Deductive thinking is thinking that leads us to a conclusion with certainty. Logic puzzles and problems (like the one below) require deductive reasoning. See if you can use your powers of deductive reasoning to figure out what color the front genius’ hat is. Post not only your answer, but your thought process, and remember—this is not based on probability. Probability is an inductive process.

Three geniuses stand in a file (one behind the other). Each can see only to the front, so the rear person can see the middle and the front, the middle person can see the front, and the genius in the front cannot see anyone.

You have five hats. Two are white, and three are red. You blindfold the three geniuses, who are utterly truthful, and put a hat--at random--on the head of each. Then you hide the other two hats and remove the blindfolds.

You then ask each genius to name the color of his hat (which he cannot see).

The rear one says "I don't know." The middle on says, "I don't know." Then the front one says, "I know."

WHAT COLOR IS THE FRONT GENIUS' HAT??????

s_cianci

Since #3 did not know the color of his hat, that means that at least one of #s 1 or 2 had a red hat. Since there'd been only 2 white hats, if #s 1 and 2 both had white hats then #3 would've known that his hat was red. Now, if #1's hat had been white, then #2 would've known that his hat was red. However, since #2 did not know the color of his hat, it then stands to reason that #1 had a red hat, thereby not allowing #2 to deduce with certainty the color of his hat.

LUCKSTONE

why is deductive logic also called symbolic logic and mathematical logic.?

Dark_crow

What you presented is not an example of deductive logic for the very simple reason that color is wholly subjective. Deductive logic is a sham.

“Before the 17th century, science was mostly a process of deductive logic. Consider the following line of reasoning used by certain CAM proponents:
1. We know through scripture that God is the creator of the universe and that God is perfect.
2. Therefore creation must be perfect.
3. If illness were real, then creation would not be perfect.
4. Therefore, illness cannot be real.
This is the basic reasoning behind the denial of illness’s reality by Christian Science as well as some forms of New Thought. Before the 17th century, this type of deductive logic was science. Some characteristics of scientific principles under this definition are those of ‘immutable law’ and ‘absolute certainty.’ We know them by logical reasoning; empirical testing is superfluous. This approach reads like a bumper sticker: ‘My mind is made up. Don’t confuse me with facts.’
Many opponents of CAM, while well educated in empirical science, are ignorant of metaphysics. They fall into the same trap but from the other side. Consider this line of reasoning:
1. We know through science that the only real powers in the universe are molecules in motion and the four forces of physics.
2. The mind and/or the spirit possess none of the four forces of physics.
3. If the mind and/or the spirit do not possess any of the four forces, they can have no aetiological effect on the physical universe.
4. Therefore, the mind and/or the spirit can neither cause nor cure disease.
Their basic modus operandi is the same as that of the Christian Scientists: logically deriving a conclusion on the basis of a metaphysical assumption. We don’t know that the forces of physics discovered to date are the only aetiological forces any more than we know that God is perfect. No experiment has ever been designed to test either proposition. Yet this seems to be the gist of Relman’s argument to Weil against mind-body medicine as cited earlier.”

Unsnarling the CAM-knot

demosthenes

well my deduction is that at least the one in the front can actually see,therefore deducting that the rest can see as well,when the one in the back says that he doesn't know there are 2 posibilities the other 2 guys are using red hats or one white and the other a red one,then the one in the middle coming to the same conclusion,if he sees the one in the front with a white hat then he would come to the conclusion he is in fact wearing the red one but he saw a red hat therefore not knowing wheather he is wearing the white one or a red one.by the time the one in the front is asked .he has in his mind that he is wearing a red hat.they always say the truth so no matter if is true or not the one in the front said what he though he was wearing that in fact is a red hat.

phooey

The front one had mind powers, was joking, or was standing in front of a mirror. But i also got something in the back of mind that i can't really explain, the front one knows his hat color because the other two don't. ??