Thursday, November 6, 2014

546: Deductive reasoning.....

It seems all so obvious. We live, we observe. We see things, see that they have properties like shape and color.

Then our mind translates these observations in words and we are able to say “Look! That rose is red.”

We even can wonder about the question “Are all roses red?” We use induction and reason, if this flower is blue and all roses are red then this can not be a rose.

To use it might look so trivial, but in fact it is the most amazing thing our brain has ever produced: inductive and deductive reasoning.

So, Aristotle observed, that we fist gather information, the inductive stage. Based on our observations we come to generalizations.

In the second stage of scientific inquiry, the generalizations reached by induction are used as premisses for the deduction of statements about the initial observations. 

Aristotle placed an important restriction on the kinds of statements that can occur as premisses and conclusions of deductive arguments in science. 

He allowed only those statements which assert that one class is included within, or is excluded from, a second class. 

On the picture next to me you see the famous Venn diagrams, which visualize the ideas of Aristotle.

John Venn,  (4 August 1834 – 4 April 1923) was an English logician and philosopher

If Sand Pare selected to stand for the two classes, the statements that Aristotle allowed are:

A       All S are P S wholly included in P
E      No S are P S wholly excluded from P
 I      Some S are P S partially included in P
O     Some S are not P S partially excluded from P

Aristotle held that type A is the most important of these four types. 

He believed that certain properties inhere essentially in the individuals of certain classes, 

and that statements of the form All S are Preproduce the structure of these relations. It tells us how Aristotle looked at reality.

Perhaps for this reason, Aristotle maintained that a proper scientific explanation should be given in terms of statements of this type. 

More specifically, he cited the syllogism in Barbara as the paradigm of scientific demonstration. 

Barbara is the medieval acronym or mnemonic for the A - A -A syllogism.  This syllogism consists of A-type statements arranged in the following way:

                   All M are P.
                   All S are M.
              ∴ All S are P.

where P, S, and M are the major, minor, and middle terms of the syllogism. 

Aristotle showed that this type of syllogism is valid. If it is true that every S is included in M and every M is included in P, it also must be true that every S is included in P. 

This is the case regardless of what classes are designated by S , P, and M

One of Aristotles great achievements was to insist that the validity of an argument is determined solely by the relationship between premisses and conclusion.

That is what he discovered, the way how our brain works to interact efficiently with its environment. Really amazing.

Thank you… ^_^

The Discussion

[13:19] Merlin Saxondale: Oh that seemed quick
[13:19] Roger Amdahl: mmm
[13:19] Roger Amdahl: quick but deep
[13:19] herman Bergson: Yes indeed Merlin, but yet as much text as always.....
[13:19] Dawn Rhiannyr: thank you Herman
[13:19] Rajamapuradjoloun Shichiroji: indeed deep!
[13:19] Rajamapuradjoloun Shichiroji: thanks herman!
[13:19] Bejiita Imako: hmm
[13:20] Bejiita Imako: interesting
[13:20] herman Bergson: the most fascinating here is the essence of deductive reasoning....
[13:20] Roger Amdahl: Does this mean that : although every tree is different from another tree ( no exact copy) we all recognise it as tree?
[13:20] Lizzy PleidesLizzy Pleides is still thinking
[13:20] Rajamapuradjoloun Shichiroji: I have to admit that this evening I had some difficulties to follow all the reasoning
[13:20] herman Bergson: Yes Roger...
[13:21] Rajamapuradjoloun Shichiroji: And I will have to study some of the things you explained
[13:21] Roger Amdahl: that is the reason .. we can see a tree in a shape of clouds ?
[13:21] herman Bergson: The most important thing here to understand is that Aristotle showed that valid resoning depends on the relations between terms, not on the content of the reasoning...
[13:22] Rajamapuradjoloun Shichiroji: I see....
[13:22] herman Bergson: No Roger...:-)
[13:22] herman Bergson: then Aristotle would say...
[13:22] herman Bergson: All trees stand on the ground
[13:23] Dawn Rhiannyr: ah ok
[13:23] herman Bergson: I see a tree in the sky
[13:23] herman Bergson: This is not a tree
[13:23] herman Bergson: The thing in the sky is not included in the class of trees...being an object on the ground
[13:23] Roger Amdahl: mm... I will search for the limit... what about a mangrove tree, that stands in water in rain season ... ( poor Aristotles)
[13:24] herman Bergson: Its roots are stil in the ground...:-)
[13:24] herman Bergson: Be they underwater tho
[13:25] Lizzy Pleides: you are our Aristotle herman
[13:25] herman Bergson: But the point is....Aristotle structured thinking.....
[13:25] Bejiita Imako:
[13:25] Bejiita Imako: YAY! (yay!)
[13:25] bergfrau Apfelbaum: :o)
[13:25] herman Bergson: And this way of thinking an reasoning lasted till the 19 century unchanged....
[13:26] herman Bergson: It showed us the method of logic
[13:26] herman Bergson: And this became the method of scientific inquiry
[13:27] herman Bergson: The weak point here is that Aristotle believed that the A type premise was the best one....
[13:27] herman Bergson: All S are P....
[13:27] Roger Amdahl: Yes , he did .... but it is basic for survival to make those mind jumps... a tiger with different striping is still a tiger... and this is the reason why we are very many fooled bye the interpretation of our vision ..
[13:27] herman Bergson: But we never can find or see all S.....past ..present and future ones
[13:29] Merlin Saxondale: Well thanks Herman....
[13:29] Dawn Rhiannyr: so better ask No S is P?
[13:29] Bejiita Imako: ah
[13:29] Rajamapuradjoloun Shichiroji: I am missing the point of what exactly "S", "P" and "A" are... :-(
[13:29] Lizzy Pleides: we can only see a little part of the entirely, so we need rules
[13:29] Merlin Saxondale: I must leave early ... something else is just starting now
[13:29] herman Bergson: Aristotle also introduced in this way a specific belief in scientific inquiry...
[13:29] Roger Amdahl: mm.. Question .... If Bergfrau's goat had tiger striping , what would a caveman see, and odd goat, or an odd tiger , or is this dependent on the personal "status" of the observer
[13:29] Roger Amdahl: ?
[13:29] herman Bergson: ok....S means 'subject' and P means 'predicate'
[13:29] Merlin Saxondale: Bye everyone
[13:30] Roger Amdahl: Bye Merlin
[13:30] Bejiita Imako: bye Merlin
[13:30] Dawn Rhiannyr: bye Merlin
[13:30] Rajamapuradjoloun Shichiroji: bye Merlin
[13:30] herman Bergson: or S = object and P = property
[13:30] Lizzy Pleides: TC merlin
[13:30] Rajamapuradjoloun Shichiroji: Oh, snap! Ok, got them!
[13:30] Rajamapuradjoloun Shichiroji: thanks!
[13:30] herman Bergson: so every object has  a property or a set of properties
[13:30] Roger Amdahl: (( or do I go off topic here ?))
[13:31] herman Bergson: The thing is , Roger, that Aristotle divided the world in classes of objects...
[13:32] herman Bergson: matter made them individual objects and properties made them into tigers, goat or trees...
[13:32] herman Bergson: And in a way that is how our mind works
[13:33] herman Bergson: So when you give the goat stripes he still has horns which a tiger doesn’t have...
[13:33] Bejiita Imako: and also its shape is different from a tiger
[13:33] herman Bergson: How many properties should the goat have to be actually a tiger ?:-)
[13:34] Bejiita Imako: try to eat you maybe
[13:34] Dawn Rhiannyr: good question
[13:34] herman Bergson: That is what I mean Bejiita...indeed
[13:34] Rajamapuradjoloun Shichiroji: all the properties of a tiger I guess
[13:34] Bejiita Imako: a goat dont try to eat you, a tiger sees you as food
[13:34] herman Bergson: yes Rajam, and then it is no longer a goat....
[13:34] Roger Amdahl: true ... how much do we need to make a conclusion ... run like hell, or prepare the BBQ ?
[13:35] herman Bergson: Main point here is that you see how such an old Greek already analyzed our methods of thinking and reasoning.....
[13:35] herman Bergson: and thus shaped scientific method
[13:36] herman Bergson: and for centuries..
[13:36] Roger Amdahl: Yes... He really was a genius, no doubt
[13:36] Dawn Rhiannyr: yes that's indeed amazing
[13:36] herman Bergson: Yes Dawn.....amazing indeed....
[13:37] Bejiita Imako: grmbllll computer &#¤&/&¤&#(#
[13:37] Bejiita Imako: !
[13:37] herman Bergson: If you consider the world he lived in compared to our information culture
[13:37] herman Bergson: Take a deep breath Bejiita :-))
[13:37] Lizzy Pleides: he obviously was more progressive than many of our contemporaries
[13:38] Roger Amdahl: We became lazy thinkers .. we prefer to google, and think ourselves.
[13:38] herman Bergson: I should be careful with that statement Lizzy.....
[13:38] herman Bergson: He is also the main cause for the secundery position in society of women...
[13:38] Rajamapuradjoloun Shichiroji: that's what amazes me! Some minds are way more ahead of their time but even of our time! What's happening to us? Are we just getting lazy or what?
[13:38] Lizzy Pleides: oh!
[13:38] herman Bergson: To him a woman was closer to an animal than to a real human being
[13:39] Roger Amdahl: *shuts up, because sitting between 2 women :)
[13:39] Dawn Rhiannyr: you better do Roger ;)
[13:39] herman Bergson: good strategy Roger :-)
[13:39] Bejiita Imako: hehe
[13:39] Lizzy PleidesLizzy Pleides pokes Roger
[13:39] Rajamapuradjoloun Shichiroji coughs....
[13:40] herman Bergson whispers: oops...I guess I better dismiss class before things run out of hand...:-))
[13:40] Dawn Rhiannyr: you want to say something Raja? :))
[13:40] Bejiita Imako: lol
[13:40] Rajamapuradjoloun Shichiroji: Yes, it's sooooooo late!
[13:40] bergfrau Apfelbaum: :-))
[13:40] Rajamapuradjoloun Shichiroji: I badly need to go home....
[13:40] Rajamapuradjoloun Shichiroji: Hehehehe....
[13:40] herman Bergson: Thank you al again for your participation....:-)
[13:40] Dawn Rhiannyr: thank you Herman... gives much to think about again
[13:40] Roger Amdahl: What he gave for reason for his thought about woman ?
[13:40] Bejiita Imako: nice again
[13:40] herman Bergson: Class dismissed :-))
[13:41] Bejiita Imako: cu soon again all
[13:41] Bejiita Imako: bye 
[13:41] bergfrau Apfelbaum: ty herman and class :o))
[13:41] Bejiita Imako:
[13:41] bergfrau Apfelbaum: byebye Bejiitaa
[13:41] Rajamapuradjoloun Shichiroji: Thanks herman, really another brilliant lecture this evening!
[13:41] herman Bergson: thank you Rajam :-)

[13:41] Bejiita Imako: YAY! (yay!)

No comments:

Post a Comment