The Peculiarity of Drawing Conclusions

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The acts of drawing conclusions are something that we do every day. We usually do this by taking a premise, then by using a series of processes we arrive at a conclusion on what things are. We create conclusions all the time, either to solve some problems or to understand the world better. However, like all things in philosophy, things are rarely so simple. Usually, if one looks hard enough, what appears to be an everyday activity that is so simple that none of us usually care to take a second look turns out to be something that we can draw inspiration from.

The problems of logic, how it works, its nature, etc. have always puzzled philosophers for a long time. It is nearly impossible to pinpoint exactly when the tradition starts, for probably it goes back as long as human civilization goes. And with the problems of logic, the problem of language also goes along with it. What does a proposition mean is usually what is more important for our day-to-day living.

The peculiarity which I want to discuss at the moment is derived from these two sets of problems, although the peculiarity rests more on the peculiarity of language. Specifically, it refers to how a proposition is never entirely self-sustained. For example, let’s just say we’re talking about perception. We have, for the sake of simplicity, and as an example, have three premises:

A: How we perceive things depends on our life’s experiences.
B: We have different life’s experiences
— — — — — — — — — — — — — — — — — — — — —— — –
C: We perceive things differently.


Or to put it differently:

How we perceive things depends on our life’s experience which is different for every people. And hence, how we perceive things are different as well.

And so we get

A^B →C

In formal logic, every premise is treated as if they’re complete wholes. It can go from L →N →S. The fact that it is a whole makes it possible for S to follow from N, and from N to follow from L. However, history has shown us that it is rarely the case. In our example, it is possible to elaborate on what does it mean by “How we perceive things”. And depending on our explanation on the “how”, it is possible that either the whole conclusion will fall apart, or the sense of the premises will change.

So instead of A^B →C, it is actually A(A1&A2)^B →C (keep in mind that I use “&” instead of “^” for A1 and A2, because their nature and relation are yet to be explored for now), and A1 and A2 have to be true according to how the speaker intends it to be in order for one to obtain C from B and A; A whose sense is constructed from the senses of A1 and A2. And it is not impossible for us to break A1 and A2 apart, like what we have done before with A. So it is possible that we have A(A1(a1&a2&a3)&A2)^B →C and so on and so forth.

However, when we do make a conclusion, we rarely, if ever, break our premises apart. A, B, and C are treated as wholes which cannot be divided further, even though in truth it is possible to divide each of them into smaller premises and find faults in any of them. In fact, it is also one of the many ways that have driven the progress of philosophical thoughts. The fact that we can break A, B, and C apart into smaller components, find a fault in any of them, then derive an entirely new conclusion from it even though it still, for example, starts from A.

For example:

A: How we perceive things depends on our life’s experiences
A1: How we perceive things
A2: Perception depends on our life’s experiences.


And we can say that A1 here means:

Perception is such that what we perceive is precisely what is outside, for consciousness is nothing but the consciousness of the outside world. Therefore, how we perceive things is direct. We immediately know what’s outside without any possibility of not knowing the things in themselves.

And so, now A1 means that how we perceive things is direct, how does it relate to A2? Let’s just say A2 is:

A2: [perception (A1)] depends on our life’s experience.
It means: our ability to recognize things is based on the things we’ve learned in the past.


Therefore, the relation between A1 and A2 becomes:

What we see is seen through different functionality lens. The functionality of a tool is informed by past experiences. We might see the same thing, a hammer, for example, but if we have never seen a hammer before, we might not know what “thing” this is, while another person who’s already accustomed to using such a tool immediately recognized it as a hammer along with how to use it. However, “knowing” what it is doesn’t mean we see two different things.

So in a sense, A is still correct. How we perceive things depends on our previous experiences. However, even though A as a statement might still be correct in that sense, it might not be the sense which the person who stated it first meant it to be. For him, it is possible that:

A: How we perceive things depends on our life’s experiences.
A1: How we perceive things
It is impossible for us to know the thing in themselves. We only know the phenomena, and this phenomenon is only possible through a series of judgments and valuation.
A2: [Perception (A1)] depends on our life’s experiences.
If perception depends on judgments and valuation, therefore how we see a thing depends on our life’s experiences. For example, for a caveman who does not know that money means something, that is, as a thing based on which we measure the value of things, for him, money is without value, or at least, its valuation is different from the eyes of a businessman who understands money. Now if the caveman fails to understand what money is to its fullest extent, then can we really say that how a caveman sees money is the same as how a businessman sees money?

Because A1 and A2, which construct the meaning of A as a whole are thought to be different from the one we previously thought of, the meaning of A is also different. Now the difference in meaning, although it is still A, affects how we obtain B before obtaining C. One might want to say that if the meaning of A from one person to the next is different, then they’re not really talking about A. Perhaps, one of them is talking about A and the other one about D instead of both of them talking about A, even though on the surface they appear to be talking about A. However, when we reduce it to both A1 and A2, that might not be the case, for their disagreement refers to the same thing, that is, in this case, how we perceive things. If they’re talking about two different things, then there will be no debate whatsoever.

Imagine the word “mine”. It is conceivable that when, for example, two persons who are walking on a field, then one of them, let’s just call him “Q”, who has lived in the area for a long time and is familiar with the field tells the other person, let’s just call him “T”, who’s new to that area, that, “there’s a mine there”. “T” might interpret it as there’s a mine there as in mining for resources or a mine which means a bomb. Now imagine that there is a misunderstanding. When “Q” says a “mine”, “Q” means that there’s a mine that was used to mine coal, but is now deserted, while when “T” hears it, he thinks that “Q” is referring to a bomb, for some reason. And when they arrive at the mine, “T” protests because he’s hoping to see a World War 2 bomb instead of an old abandoned mine. “Q” can then reply, “but it’s a mine!”. Here we can clearly see that while they’re both referring to a “mine”, in their mind, they’re thinking of two different things, E and F. And in this case, there will be no debate. There might be protests if T thinks that he has been wronged (for some reason), but there will be no disagreement over what a mine is. They’ll both understand that they think of two different things, but that will be it.

Now let’s return to our previous example of perception. Can we think of people disagreeing about the meaning of A1 and A2 as actually talking about two different things in the same sense as the mine example before? In this case, the disagreement revolves around the definition of perception, and along with it, how perception works. How perception works and the definition of perception, in this case, affects one another. One cannot define perception without roughly outlining the supposed workings of perception, and vice versa. If that’s the case, then it is clear that when they disagree on how perception works, they also disagree on its definition, and vice versa. However, unlike the previous case, in this one, none of them will just dismiss it as a simple misunderstanding. Even though they’re using different definitions of perception, they won’t think that they’re referring to two different things. In their mind, it is still about A1 and A2, and this sameness isn’t just apparent. They both know that when they mention the word “perception”, they’re referring to one and the same thing despite their differences in definition. And we both apparently know that they’re talking about the same thing as well. That’s the reason why they have to disagree over it instead of just understanding that it is a misunderstanding and walk away. From here, we can realize that a word’s definition isn’t the essence of it. If a word’s definition is the essence of the meaning of the word, then by defining two words differently, there will just be a misunderstanding. The reason why A can be broken down into A1 and A2 is because A has to mean in a certain sense only for it be different in its details. So even though they’re defining perception differently, they’re in a sense still referring to the same thing, opening the possibility of A being broken up and interpreted in a different way, depending on its relations with other rules of the game being played, while at the same time not being dismissed as a misunderstanding between the two. Therefore, a difference in definition does not necessarily mean that they’re talking about two different things

In this case, Wittgenstein is right. A word doesn’t refer to one particular thing as the essence of the meaning of the word. The meaning of the word is defined, in this case, by how the word is used. It is a part of a language game. The written definition of it is just like a guide to help people understand the usage of the word on a case-by-case basis. However, what the word means itself overflows from the definition. A definition can’t contain the whole meaning of the word. In our everyday life, it is even not entirely necessary for us to be able to define a word whenever it is asked. As long as we can use it according to the proper rule of the game being played, we have understood what the word means. This brings us to the peculiarity of drawing conclusions. Ideally, for a conclusion to be drawn, each premise has to be self-contained. Each premise has to be true (or false) according to its rules so that we can draw valid conclusions from each of the premises. However, with the peculiarity of what a word can mean, it is impossible to have a thoroughly self-contained premise. Each premise is like a piece of cloth with its thread hanging from all its sides, and when one of the thread is pulled, the premise unravels and falls apart. And if that’s the case, then how can we ever draw a valid conclusion?

Every time we draw a conclusion from a certain set of premises, it is impossible for us to thoroughly make sure that every premise is true. Even if a premise is apparently true, but because each premise can theoretically be broken up, it can never be certainly true. Just as we have seen before, A can be broken up to A1 and A2, and C, which can be obtained if we follow A^B before going to C, can only be true depending on how A1 and A2 are interpreted, and therefore what does A mean. Depending on what A means, it can make B means something different from the person stating first conceives it to be just because it is connected to A in a different sense, then if B means something different, it is entirely possible that we won’t obtain C, assuming B is still relevant at all (after all, if premise A is about pizzas and premise B is about cars, for example, it doesn’t matter if both premises are true. It might not make sense if we suddenly talk about cars when we’re talking about something else). This means that for C to be valid, then A has to mean exactly so and so, and B must also precisely mean so and so in relation to A. But this exactness isn’t going to be found in real life. When we draw a conclusion, the thought that A is composed of A1 and A2 (keep in mind that even A1 and A2 can be further dissolved into smaller propositions) might not even cross our minds. And if they don’t cross our minds, what kind of status do they have? Is it possible that their status is that they are simply assumed to be such and such inexplicitly? While it is possible to dissolve it, we first assume that the premise’s meaning is such and such, and therefore if it is to be dissolved, the components will have to be such and such. The meaning of A is such, therefore, if A is built from A1 and A2, then to construct the meaning of A that is such and such, it has to follow that A1 and A2 must mean such and such. This we do without explicitly assuming it as such, for in most cases, we don’t bother to think that far. The meaning of A itself is enough, and if someone asks us about the details, it naturally follows from A through deductive reasoning. With one stroke, we have formed a premise which contains A1 and A2 assumed to be such and such even without realizing it, otherwise, there will be an impossibility of moving from one premise to another.

What is the proof of this inexplicit assumption? It is that we can define and explain what every premise means. If we can obtain the meaning of the premise, it means that the meaning which composes the meaning of A has to be thoroughly elucidated as well, otherwise, there can be no A. So even if A1 and A2 might follow from A through deductive reasoning, the premise itself is still built from A1 and A2. In this case, therefore, deductive reasoning does not serve to create something new, something which follows from A, but it is to elucidate even further what A has to mean. However, there are cases that when we ask a person what does a premise mean, at some point, he’ll realize that one of the building blocks of a premise means nothing, that his conclusion has been based on something that cannot be obtained. If that the case, how does he draw his conclusion? Can his conclusion be just dismissed as false?

That might not be the case, for if we trace it further, there will always be a point where we reach something that is indefinable and/or beyond the reach of our understanding. Take the premise:

A2: [perception (continuity from A1)] depends on our life’s experience

It is further elucidated into

A2.1: Knowledge and understanding compose our life’s experiences
A2.2: Our life’s experiences inform us on how to make sense of what we see

— — — — — — — — — — — — — — — — — — — — — — — — —
A2: knowledge and understanding inform us on how to make sense of what we see (which is equal to [perception] depends on our life’s experiences).


Then we can further break apart, for example, A2.1, into smaller components. However, we might not know how precisely does knowledge and understanding work, nor how exactly to define it. Just like what we’ve seen with perception, it is possible that disagreements regarding the definitions and the workings of knowledge and understanding lead to two differing conclusions. But even worse, such as what we have in this case, we even might not know at the moment what is the right definition of knowledge and/or understanding nor how they work. Even if we know what knowledge and understanding mean, just like what we’ve seen previously with perception, it is not enough to make sure that we know that it is so. But if we cannot define nor explain the workings of understanding and knowledge, does that mean that our premise will never obtain its necessary truth value? What is there to assume if the thing that we’re supposed to be assuming now lies beyond the breath of possible assumption because it is beyond our capabilities to do so?

This means that it is not entirely possible for us to immediately assume inexplicitly that A1 and A2, along with their components, are defined and how, if we’re talking about things having particular functions, it works. And since it is said to be inexplicit, what difference does it have if we instead just don’t actually think about it at all. Since we cannot always assume the components to be such and such, then it is possible that when we are making a premise, we completely gloss over it instead. Instead of the components assumed to have always been there before being elucidated later when someone asks us to do so, it is entirely possible that there’s no such assumption, and the elucidation of its components come only after someone (or we ourselves) asks what exactly does that mean. It means that instead of deductive reasoning just elucidating what is already there from A, it is possible that when we explain what A is, we’re really deriving something new out of it. So instead of A(A1&A2)^B →C, it is possible that we take A off from the chain of A^B →C, then we create another chain of premises (e.g. A1^A2 →A). Then A1 and A2, if we want to connect it to the A^B →C links, becomes A1^A2^B →C. But even so, the senses of A1 and A2 are contained in A. Therefore, can we really think of it as an entirely different premise from A? After all, don’t A1 and A2 come from A i.e. A1 and A2 are the meaning of A? So what’s the relation between A1, A2, and A?

If A1 and A2 are the meaning of A, is it not the same as A1 and A2 are A? If that is the case, then it doesn’t really mean that A1 and A2 are something which are new. Unlike B and C, who mean something other than A, but follows from A, A1 and A2 are basically what A means. So it is not new in that sense. Even though, upon closer inspection, A1 and A2 might be interpreted differently, therefore making A has a different meaning than what the first person stating it means A is, it is still, in a sense, A. It is still true that how we perceive things depends on our life’s experiences, but just in a slightly different sense, a difference that might not warrant replacing the symbol entirely with something else. Therefore the case is different from when in A^B →C, B is then replaced by F, C in a sense will still retain its meaning as a premise, although now, depending on the relation of A and F, C may now be thought as false (or still true, in a certain sense). However, A, B, F, and C are different entities. The meaning of C isn’t composed of A and/or B, nor the meaning of B composed from C and F, etc. It follows from the previous premises, it is only obtainable if we follow from previous premises, but its meaning isn’t consisted of previous premises. So even if deductive reasoning makes something new (A1 and A2), it doesn’t make something new in the sense of B and C.

But is it not possible that when we change the meaning of A1 and A2, A itself will cease to be A? But then how can we say that A1 and A2 compose the meaning of A? Won’t it be, instead of composing the meaning of A, it is the source of A’s destruction? Even when we say that A1 and A2 might mean something different from what the first person stating it means it to be, is it not possible that it has become something else, L, for example, instead of remaining to be A? Let’s return to our first example:

A: How we perceive things depends on our life’s experiences.
B: We have different life’s experiences
— — — — — — — — — — — — — — — — — — — — — — — —-
C: We perceive things differently.


We’ve seen before that depending on what both A1 and A2 mean, A might mean something different, and even if the sentence itself technically speaking hasn’t changed, doesn’t it now signify something different? If the symbol is the same (e.g. A), now that it means something different, then shouldn’t it no longer be A? Perhaps even though the sentence itself technically looks the same, the similarity is just skin deep. Perhaps if we state it, instead of as “A”, we state it as A1&A2, (although depending on the interpretation, it might as well be A1&Z2), we might realize that even though the label is A and the words in the sentence are the same, they’re still essentially different. So in short, if we have:

(1)
A: How we perceive things depends on our life’s experiences
A1: How we perceive things is direct
A2: How we recognize things depend on what we learned in the past


Then we also have:

(2)
A: How we perceive things depends on our life’s experiences.
A1: How we perceive things is affected by judgment and valuation
A2: Our judgment and valuation is based on what we’ve learned in the past


We can see that label A1 and A2 are just labels. In meaning, while (1) means something else, that is, we can see the same thing, while (2) means we cannot see the same thing, they cannot both be A. While (1) might be A, while (2) might just be D. It is because in (1), A is composed of A1 and A2, in (2), D is composed of Z1 and Z2.

However, there are two problems with regarding thinking it as containing an entirely different kind of meaning. First, just as we have seen, even if we disagree on what composes a given premise (A, for example), it is possible that the premise itself is still agreed upon by both parties in a certain sense. In this case, in (1) it means that there are differences in perception of functionality even though what is perceived as the same tool, a hammer for example, but in (2) it means what we perceive is to an extent different in itself. While the sub-premises of A have served to restrict its sense, taken in itself, A means something that in a sense is shared and understood by both parties, that in a way, what we perceive can be dependent on our past experiences. If that is the case, then A1 and A2, the sub-premises, might only serve as a restrictor and as a sub-note, linking A to a bigger picture that is bigger than what A says. In other words, the sub-premises are chaining A into a sense which doesn’t come from A itself but from what A relates to in something that is outside of A.

Second, this can only be true if we take into account the direction of the argument. If it goes from A1^A2=A, then still taking into account that A1 and A2 are what composes the meaning of A (its conclusion) like we’ve discussed before, then it is true that if it is made out of Z1 and Z2 (although as we might see later this isn’t as simple as it seems), then it might not precisely be A. The direction of the argument goes from Z1 to D. However, it is not impossible for us to go the other way around, that is, from A to A1 and A2. In short, instead of A coming from A1 and A2, A serves instead as the basis of meaning for A1 and A2. In other words, A1 and A2 have to be such and such so that A is obtained. If that’s the case, like we’ve stated before, even if A1 and A2 serve as the meaning of A, in actuality this might just be something technical. In actuality, instead of A1 and A2 serving the meaning of A, it is A that makes A1 and A2 what they are. In this case, and taking into account the first problem mentioned in the paragraph before, since the direction of the argument is from A to A1 and A2, A still means the same but its meaning is modified in relation to a greater argument by A1 and A2. However, A is still A.

Does the second case violate the rule of logic? Can its “conclusion” (because we have seen before that the relation between A1, A2, and A, isn’t exactly the same as A, B, and C) serve as the source of its own sub-premises? Is it possible that the direction of argument is just a veil for inductive and deductive reasoning? On the contrary, perhaps the direction of the argument is what determines whether we use deductive reasoning for this one case or inductive reasoning. It all boils down to which premise is going to be made as the basis of all premises. If what is going to be made the basis of the reasoning is A, then A1 and A2 are derived from A. In other words, what A1 and A2 mean have to conform to the sense of A. Therefore A1 and A2 can only serve as an elucidation for A, not the premises based on which A is actually made. While if it is A1 and/or A2 which is (are) to be made paramount, then it is true that A has to come from A1 and A2, instead of the other way around, and therefore A is the conclusion of A1 and A2, not the other way around.

And so, what makes a premise to be the anchor from which we are to link other premises? As we have seen, there is no basis on which we can confidently say that A1 or A2, something that we say to be what compose A, is the anchor. We have seen that it is possible that A1 can A2 are only elucidations for A, which is the anchor, and things can go the other way around as well. And whichever premise becomes an argument, it cannot escape the “elucidation problem”, that the premise can be broken up into further smaller premises in order to clarify its meaning. And it is not that we always have the capability to assume the sub-premises to be so and so. In fact, like what has been stated before, it is not always possible to do so, nor is it always required to be done. Not one premise can serve as an adequate ground that is not infallible in itself. No premise can be regarded as totally whole and final. And so, in the end, even if logic demands totality and finality, even philosophy itself is dependent upon the general form of language in order for it to function the way it is, despite its habit of violating the rules it owes its existence and smooth functioning from. Wittgenstein is right. In a proposition, there can be no one-on-one correspondence with a certain object. This whole problem is only possible if there is a need to elucidate the whole essence of a word. This problem only arises if we misuse language. But then in actuality, language works without the need for such an essence.

The only requirement for a conclusion to be drawn is that each premise shows an apparent “wholeness”, and this apparent “wholeness” is dependent on the understanding of each word. But since the understanding of each word is never in itself fully rigid and self-contained, the propositions based on which will never truly satisfy the requirements of formal logic in that sense. Nor does it need to be. In this case, it is almost as if the way we treat propositions and concepts are rather similar. “Wholeness” is only relative wholeness compared to something less. It is dependent upon our skills and experience and the situation around us. For the inexperienced eye, a car is just a car, a whole based on which functions can be derived from. For the experienced, a car is composed of a multitude of smaller elements. With propositions, for the inexperienced, perception might just be that, perception, something that is whole. However, for someone who might have engaged in epistemology for a long time, perception tells more than meets the eye. Therefore, a wholeness of a thing (or a concept) to an extent depends on the satisfaction of a certain standard of exactness, which itself cannot (or must not) be truly exact. It is whole as long as it permits smooth functioning of the discussion and the understanding of the task at hand; as long as each party understands what’s being referred to in the murkiness of the language games surrounding it. If that is the case, since “wholeness” is nothing but a relative term, a conceptual tool to outline the limit of the topic of discussion, then philosophy is destined to never be finished.

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