary” without actually losing the main idea. Therefore, in Q →B, (Q) is the “primary”, and (B) is the secondary, and when it is continued to B →C, the B becomes the “primary” for the chain, and (C ) the “secondary”, before (C ) becoming the “primary” in the next chain, and so on and so forth. Note that this division is only to make it easier to dissect long chains. There is no actual necessity it has to be done in that manner.
But then, one might wonder, in a single chain like the one mentioned before, it is easy to see where is going to where. Each premise can be said of “not standing on equal footing” with one another, as (D) actually coming out from (C ), and (C )coming out from (B), and so on and so forth. But real-life arguments are rarely that simple. What if in the whole chain, some premises supposedly stand on equal footing with some premises, as in for example A^B=C →D^Y=Z? How are we to break this one apart? In this case, since (C )is made out of the relation between (A) and (B), then (A) and (B) serve as the “primary” for (C ), since in that operation, (C ) can only be obtained as “true” if A^B, provided that both of them are “true” . This means that the directionality of argumentation can only be used if in a chain there is a conclusion of something. In itself, A^B might not mean anything. It’s like saying two different statements without doing anything with them. Therefore in the chain A^B=C →D^Y=Z, we can break it to A^B=C, then C →D, then finally to D^Y=Z.
The Elucidation Problem and the Directionality of Argumentation
Even though at first the directionality of argumentation seems simple enough, things begin to change when we start to talk about meaningful propositions. As we can see, all our previous discussions were limited to logical symbols and notations without their meanings (e.g. Q^F=G). As a result, it allows us to treat the premises as if each of them is fully self-contained and the only thing affecting the result of the argument is whether each premise is “true” or “false” and the logical operation being done to it. Even the notion of “true” and “false” here take a symbolical role, because since there is no meaning, there is no standard against which the proposition is to be judged, nor can it be judged at all. This almost ideal operation leaves one important thing from the whole picture, that is, the influence of the premises’ meaning on the logical operation.
This is especially important when we realize that it is impossible for us to fully explain a proposition down to its last detail. There is always something in a proposition that can be regarded as “unclear”, or even “in need of a revision”. This is the “elucidation problem”. Simply put, the elucidation problem is about the impossibility for a proposition to have a fully self-contained meaning. It is always possible to break a premise apart into multiple smaller sub-premises (e.g. from (A) into, (a1), (a2), (a3), and so on and so forth) and try to figure out the meaning of these smaller sub-premises. These smaller sub-premises, if one is willing, can then be changed in interpretation in order to change the meaning of the larger premise by just a little bit which can then influence the whole chain of the logical operation. While some might question whether, as a result of this operation, the meaning of the proposition might actually change from (A) to an entirely new one e.g. (X), this will not be our discussion here. For now, it is enough that we understand no proposition can be self-contained, that every proposition can be broken apart into smaller propositions, and so on and so forth.
This problem that we have can then result in a new addition to the directionality of argumentation, specifically, when we want to determine the relationship between the sub-propositions of (A), for example, and (A) itself. Now even though at a glimpse the relation between a proposition and its sub-propositions might appear to be a1^a2=A, how the argument work doesn’t exactly follow this line of logic. For the sake of clarity let us first make an argument consisting of three propositions before taking apart one of its propositions into its sub-propositions and see how it can affect the larger picture. Suppose we have:
(1)
A: How we perceive things depends on our life’s experiences.
B: We have different life’s experiences
— — — — — — — — — — — — — — — — — — — — — — — — — <therefore>
C: We perceive things differently.
In this scenario, we see A^B=C. If A or B is false, or if both of them are false, then the conclusion (C ) cannot be obtained. However, it is clear that due to the failings, or perhaps the virtue of our language, it is impossible for us to create a clean-cut proposition. For example, it is possible that in an attempt to disprove this whole argument, one breaks proposition (A) without changing the wording nor even the entire sense of it, but just enough to make it means a little bit different so that (C )might also be a little bit different, but different enough to prevent it from obtaining the next conclusion derived from (C ).
For this, let’s expand this argument to add another proposition after (C ). Let’s call it proposition (D):
D: The world is constituted by consciousness.
The chain A^B=C →D can be obtained because if we perceive things differently, then it is impossible to know how the world truly is, and therefore the world as such is constituted from how it appears to us, therefore the world is constituted by consciousness. However, since it is impossible to have a fully contained argument, it is possible for someone to break A apart into smaller pieces. Now suppose a philosopher wants to argue against premise (D), but he agrees that premise (A), (B), and (C )is correct, in a sense.
Suppose that in order to retain (A), (B), and (C ), he breaks (A) down into its sub-premises:
a1: How we perceive things
a2: Perception depends on our life’s experiences.
However, before we see how this philosopher defines both (a1) and (a2) in a “novel” way, we see how (a1) and (a2) are previously intended. Note that perhaps in its first conception, the thought of (a1) and (a2) as such might not even cross the mind of the first philosopher creating the argument, something which becomes relevant when we discuss its effects on the directionality of argumentation:
A1: We can only perceive things through judgement on the raw data that we have. Our retina only receives sense data that is not yet arranged into a coherent, intelligible whole. This arrangement can only come through judgement.
A2: Since our judgement is trained and based on our experience, our differing judgements might result in seeing the same thing differently, like for example a banker seeing money is different from a tribe that has never had the concept of money before seeing money for the first time.
If both (a1) and (a2) are elaborated in that way, then A might imply that it is impossible to know the world as it is, since how the world appears to us depends on us whose perception is limited by experience, even though its “sense” might remain the same.
However, imagine that the philosopher who wants to refute the first philosopher’s argument disagree with the implication of A. Suppose he elaborates both (a1) and (a2) into the following:
A1: The way we perceive things is direct to the thing in itself, even though what we currently “see” is limited to our current position. However, we can grasp the thing as how it is.
A2: Our ability to recognize a thing is based on the things we’ve learned in the past.
For this, we then need to ask, what is the relation between (A) and (a1) and (a2)? Now that (a1) and (a2) are different, should it be conceived as not (a1), and (a2), but as (x1) and (x2) leading to a whole new premise, e.g. (X)? It may be so, but that’s not our main discussion at the moment. The example above has made it clear that how the sub-propositions are defined can determine what the proposition means, or at least, how it is intended to be. Even though here we might think that (a1) and (a2) are not in themselves propositions, but just an elaboration of what (A) means, therefore in essence, they are (A), but just in more lengthy sentences, it is still the case that even if their sense is contained in (A), elaboration brings to light new information not at first clear in (A). That’s why it is possible for the two philosophers discussed above to have two contradictory understanding of (A) as a sentence, because while in a sense when stating (A), the first philosopher already has a certain conception of (A), the second philosopher can still determine that proposition (A) as a sentence is technically true but only if it is conceptualized in some different manner. The sub-propositions of (A), while in a sense are (A), are so only in a sense of “as the elaboration of (A)”, not of (A) only. Therefore, the question: “Which comes first, the whole idea of (A) first, then (A) as its manifestation, or instead (A) first, then elaborated when asked further” can still be asked.
In a sense, the question above can then be dissolved in terms of the directionality of argumentation. “Which comes first” in this case is the same with “which one is the “primary”, albeit perhaps under a slightly different context than when we’re dealing with a chain of disparate propositions. Since technically the sub-propositions of (A) are different then (A) itself, even if the final sense is the same, we can ask whether or not it takes the form of a1^a2=A? As we have seen, technically, it does. We might at first be compelled to say that it is (a1) and (a2) that are first thought, before we then say (A). But then doing so will mean ignoring the fact that (a1) and (a2) can then be broken apart again into smaller propositions. However, in our everyday life, it is impossible to keep on going backward and start from the beginning. In fact, the thought of what a proposition actually means as a whole never entirely cross our mind. Usually, for us, it is enough that we say that something is such and such without actually going into detail how each of our words is meant to be understood. In other words, usually, we only start from (A), and not the sub-propositions. Only when people ask us to elaborate on (A) does the thought come by to think what builds (A). It is only then do we elaborate on the sub-propositions of (A). However, when we do so, we usually take (A) as the “primary” and the sub-propositions as the “secondary”. We elaborate on the sub-propositions of A based on what we think (A) means. Theoretically, (A) “comes” out from (a1) and (a2), but effectively, (a1) and (a2) can come out from (A) as well.
The Directionality of Argumentation and Meaning
Previously, we’ve seen how meaning can affect the directionality of argumentation, even though the example before deals more with the thought process behind forming a proposition. And thus, we are yet to see how meaning directly affects the directionality of argumentation when it comes to a chain of disparate propositions instead of just a proposition with its sub-propositions.
Some might wonder, what does “meaning affects the directionality of argumentation” means? Is it not a matter of fact that for an argument to be sound, each proposition needs to be what is the case in real life. For example, if we want to have a sound argument, then it is clear that if we have two propositions:
A: Socrates is a man
B: All men are mortals
Then we will have the following argument:
(2)
B: All men are mortals
A: Socrates is a man
— — — — — — — — — — — — — — — — — — — — — — — — — <therefore>
C: Socrates is a mortal
Here it is clear that (B) is the “primary” and (A) is the “secondary”, since (A) is based on (B), leading the operation to obtain the conclusion (C ). In fact, if we want to obtain a sound conclusion, it cannot go the other way around. Or perhaps going the other way around would not just make it impossible to obtain (C ), but would actually prevent any logical operation from being done on (A) and (B). In a sense, the meaning of the propositions themselves determines which proposition should be the foundation of which if we want to have a sound argument, or to have an argument at all.
Indeed it is a sort of a truism if “meaning affects the directionality of argumentation” only means what was just stated before. But, it is not what I mean exactly. As we have seen before in the previous section, for every proposition, there are, connected to it, a whole idea about the thing in question from which the proposition is abstracted and in which the proposition has a sense. It is impossible for us to go all the way back to the beginning when we form a proposition. Usually, it is necessary that we first have a background against which the proposition which we make is singularized and made clear, just as when the first philosopher states that (A) means such and such, it means such and such only against a background of thought which he has made against and in which the (A) could be understood in the way which he intends it to be. This connection is signified by the sub-propositions of each proposition which, through its clarification of the full sense of the propositions, also signifies its place among the interconnected ideas which are the knowledge and the form of life of an individual.
To make this clearer, it is best if we first see how it actually works in a given argument. Take for example a set of premises regarding the origin of the universe:
X: Different laws of physics could result in different particles being formed.
Y: The formation of uranium is only possible the laws of physics are exactly the way it is now.
From these, we can get two different conclusions, either it might mean:
(3)
X: Different laws of physics could result in different particles being formed.
Y: The formation of uranium is only possible the laws of physics are exactly the way it is now.
— — — — — — — — — — — — — — — — — — — — — — — — — <therefore>
A: The world “orderly”, i.e. it is precise enough in its laws so that uranium can form
or it might mean:
(4)
X: Different laws of physics could result in different particles being formed.
Y: The formation of uranium is only possible the laws of physics are exactly the way it is now.
— — — — — — — — — — — — — — — — — — — — — — — — — <therefore>
B: The laws of physics happen to allow uranium to exist out of luck.
Note that both conclusions can indeed be found in real life. Conclusion (A) means that the world cannot randomly come into existence because the fact that uranium, a relatively complex element, exists means that the universe is quite orderly, while conclusion (B) means the existence of uranium is of no particular importance i.e. it is an accident in nature. Conclusion (A) in scenario (3) can only be obtained if the premise (Y) is the “primary” and premise (X) is “secondary”. By treating the existence of uranium as a “must”, it follows from it that if a small change in the laws of physics would produce different results (perhaps, a world with no uranium), then it is reasonable to think that therefore the world is precisely ordered, or must not be that chaotic for this world to have uranium.
On the contrary, in (4), premise (X) is taken as the “primary” while premise (Y) is taken as the “secondary”. Because in this scenario the relationship between (X) and (Y) is reversed, then this time it is the laws of physics which become the foundation on which everything else is built. Since the laws of physics, in this case, are treated as not following anything, i.e. they are, like a dice thrown onto a table, can make anything by random (after all, we might not be able to think of a really good reason on why the laws of physics have to be like the ones we have currently if they are taken as the foundation of thought), then the existence of uranium becomes something that might not be that important. It just happens to exist under the mercy of our current laws of physics. There is no necessity for the existence of uranium. It can exist, or it cannot, hence the conclusion (B).
From the example above we can see that even though the directionality of argumentation to a certain extent is based in part on the logical operation done to a certain chain of propositions since after all, the easiest way to see which proposition comes from which is by seeing what logical operation is done to each proposition, but when it comes to propositions with meanings, more often than not what controls which argument comes from which is instead the thought behind any proposition there is in a chain of propositions before the logical operations. The example above shows that other than the truism which we first talked about regarding how, as a matter of course, in order to make a sound argument, each meaningful propositions seems to determine by its own meaning which one can be the “primary” and which one the “secondary”, it is also possible that the conclusion derived from seemingly two simple propositions to differ significantly only because the thoughts connected to the sense of the proposition differ from one person to the next. This is not to say that every person understands the definition of the words differently, but it is just that the at times arational connections formed between ideas that consist the person’s knowledge differs in arrangement, even if the building blocks i.e. the meaning of the words understood are probably the same.