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Category Archives: Logic

Summary: Einstein vs. Logical Positivism by Rossen Vassilev Jr.

Epistemology, Logic, Metaphysics, Philosophy of Science February 26, 2022 Leave a comment

The original article can be found at: https://philosophynow.org/issues/133/Einstein_vs_Logical_Positivism

Vassilev begins his article by pointing out that Logical Positivism was a philosophical movement that originated in the 1920s. Arguably its most critical mission was to establish the same methodology of science and mathematics for other fields, particularly philosophy. The logical positivists dismissed any and all ‘non-scientific’ speculation from genuine analysis or explanation. They insisted that such statements were literally meaningless; only statements that could be logically verified or corroborated through experiment/observation have meaning. This was known as the Principle of Verification (or Verification Principle) and was the driving philosophical and epistemological force behind the Vienna Circle (a particularly influential group of logical positivists).

According to the Principle of Verification, the meaning of any statement lies in its method of verification. Moreover, statements about, say, God or art or ethics would all suddenly be technically meaningless according to the logical positivists. Logical positivists were excited at this prospect because they were very much committed Naturalists. But not all philosophers were on-board with their philosophical approach or its underlying intentions.

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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.