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29 votes
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Why do universities not teach constructive mathematics to CS undergraduates?

Let me offer a few thoughts, specific to mathematical pedagogy in computer science (in particular for the states): (a): a typical BS computer science program barely has time to touch on computational ...
emesupap's user avatar
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17 votes

Why do universities not teach constructive mathematics to CS undergraduates?

"Constructive mathematics is distinguished from its traditional counterpart, classical mathematics, by the strict interpretation of the phrase “there exists” as “we can construct”." The ...
Jo Wehler's user avatar
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16 votes

Why do universities not teach constructive mathematics to CS undergraduates?

So we're clear, mathematical constructivism is a logic/philosophic approach to conceiving mathematical activity. That's pretty remote from undergraduate CS pedagogy. From WP: In the philosophy of ...
J D's user avatar
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11 votes
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How come intuitive thinking is related to constructing a proof?

Intuitionism is a philosophy of mathematics that was introduced by the Dutch mathematician Luitzen Egbertus Jan Brouwer (1881–1966): he developed a very personal philosophy of mathematics that founds ...
Mauro ALLEGRANZA's user avatar
8 votes

Have I contradicted the "law" non-contradiction?

No, you did not contradict LNC. In your program (( A == A ) and (A != A)) is true, but you also changed the function of '==' and '!=' so that '!=' is not longer a negation of '==': Your '==' function ...
E...'s user avatar
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6 votes

Why do universities not teach constructive mathematics to CS undergraduates?

So there's something which might be worth discussing here; namely, given that the primary dispute between constructivists and classical mathematicians relates to the transfinite, does the dispute ...
Paul Ross's user avatar
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6 votes

Why do universities not teach constructive mathematics to CS undergraduates?

Due to many reasons, main ones are follows: It is computer science program, and not philosophy program. Certainly, foundations are in philosophy (mathematical logic), but curriculum focusses on well-...
Ajax's user avatar
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5 votes

How Relativistic is Social Constructivism?

I do not think that Searle will agree on labelling with "Social constructivism" his theory about Social relaity. According to Ian Hacking, Searle's book The Construction of Social Reality (1995), is ...
Mauro ALLEGRANZA's user avatar
4 votes

Is perspectivism a subtype of relativism?

From the OED... Relativism is the doctrine that knowledge, truth, and morality exist in relation to culture, society, or historical context, and are not absolute. Perspectivism is the theory that ...
Marco Ocram's user avatar
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4 votes

Why would constructivists object to the common definition of a function?

This connects with something Thomas Forster said, when he rightly highlighted the distinctively modern conception of a function as any old pairing of inputs and outputs, whether we can define it or ...
Julius Hamilton's user avatar
4 votes

How come intuitive thinking is related to constructing a proof?

The second sentence of the SEP's article on mathematical intuitionism gives a pretty good explanation of why it is named as it is: Intuitionism is based on the idea that mathematics is a creation ...
Not_Here's user avatar
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4 votes
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What does mathematical constructivism gain us philosophically?

It does bring in more than (ephemeral) security of foundations, but what it is more of is different for different people. The early intuitionists like Brouwer and Weyl saw mathematics as free play of ...
Conifold's user avatar
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3 votes
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For a mathematical realist, is there a distinction between real mathematical objects and constructed mathematical objects?

Yes there is. Maddy takes this position in Perception and Mathematical Intuition, and so do recent mathematical Aristotelians. The alternative of believing it all real usually comes with full blown ...
Conifold's user avatar
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3 votes

Have I contradicted the "law" non-contradiction?

Maybe you would understand @Logikal comments if you think about it like this: A physical machine (computer) takes a set of input conditions, then evaluates/operate according to a predetermined logic ...
christo183's user avatar
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3 votes

What condition(s) must be met to claim that something exists?

Following Quine, a fairly popular approach to the question of what exists is to say that those things exist that are indispensable to our best scientific theories. On this view, electrons exist ...
Bumble's user avatar
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3 votes

Why do universities not teach constructive mathematics to CS undergraduates?

There seems to be three questions here: Why not teach nuanced philosophy Why not teach constructivism, a particular approach to mathematics Why are you even teaching Calculus I Why teach Calculus is ...
Cort Ammon's user avatar
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2 votes

What condition(s) must be met to claim that something exists?

What condition(s) must be met to claim that something exists? The conditions for making any claim whatsoever are that you be able to make that claim. This is probably not the answer you are looking ...
Speakpigeon's user avatar
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2 votes
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Is perspectivism a subtype of relativism?

Is perspectivism a subtype of relativism? Yes. Relativism in its naive form is that truth is merely relative, so perspectivism, which asserts that truth is relative to the perspective of the agent is ...
J D's user avatar
  • 28.5k
2 votes

To what extent can reality be described as 'culturally constructed'?

There are myriad answers to this question and all of them, informed by their own experience, and thus, different. Ultimately, constructions (like mathematics) point to a universal experience. ...
Al. H's user avatar
  • 21
2 votes

What condition(s) must be met to claim that something exists?

There are several accounts of existence. The two most popular are probably the classical notion and the Frege/Russel notion. The classical notion is that existence is something that some objects have ...
David Gudeman's user avatar
2 votes

Is the axiom of dependent choice constructive?

The Axiom of Dependent Choice (ADC) can be considered constructive (or perhaps more correctly, effective) as Schechter wrote, for the reason that it does not have any of the paradoxical consequences ...
Mikhail Katz's user avatar
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2 votes

Are Bourbaki and Deligne Mathematical Realists?

Bourbaki have insisted that they are interested in the way mathematicians do their work rather than in foundations, and there are indications that their philosophy of mathematics is not carefully ...
Mikhail Katz's user avatar
  • 1,461
1 vote

Is the axiom of dependent choice constructive?

Whether AC has counterintuitive/nonconstructive ramifications is a finely parsed question. In "Types, Sets, and Categories", John L. Bell says (pg. 43): ... to assert AC under the “formulas-...
Kristian Berry's user avatar
1 vote

What condition(s) must be met to claim that something exists?

I think, the question is not well posed: The word "exists" has several different meanings. Something exists if it's part of our universe. As such, horses exist, but unicorns don't. This ...
cmaster - reinstate monica's user avatar
1 vote

What condition(s) must be met to claim that something exists?

I would say anything that can be perceived from six senses " touch, sight, hearing, smell, taste or thought " can be claimed of existing. For example : I see a bat in front of me so I claim ...
AbduRahman's user avatar
1 vote

Why do universities not teach constructive mathematics to CS undergraduates?

Interesting question. I suspect there could be researchers who thinks similar to this person (well, except for the Calculus dismissal). The following is about how people writes software today and how ...
JosEduSol's user avatar
  • 317
1 vote

Actual and potential truth for neo-verificationists

The following passage that I am quoting at length from Dag Prawitz ("Intuitionistic Logic: A Philosophical Challenge" in Logic and Philosophy edited by G. H. von Wright, Hague, Martinus ...
Tankut Beygu's user avatar
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