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THE QUANTUM of EXPLANATION

~ Science, logic, and ethics, from a Whiteheadian Pragmatist perspective (go figure)

THE QUANTUM of EXPLANATION

Tag Archives: algebraic reasoning

Foolish Consistency?

18 Saturday Oct 2014

Posted by Gary Herstein in Critical Thinking, Logic, Philosophy of Logic

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Tags

algebraic reasoning, Compartmentalization, Critical Thinking

So I’ve previously floated some remarks about Emerson’s famous quote about a foolish consistency being the hobgoblin of a narrow mind. It seems reasonable that there might be something like a foolish consistency, but is that evident reasonableness actually validated in practice? And how might a person with a logical turn of mind validate, in turn, that reasonableness in theory? I’d like to explore this subject a bit by offering some informal remarks on formal logic, the thought being that there are actually reasons for learning the latter, yet intelligent things that can be discovered pursuing the former.

Formal logic, as it is traditionally taught and interpreted, holds that a formal contradiction is the End of Days. It is the thing that causes Jason Voorhees to drop his machete, Freddy Krueger to weep like a baby, and Michael Myers to pee himself hiding under his bed. It is the gate kicked open on the Pit of Hell, the black hole that swallows the universe, the Cubs winning the Series. OK, maybe not the “black hole” thing.

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Thinking about Thinking 3: Statistical modes

22 Friday Aug 2014

Posted by Gary Herstein in Climate Change, Critical Thinking, Philosophy of Logic, Philosophy of Science

≈ 5 Comments

Tags

algebraic reasoning, Climate change Denial, Critical Thinking, Logic, mathematics, Relational thinking, Statistics

Statistical thinking is one of the most important formal methods of engaging reality available to human beings. Sadly, it is also one of the more difficult, because human beings, in general, have absolutely no intuitive sense regarding probabilistic claims or statistical analyses. The people who do such things – even the ones that do them poorly – only reach such a stage of analysis after a significant amount of disciplined education. For the rest of us (and I must perforce include myself in this list) our statistical guesses only rise to the level of the merely appalling on those rare occasions that they are not completely idiotic. Quite usable texts can be had for the downloading (although the interested reader might consider supporting the Open Intro foundation), but one still requires no small measure of determination to “climb Mount Statistics” on one’s own. It is a challenge I’ve never completed at any substantive level, making this post more than a trifle daunting. However, even lacking any measure of expertise on the subject, there remain a few intelligent things that can be said, even by someone like me.

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Thinking about Thinking 2: Algebraic Reasoning

13 Wednesday Aug 2014

Posted by Gary Herstein in Critical Thinking, General Philosophy, Philosophy of Logic

≈ 3 Comments

Tags

algebraic reasoning, Relational thinking

“I’m never going to use that!” Variations of this war cry are frequently lodged in protest against that Torquemada-ish, 7th level of hell known as “high school algebra.” I am inclined to sympathize with this lament, but not for the reasons one might suppose. The problem, you see, lies not in the pragmatics – the usefulness (or lack thereof) of the subject – but rather in the pedagogical techniques and intentions with which it is presented. Algebra, as it is almost universally taught in secondary school, is little more than a peculiarly mangled arithmetic. Algebra as it ought to be taught is relational logic, it is algebraic reasoning.

So what does the above mean?

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Science, logic, and ethics, from a Whiteheadian Pragmatist perspective (go figure)

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