about two differrent opinions in mathematics Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Definition of “non-constructive proof”What did Gauss think about infinity?What would happen if ZFC were found to be inconsistent?Mathematics, Philosophy and writing.About mathematics and the physical worldHow much are mathematics driven by applications?What is more important in Mathematics, Theorems or its Proofs?Some Philosophical Questions About Mathematics and LogicAre there still mathematicians who don't accept proof by contradiction?About proofs that we cannot verify every step by hand
Is it possible to boil a liquid by just mixing many immiscible liquids together?
What is the longest distance a 13th-level monk can jump while attacking on the same turn?
Does accepting a pardon have any bearing on trying that person for the same crime in a sovereign jurisdiction?
Did Xerox really develop the first LAN?
If Jon Snow became King of the Seven Kingdoms what would his regnal number be?
Why don't the Weasley twins use magic outside of school if the Trace can only find the location of spells cast?
Why are there no cargo aircraft with "flying wing" design?
Are my PIs rude or am I just being too sensitive?
Sorting numerically
Is there a Spanish version of "dot your i's and cross your t's" that includes the letter 'ñ'?
What is a Meta algorithm?
Should gear shift center itself while in neutral?
IndentationError when pasting code in Python 3 interpreter mode
Why was the term "discrete" used in discrete logarithm?
List *all* the tuples!
Is there a way in Ruby to make just any one out of many keyword arguments required?
macOS-like app switching in Plasma 5
Java 8 stream max() function argument type Comparator vs Comparable
How does cp -a work
How to say 'striped' in Latin
What is this single-engine low-wing propeller plane?
Can inflation occur in a positive-sum game currency system such as the Stack Exchange reputation system?
Single word antonym of "flightless"
Is it true to say that an hosting provider's DNS server is what links the entire hosting environment to ICANN?
about two differrent opinions in mathematics
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Definition of “non-constructive proof”What did Gauss think about infinity?What would happen if ZFC were found to be inconsistent?Mathematics, Philosophy and writing.About mathematics and the physical worldHow much are mathematics driven by applications?What is more important in Mathematics, Theorems or its Proofs?Some Philosophical Questions About Mathematics and LogicAre there still mathematicians who don't accept proof by contradiction?About proofs that we cannot verify every step by hand
$begingroup$
My question is: what is the name of mathematicians who ignore the proofs by contradiction and say all of the proofs should be constructive, and what is the name of opposite opinion?
philosophy
asked Mar 26 at 6:09
eddieeddie
11
$endgroup$
add a comment |
$begingroup$
My question is: what is the name of mathematicians who ignore the proofs by contradiction and say all of the proofs should be constructive, and what is the name of opposite opinion?
philosophy
asked Mar 26 at 6:09
eddieeddie
11
$endgroup$
5
$begingroup$
The first are "constructivists", the second are "mathematicians".
$endgroup$
– Lord Shark the Unknown
Mar 26 at 6:11
2
$begingroup$
The first ones are the idiots and the second the cool guys. ;-)
$endgroup$
– amsmath
Mar 26 at 6:12
$begingroup$
Useful reading is Eric Schechter's 2001 expository paper Constructivism is difficult.
$endgroup$
– Dave L. Renfro
Mar 26 at 6:34
add a comment |
$begingroup$
My question is: what is the name of mathematicians who ignore the proofs by contradiction and say all of the proofs should be constructive, and what is the name of opposite opinion?
philosophy
asked Mar 26 at 6:09
eddieeddie
11
$endgroup$
My question is: what is the name of mathematicians who ignore the proofs by contradiction and say all of the proofs should be constructive, and what is the name of opposite opinion?
philosophy
philosophy
asked Mar 26 at 6:09
eddieeddie
11
asked Mar 26 at 6:09
eddieeddie
11
asked Mar 26 at 6:09
eddieeddie
11
asked Mar 26 at 6:09
eddieeddie
11
asked Mar 26 at 6:09
eddieeddie
11
11
5
$begingroup$
The first are "constructivists", the second are "mathematicians".
$endgroup$
– Lord Shark the Unknown
Mar 26 at 6:11
2
$begingroup$
The first ones are the idiots and the second the cool guys. ;-)
$endgroup$
– amsmath
Mar 26 at 6:12
$begingroup$
Useful reading is Eric Schechter's 2001 expository paper Constructivism is difficult.
$endgroup$
– Dave L. Renfro
Mar 26 at 6:34
add a comment |
5
$begingroup$
The first are "constructivists", the second are "mathematicians".
$endgroup$
– Lord Shark the Unknown
Mar 26 at 6:11
2
$begingroup$
The first ones are the idiots and the second the cool guys. ;-)
$endgroup$
– amsmath
Mar 26 at 6:12
$begingroup$
Useful reading is Eric Schechter's 2001 expository paper Constructivism is difficult.
$endgroup$
– Dave L. Renfro
Mar 26 at 6:34
5
5
$begingroup$
The first are "constructivists", the second are "mathematicians".
$endgroup$
– Lord Shark the Unknown
Mar 26 at 6:11
$begingroup$
The first are "constructivists", the second are "mathematicians".
$endgroup$
– Lord Shark the Unknown
Mar 26 at 6:11
2
2
$begingroup$
The first ones are the idiots and the second the cool guys. ;-)
$endgroup$
– amsmath
Mar 26 at 6:12
$begingroup$
The first ones are the idiots and the second the cool guys. ;-)
$endgroup$
– amsmath
Mar 26 at 6:12
$begingroup$
Useful reading is Eric Schechter's 2001 expository paper Constructivism is difficult.
$endgroup$
– Dave L. Renfro
Mar 26 at 6:34
$begingroup$
Useful reading is Eric Schechter's 2001 expository paper Constructivism is difficult.
$endgroup$
– Dave L. Renfro
Mar 26 at 6:34
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Both descriptions can include multiple perspectives. The first view could describe either constructivists or people who don't accept the low of non-contradiction; this latter group is called paraconsistent logicians. The second view could describe either classical logicians or those who are neither classical nor paraconsistent, such as the intuitionists.
answered Mar 26 at 6:32
J.G.J.G.
33.5k23252
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3162791%2fabout-two-differrent-opinions-in-mathematics%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Both descriptions can include multiple perspectives. The first view could describe either constructivists or people who don't accept the low of non-contradiction; this latter group is called paraconsistent logicians. The second view could describe either classical logicians or those who are neither classical nor paraconsistent, such as the intuitionists.
answered Mar 26 at 6:32
J.G.J.G.
33.5k23252
$endgroup$
add a comment |
$begingroup$
Both descriptions can include multiple perspectives. The first view could describe either constructivists or people who don't accept the low of non-contradiction; this latter group is called paraconsistent logicians. The second view could describe either classical logicians or those who are neither classical nor paraconsistent, such as the intuitionists.
answered Mar 26 at 6:32
J.G.J.G.
33.5k23252
$endgroup$
add a comment |
$begingroup$
Both descriptions can include multiple perspectives. The first view could describe either constructivists or people who don't accept the low of non-contradiction; this latter group is called paraconsistent logicians. The second view could describe either classical logicians or those who are neither classical nor paraconsistent, such as the intuitionists.
answered Mar 26 at 6:32
J.G.J.G.
33.5k23252
$endgroup$
Both descriptions can include multiple perspectives. The first view could describe either constructivists or people who don't accept the low of non-contradiction; this latter group is called paraconsistent logicians. The second view could describe either classical logicians or those who are neither classical nor paraconsistent, such as the intuitionists.
answered Mar 26 at 6:32
J.G.J.G.
33.5k23252
answered Mar 26 at 6:32
J.G.J.G.
33.5k23252
answered Mar 26 at 6:32
J.G.J.G.
33.5k23252
answered Mar 26 at 6:32
J.G.J.G.
33.5k23252
33.5k23252
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3162791%2fabout-two-differrent-opinions-in-mathematics%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
5
$begingroup$
The first are "constructivists", the second are "mathematicians".
$endgroup$
– Lord Shark the Unknown
Mar 26 at 6:11
2
$begingroup$
The first ones are the idiots and the second the cool guys. ;-)
$endgroup$
– amsmath
Mar 26 at 6:12
$begingroup$
Useful reading is Eric Schechter's 2001 expository paper Constructivism is difficult.
$endgroup$
– Dave L. Renfro
Mar 26 at 6:34