Sentential Logic Practice: Assessing a Proof of King’s Argument about the Purpose of Life

Recall that King set up his argument as follows:

Premise 1: Either our life’s purpose is achievable or it is not.
Premise 2: If it is achievable then after it is achieved we no longer have a purpose.
Premise 3: Then our lives would be futile.
Premise 4: If it is not achievable then attempting it would end in failure, and to continue would be futile.
Conclusion: Therefore, either way, our lives are ultimately futile.

Let’s begin by defining our library of symbolic terms:

A = Humanity’s life purpose is achievable at some point before death
N = A human’s life purpose ceases to exist if it is achieved
F = Human’s life purpose is futile if it ceases to exist
U = Attempting to achieve humanity’s life purpose will end in failure

This argument is definitely a valid one because we can assemble and test a sample derivation:

So if we provisionally assume A (‘Our purpose is achievable’), then we can eventually achieve it. Once we do, since our life purpose is like a desire that is eliminated (or ceases to exist) once it is satisfied, we no longer have a life purpose (N). And if we no longer have a life purpose, then our lives would be (or become) futile (F).

Now, if we provisionally assume ~A (‘Our purpose is NOT achievable’), then we will never be able to achieve it. It will always elude our grasp or its own completion. If our purpose is not achievable, then attempting to achieve that purpose would end in failure and our lives would be (or become) futile (U & F).

Regardless of whether our life purpose is achievable or not, King reasons, our lives would be (or become) futile, inevitably. That would hold true for everyone at all times and in all places.

The problem is that we have no reason to believe that a purpose is a one-and-done type of deal. It could be that life’s purpose is similar to being virtuous (i.e. it is an ongoing process rather than a completed product). Even if our life’s purpose were fulfilled, there are still various hypothetical situations and contexts in which one could reasonably expect to either have to (1) maintain the completion or fulfillment of their life’s purpose or (2) complete or fulfill a new or modified purpose for their own life.

There is no logical contradiction in this alternate definition of purpose. King’s article definitely gives us much to reflect upon, but ultimately his analysis relies on a faulty definition (or understanding) of purpose; an alternative definition provided can sidestep this problem though, thereby undermining the soundness of his argument’s conclusion.

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