Sentential Logic: Rules of Inference for Deriving Proofs

Epistemology, Logic February 4, 2022 Leave a comment

EXCELLENT RESOURCE AVAILABLE HERE: https://courses.umass.edu/phil110-gmh/text/c05.pdf

Ampersand-In (&I): If one has available lines, A and B, then one is entitled to write down their conjunction, in one order A&B, or the other order B&A.

Ampersand-Out (&O): If one has available a line of the form A&B, then one is entitled to write down either conjunct A or conjunct B.

Wedge-In (∨I): If one has available a line A, then one is entitled to write down the disjunction of A with any formula B, in one order AvB, or the other order BvA.

Wedge-Out (∨O): If one has available a line of the form A∨B, and if one additionally has available a line which is the negation of the first disjunct, ~A, then one is entitled to write down the second disjunct, B. Likewise, if one has available a line of the form A∨B, and if one additionally has available a line which is the negation of the second disjunct, ~B, then one is entitled to write down the first disjunct, A.

Double-Arrow-In (↔I): If one has available a line that is a conditional A→B, and one additionally has available a line that is the converse B→A, then one is entitled to write down either the biconditional A↔B or the biconditional B↔A.

Double-Arrow-Out (↔O): If one has available a line of the form A↔B, then one is entitled to write down both the conditional A→B and its converse B→A.

Arrow-Out (→O): If one has available a line of the form A→B, and if one additionally has available a line which is the antecedent A, then one is entitled to write down the consequent B. Likewise, if one has available a line of the form A→B, and if one additionally has available a line which is the negation of the consequent, ~B, then one is entitled to write down the negation of the antecedent, ~A.

Double Negation (DN): If one has available a line A, then one is entitled to write down the double-negation ~~A. Similarly, if one has available a line of the form ~~A, then one is entitled to write down the formula A.

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

Logic January 28, 2022 Leave a comment

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.

Commentary: Looking for the Purpose of Life by Brian King

Logic, Metaphysics, Philosophy of Religion January 16, 2022 Leave a comment

*The original article can be found at: https://philosophynow.org/issues/147/Looking_for_the_Purpose_of_Life

Brian King writes a solid introductory piece about what the purpose of life may be and why it is such a thorny question for philosophers to answer.

*Video below unrelated, but still entertaining and quasi-relevant!*

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Brief philosophical insights

General Philosophy, Metaethics, Metaphysics December 30, 2021 Leave a comment

What if we combined Schroedinger’s cat with Santa Claus? Would Santa Claus only exist if we believed in him in that moment? Would he only exist for those who believed in him? If so, would non-believers ever receive any coal in their stockings? Then, let’s go one step further with this line of reasoning. If Santa Claus only existed if we believed in him, what would it mean for those who did not believe in God/Allah? How could we either blame or praise anyone if they simply did not share our same beliefs?

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