The metaphysical presuppositions of formal logic

&gt; This has some notoriously odd results (known as the “paradoxes of material implication”)<p>&gt; You’ll still get weird results (known as the “paradoxes of strict implication”)<p>This is obviously building up to the concept of relevance logic (called &quot;relevant logic&quot; in the UK and Australia) – <a href="https:&#x2F;&#x2F;plato.stanford.edu&#x2F;entries&#x2F;logic-relevance&#x2F;" rel="nofollow">https:&#x2F;&#x2F;plato.stanford.edu&#x2F;entries&#x2F;logic-relevance&#x2F;</a> – and no doubt Feser knows about it, but isn&#x27;t taking the reader there. It seems to me an odd omission.<p>A lot of his argument is actually against <i>classical logic</i>, not <i>formal logic</i>. Many philosophers and logicians agree that classical formal logic is deeply flawed, and have proposed various non-classical formal logics in response (relevance logic, constructivist&#x2F;intuitionistic logic, paraconsistent logic, among others). But in this blog post he doesn&#x27;t interact with or mention any of that work.<p>&gt; To show that the eternalist conclusion really follows, and does not merely falsely appear to do so, would require independent metaphysical argumentation<p>I&#x27;ve never understood how Feser manages to believe in both presentism and divine eternity. In my mind they are mutually exclusive propositions. Atheism and process theism &#x2F; open theism both go well with presentism. But the eternal God of classical theism, who knows all of time as one single moment, seems to me to have an eternalist approach to time as an inevitable consequence.

This article does a great deal to point out the problem, but then just kicks the can down the road.<p>Yes, metaphysics comes before Logic but metametaphysics comes before metaphysics. Ad infinitum.<p>All this does is shift the discussion from the laws of logic to the laws of metaphysics - it is turtles all the way down.<p>There is no way to get off this hamster wheel without a shift of perspective, but computer scientists should feel right at home anywhere recursion arises.<p>Focus on the laws and the lawmaker. What are laws? Why do we create laws? What do we use laws for? How effective are we at encoding these laws in language?<p>When we think of laws as designed rather than discovered we become more conscientious in our own inventions.

Edward Feser doesn’t seem to me to be genuinely interested in challenging his own presuppositions through metaphysics or philosophy, or in communicating the work of others to a wider audience. If the posts that appear on this site are anything to go by, he seems to specialize in a specious species of polemic and obfuscation designed solely to justify and promulgate his political and religious views. If it lends a sense of purpose to his life, makes him a living or gives him a feeling of self-importance&#x2F;bolsters his worth among his peers, who am I to criticize? Perhaps it is actually a deep satire with some ulterior motive. As an agnostic, one can only hope that a capital punishment for more catholic thinkers is never re-introduced. <a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Edward_Feser" rel="nofollow">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Edward_Feser</a>

This seems too vague to me, like a lot of philosophical posts out there.<p>&gt; For example, if it is true that Aunt May believes that Spider-Man fights crime, then even though Spider-Man = Peter Parker, it does not follow that Aunt May believes that Peter Parker fights crime.<p>If you can&#x27;t substitute Peter Parker for Spider-Man, then they are by definition not equal...

It&#x27;s difficult to engage with the content of the article head-on because it&#x27;s pretty dense with concepts, but it made me think of two points -<p>First, when trying to put together a chain of truth-functional syllogisms, if-then logic doesn&#x27;t really suit the requirements. For propagating boolean truth through the network, digital AND gates are a better fit. If two propositions are false, you really do want the conclusion to be false, not true. If one of the propositions are false, you want the conclusion to be false, regardless of whether the first or second propositions are false. Also, in this case, truth is more an intuitionist concept than a classical concept; where the truth value represents provability - false means &quot;it is false that this conclusion is proven true&quot;, not &quot;the semantic meaning of this conclusion is false&quot;.<p>Second, I&#x27;m not too familiar with the differences of materialist logic, but it seems that the goal of trying to nail down the semantic meaning of every statement is a goal that will never be met. It seems a more tractable goal to have your machinery reflect the form-validity rather than the content-validity - fully judging the semantic content is something that ultimately is better judged by the people experiencing the content.

Essentialists are map-makers eternally searching for a map that exactly matches the territory, and will forever be disappointed.<p>Some of the metaphysical problems with logic that the article tries to approach do exist, but in my opinion they are the domain of decision theory, not philosophy.

It&#x27;s important to sometimes step back and think about whether what you are doing actually makes sense. There are some assumptions about how formal logic is done in ITP (interactive theorem proving) systems that should be challenged. Here is my opinion about that: <a href="https:&#x2F;&#x2F;doi.org&#x2F;10.47757&#x2F;practal.1" rel="nofollow">https:&#x2F;&#x2F;doi.org&#x2F;10.47757&#x2F;practal.1</a>

IMO This article is a mess.<p>Starts with an interesting premise, the foundations of logic (or rather, what people are taught as the foundations of logic) introduces unspoken assumptions. Then it goes on to illustrate with the worst example I can think off.<p><pre><code> modern physics’ mathematical representations [...] tend to insinuate an eternalist rather than presentist conception of time. </code></pre> I don&#x27;t know which modern physicists he talks about, but pretty much any physicist will tell you time has a starting point, and none will make any claims to the existence or non-existence of an ending point. If anything, the lesson from modern physics is to enjoy the (relatively) brief period of time our planet is hospitable to humans.<p>Then it descends further into an unnecessarily jargon that can only be described as a debate about the sex of angels.

Category theory would help them. Yoneda&#x27;s lemma tells us that elements of collections are uniquely isomorphic to the transformations which create those elements. This explains the butterfly effect where seemingly-unrelated parts of logical statements are causally connected.<p>This post would have had bite 70 years ago, before we had &quot;formally formal&quot; theories of categories which can subsume any possible set theory. But now the door is closed. Interestingly, the transformations seem to be more important than the elements; whether a logic is e.g. reversible is a property of transformations and not collections.