One of the questions of philosophy is the truth of the immortality of the soul. Many philosophers have attempted to answer it. This is certainly true of Plato and Socrates. Plato answered this question in his dialogue Phaedo. In it are outlined four proofs that Socrates uses to prove the immortality of the soul. Through two objections from Socrates’ disciples, the first three proofs are shown to be weak of standing. Socrates then moves onto his fourth and final proof, which is considered to be his best. There seems to be a crucial problem with Socrates’ reasoning, however. It deals with the difference between a “given,” or self-defining truth, and a “proof.” Socrates says he is attempting to prove the immortality of the soul, but really he is only defining the soul as immortal. 
Socrates starts his final proof of the immortality of Soul first by telling those around him that he believes that teleological explanations of the world are superior. “…[W]e must discover how it is best for that thing to exist, or to act, or to be acted upon.” (97c-d) Socrates goes on to say that the ultimate purpose of the world is to “imitate” the Forms. With this in mind, Socrates says that an essence is the pattern or blueprint, the Form. Each essence has essential attributes. Without these essential attributes it wouldn’t be the specific essence that it is. It is with this fact, that essences need their essential attributes, that Socrates continues with his proof.
Socrates wants to show that Life is an essential attribute of Soul. If he can do this then Soul cannot plausibly be linked with Death and therefore Soul will be proven to be immortal. His reasoning behind this is that in the Realm of Forms, an essence cannot have both sides of a duality participating as an attribute at the same time. Therefore, if one side of the duality is an essential attribute, then the opposite end of the duality can never be linked with the essence. Socrates develops his proof with the theme that the Greek idea of the soul is of “the mover.” For something to affect or “move” the reality of particulars around it, said something must have a soul (105c). So Soul, as “the mover,” has the attribute of Life. It would not be the soul if it were not alive. To make this link binding and essential, Socrates uses an analogy. Socrates says that on an Odd-Even continuum, Three is always Odd. By its very nature it can only be Odd, it can never be Even. Four, on the other hand, by its very nature, can only be Even (103e-105b). Therefore, Socrates says that Soul, by its very nature, can only be linked with Life (105e). Just like Three only being Odd and Four only being Even. Game, set, and match.
One thing about Socrates’ analogy seems to strike a strange chord, though. His use of mathematics in his analogy is slightly suspect. Mathematics, numbers specifically, are self-defining. In geometry this is called a “given.” A given is just that because it defines itself. You don’t prove a given. They are the groundwork from where all other proofs are built. A given is therefore a definition that has a specified, self-defining meaning. A proof, on the other hand, is “a process that establishes … a truth or fact.” (Angeles 245)
This difference between a “given” and a “proof” is where Socrates would raise an objection. To Socrates both a given and a proof are definitions and “… a definition [is] a clear and fixed concept.” (Stumpf 39) While a particular event or thing may vary from instance to instance, each varied instance would revolve around a certain essential nature, or definition. (Stumpf 40) This definition was to Socrates the Form of what was being defined. Socrates devoted his entire life to finding the true definitions of things and the process through which he achieved this was dialectic. By asking questions like “What is a pious act?” and “What is virtue?” Socrates was hoping to give definition to such abstract concepts as piety and virtue.
The catch is that there is a fundamental difference between what Socrates called a definition and what is considered a given. This difference can be summed up by two separate types of definition: a nominal definition and a real definition. A nominal definition is “…any definition that explains the meaning of a word or symbol.” (Angeles 66) Opposed to that is a real definition which gives the essence or definition of a thing. The key difference between the two lies within a word or symbol versus a thing. An example of a word or symbol definition is “A square is a plane figure with four connected straight sides that form four angles that total 360.” An example of a definition of a thing is “Piety is that which is loved by the Gods.” The former is a mathematical given and receives its meaning from that which it is specified; it is self-defining. The latter is clearly debatable and is, in fact, debated by Socrates in the Euthyphro. The definitions or essences that Socrates is looking for could easily be called real definitions and the debating process through which these real definitions are found called dialectic.
As has been said, Socrates’ search for essences was through dialectic. However, you can’t “find” nominal definitions through dialectic. They are self-defining. Therefore, nominal definitions can’t be swept into the category of real definitions. Socrates ignores this fundamental difference between defining a word or symbol and defining a thing. He sweeps both under the same heading. It is this sweeping motion that causes Socrates problems in his proof of the immortality of the soul.
Socrates, by comparing Soul to mathematical givens, is basically saying that Soul, having the essential attribute of Life, is self-defining, a given. By calling Soul self-defining means that it cannot be proven through dialectic. It is to be taken as fact. But this defeats the purpose of Socrates trying to justify his claims. Socrates’ entire life was spent showing that other people do not have wisdom and, because he admittedly has none, that he is the wisest man alive. By calling Soul self-defining Socrates is admitting to know something: Soul has the essential attribute of Life. This is why Socrates tries to prove it and why he sweeps nominal definitions in with real definitions. If he can prove immortality, he can say that the link is logically and rationally evident given the clues provided. If the link is self-evident then the link is a given, the clues be damned.
Say we move beyond this development and consider Soul as being a separate entity to Body. Socrates makes it perfectly clear that Soul is separate from Body. Soul being the mover and a separate entity is to be taken as self-evident. And as has been stated Soul, as “the mover,” has the essential attribute of Life. If Soul was an essential attribute to Life then it would quite an easy thing to say that Soul is immortal. For something to have Life it must have a soul. But this is certainly not the case as we see that a tree is alive, yet does not have a soul. If it had a soul it would be able to affect and move the reality around it. A case can be made for a tree affecting the reality around it. Its root structure pushes the dirt out of the way so it can sink its roots further into the earth. The tree takes in water, sprouts leaves, and can even push objects out of the way if its trunk grows in a way that pushes against other objects. It is irrelevant whether Socrates meant trees have souls or not. “Then the soul always brings life to whatever contains her?” (105d) Socrates asks of his disciples. It is Socrates’ entire argument that Life is an essential attribute of Soul.
Now consider Body. Body moves up and down the Life-Death continuum. Why can’t Soul, as a separate entity, move up and down the Life-Death continuum? It has already been shown that if Soul’s immortality isn’t taken to be self-defining then it must still be proven that it is linked to Life. In looking at Soul as a separate entity and having its own Life-Death continuum a picture of Soul can be made from the one Socrates was proposing. It seems plausible that Body can be looked at as the material form of the Life-Death continuum. The arms, legs, and torso of a man, the trunk, leaves, and roots of a tree, a blade of grass; all of these can be considered the body of each particular living thing. Soul, then, can be considered the immaterial form of the Life-Death continuum. When Soul is linked with Body, Life arises. If not every living thing has a soul it can be said that Body is “clicked” into the Life position, but Soul is still in the Death position. Either way, it is the combination of Body and Soul that gives things the capability to act upon reality.
To illustrate this combination we can use the analogy of a sperm and egg. By themselves they aren’t much. When the two are fused together, however, is when life begins. Together the sperm and egg transform themselves into a living creature. When this living creature dies you don’t get back the sperm or the egg, though. When Body and Soul are fused together you get a living creature that can act upon its reality. When this living creature dies it is entirely conceivable that you get nothing in return. It is also conceivable that just Soul can be “clicked” on. I’m not proposing that it can or cannot, I’m merely proposing that the possibility of Soul having the attribute of Death exists.
Socrates was trying to prove, through dialectic, that Soul had the essential attribute of Life. What he gave us, instead, was a nominal definition of Soul in which it had the essential attribute of Life. A nominal definition cannot be proven, however, because a nominal definition is just that because it is just now being given meaning. In place of Socrates’ proof, a different kind of connection between Body and Soul and the Life-Death continuum has been offered, given the clues provided.
The only question that remains is why did Socrates lump “givens” and “proofs” into one category of definitions? Maybe Socrates had a moment of weakness before his death and wanted something concrete to pass on to his disciples, something for them to build on. This seems unlikely as the problem didn’t lie in the logic of his last argument, but in the structure of his logic, specifically in the way he categorized the answers he was given through dialectical reasoning. Maybe Socrates had a definite goal in mind when he set out to find the definitions of abstract concepts like piety, virtue, and the immortality of the soul and it clouded his judgment. All of these answers are pure speculation, though, and shouldn’t be bothered when considering Socrates’ value to philosophy. He gave us the process of dialectical reasoning and it was through this type of truth-seeking that allowed philosophy to become the force that it is. And it was this type of truth seeking that Socrates performed and espoused his entire life and he no doubt would have wanted it continued after his passing.
 Since this dialogue is considered one of Plato’s Early Dialogues, it is difficult to distinguish where Socrates’ philosophy stops and Plato’s picks up. Because of this I am using Socrates as the creator of the proofs as he is the protagonist in the dialogue.