Chapter 8 - Reasoning And Decision Making Flashcards
(50 cards)
What is a symbolic representation, and what is an analogical representation?
Symbolic representation: an arbitrary string of letters that represents an item, however they are abstract and do not have relationships to the objects, only the meaning has a relationship.
Analogical representation: This is a visual representation of some information, representing the meaning of the word.
Can an analogical representation construct many different symbolic representations?
Can a symbolic representation construct many different analogical representations?
Provide examples of each…
An analogical representation can construct many differently worded symbolic representations, however the overall general meaning is the same, it is just written in different ways.
Ex: if you are given an image of someone throwing a ball, you can write it as: Ben throws the ball, or the ball is thrown by Ben. Overall it has the same meaning but it can be written in different ways.
ONLY ONE MEANING CAN COME OUT OF AN ANALOGICAL REPRESENTATION.
Symbolic representations if written ambiguously can provide many different analogical representations, based on where the emphasis in the sentence is placed.
Ex: “The spy saw the man with the binoculars”, could either be drawn as a man seeing someone who is wearing binoculars, or a man looking at someone through binoculars.
MULTIPLE ANALOGICAL MEANINGS CAN COME OUT OF ONE AMBIGUOUS SYMBOLIC REPRESENATION.
If symbolic representations can have multiple analogical representations, what does this mean for interpretation of stories and hence encoding of the information in those stories?
Because of this, stories can be interpreted many different ways, and based on the context in which the story was listened to people may encode it with different information being highlighted.
How do writing and reading go through the stages of reality, symbolic and analogical representations?
For writing, ones ability is based on how they can encode information from reality into an analogical representation that they can then write about symbolically (through words).
For reading, ones ability is how well they can interpret what is going on accurately and produce a strong analogical representation that they can understand and relate to reality.
What makes someone a better problem solver?
Ones ability to represent something analogically and make a picture/plan in your head will determine how well you can simplify the problem by eliminating irrelevant information.
What are the definitions of problem solving and decision making?
Problem solving: Finding a way around an obstacle to reach a goal, and the first step in this is building a strong analogical representation of the problem.
Decision making: A cognitive process that results in the selection of a course of action or belief from several options. Sometimes mental shortcuts can be used, but sometimes they can be misleading.
What is the Buddhist monk problem and what is a productive and unproductive representation of it?
One morning, a Buddhist monk sets out at sunrise to climb a path of the mountain to reach the temple at the Summit hero arrives at the temple just before sunset. A few days later, he leaves the temple of sunrise to descend down the mountain travelling faster since it is downhill. Is there a spot along the path of the Uncle occupy at precisely the same time of day on both trips?
Unproductive representation: Naturally you would try to think of this in terms of mathematics, but it is not that complicated.
Productive representation: the two monks start at sunrise on the same path going opposite directions, they must meet at a spot at the same time, even if it is not the directly in the middle fo the descent.
How does background knowledge on a subject affect the ease with which a problem can be solved? What is an example of this?
The more background knowledge someone has, the more effectively they can perceptually chunk the problem and decide how to solve it based on previous patterns. An example of this would be the grouping of some problems. The novice would group based on appearance, but this is not effective because they may not be able to be solved in the same way. The expert would group based on the approach taken to solve the problem, (based on previous knowledge and chunked information in memory) and hence will not group based on similar experience.
This is because experts have specific knowledge in certain problem domains, and hence can connect certain problems together based on the schema they have in their mind. So they can quickly establish connections between certain information and hence present accurate models of the information which novices cannot do.
Because the experts were sorting problems based on their meaning and the way in which to solve them, they took a lot longer to sort the problems, however overall they were able to solve them much faster. This is because they tried to understand the problems before solving them.
What could be a disadvantage of being an expert in a certain specialty?
Experts have specific information encoded in their brain and so they may not be able to think outside of the box because they are constantly trying to relate information back to what they previously knew.
How you _______ a problem effects how _______ you solve a problem.
How you represent a problem affects how quickly you solve a problem. The more effectively you organize it, the more quickly you can solve it.
What does it mean for a conclusion to be valid?
This means that the conclusion can only be represented in one way by the premises and hence it must always follow from the premises. Don’t attach real world meaning to it because empirical truth does not always match validity.
What are three recurring themes when trying to use logic and reasoning?
- We are often influenced by general world knowledge stored in our memories when trying to make judgements. So previous context will influence how we interpret something, and hence it may not be valid but we think it is due to empirical truth.
- We are more capable of thinking in concrete ways then abstract ways, which is why we often try to attach an example. But again empirical truth will interfere so instead draw out venn diagrams to model and understand the problem.
- We tend to search for evidence that confirms our decisions, beliefs and hypotheses. So if you are skeptical, you will be more likely to search for negative evidence, or evidence that refutes that rule.
When problems are presented in an abstract form, people are:
Generally poor at solving problems. They will be much better at solving them when seen as real life concepts or solutions.
Therefore, world knowledge often prevents us from seeing pure logic, and sometimes allows us to see it.
What is deductive reasoning?
Begins with some specific premises that are assumed to be true and based on those premises a conclusion is drawn. A conclusion is valid if it follows the principles of logic. And deductive reasoning is used to determine if the conclusion is valid. So based on a general rule that is assumed, can you draw a valid conclusion?
What is a syllogism? What type of reasoning does it use to solve?
An instance of a form of reasoning where a conclusion is drawn from two given or assumed propositions (premises) each of which shares a term with a conclusion, and shares a common middle term that is not present in the conclusion. This is just an argument from philosophy.
This uses DEDUCTIVE reasoning, where a general rule is taken and is used to create a more specific example, or you can draw conclusions from previous known facts and definitions.
In summary:
A three statement logical form where the first two are premisdes that are assumed to be true, and the third part is a conclusion based on those premises.
An argument will be valid if the conclusion is a consequence of the premises. It’s invalid if it has a counterexample, and so the premises don’t necessarily prove the conclusion.
How to solve a syllogism since real life examples can be misleading?
You use Venn diagrams!
All A’s are B’s — then all A’s must fit inside the B circle.
This doesn’t mean that all B’s are A’s necessarily, because there could be some B’s that the A circle doesn’t cross.
No A’s are B’s — Two separate circles, and this is the universal negative.
Some A’s are B’s — put the circles partially overlapping but not completely.
Then, once you have done this for the premises, see how you can combine them into a bigger Venn diagram. Create all the possibilities. Then, evaluate the conclusion taking the Venn diagrams that are relevant. If they represent the same situation, then that is the conclusion that follows every time. If there are multiple Venn diagrams that can be made, then we cannot assume that conclusion every time and hence it is invalid.
A ________ conclusion does not always mean it has _________ _______.
A valid conclusion does not always mean it has empirical truth. The truths of the facts interfere with the actual logic, which is determined by how the statements follow from each other.
If the premises can never be true while the conclusion is false (only one possible Venn diagram can be drawn which represents that conclusion), then it is valid. You can’t get any other conclusions from those premises.
What is conditional reasoning?
Conditional reasoning is an if then statement, where there is an antecedent (if this is true) and a conclusion (then that is true).
Conditional reasoning involves a logical determination of a conclusion or no conclusion if one part of the if/then statement is assumed to be true or not true. If we use a statement that says if A then B, we are saying if A is true so is B. How do we prove that this is valid (what are the two things we would need to check?)
To prove this is valid, we would need to check that when the antecedent is true, the consequent is true, and when the consequent is false, the antecedent is false.
If the consequent is true, then this doesn’t tell us anything because the conditional only says if the antecedent is true then the consequent must be. But if the consequent is true, that doesn’t meant the antecedent must be. It could have come from some other factor.
If the antecedent is false, there is no reason to check the consequent because the rule doesn’t say what the consequent is when the antecedent is false.
Therefore, only if the antecedent is true must we check the consequent, because the rule says that both must be true in that case.
If the antecedent is true then we must check the consequent, because it says if it’s true the consequent must be, but if the consequent is false whilst the antecedent is true then this wouldn’t work out.
If the rule says “If P is true, then Q is true,” what can we say about the following four possible conclusions?
- P is true
- P is not true
- Q is true
- Q is not true
- AFFIRMING THE ANTECEDENT: If P is true, then based on this rule we can assume that Q is true (as long as this argument is always valid). This is an outcome we can determine easily.
- DENYING THE ANTECEDENT: If P is not true, the rule doesn’t say anything about the consequent. It could be true or not true, and so no definite solution can be drawn from this.
- AFFIRMING THE CONSEQUENT: If Q is true, then that doesn’t necessarily mean that P is true. It’s only saying if P is true then Q must be, but Q could also be true when P is not.
- DENYING THE CONSEQUENT: Here, it says that if P is true, then Q is true. So if Q is not true, it cannot be the case that P is true because Q must be true when P is true. Therefore, this can be determined with certainty as long as the rule is valid — that P must be false if Q is false.
What is modus ponens? What is modus tollens?
Modus ponens: This is affirming the antecedent, and this draws a constant conclusion that the consequent must be also affirmed every time.
Modus tollens: This is denying the consequent, meaning that if the consequent is false so must be the antecedent or else it isn’t valid.
These are the two conclusions that can be drawn with certainty once affirmed or denied.
When you are given that the antecedent is true, what do people normally say about the consequent and how good are they at inferring the truth?
When given that the antecedent is true, almost everyone was accurate in concluding that the consequent must also be true. So modus ponens was very easy to understand for people, no matter if in concrete or abstract form.
For modus tollens, how accurate were people in making inferences based on the conditional?
Denying the consequent is harder for people to understand and think about, because people may say that the antecedent doesn’t have to be false is the consequent is, when in fact it does.
So when presented in abstract form, people only made correct inferences 57-77% of the time. However, when presented in everyday experience form, people were accurate 87.5% of the time, because we tend to think in terms of concrete evidence.
What is the Wason selection task? What is the most common response and what is the correct response?
The Wason selection task has 4 cards placed in front of someone, and people are told that a card with a vowel on it will have an even number on the other side.
One card has a vowel, one has a consonant, one has an even number, and one has an odd number.
*Note: A very important thing here is that this DOES NOT mean that if a card has an even number on one side, it has to have a vowel on the other side. It only means that if it doesn’t have an even number on one side, that it must not have a vowel on the other side. This is modus tollens (denying the consequent)!
When asked which two cards to turn over to ensure that the rule is valid (always followed), what two cards would you turn over?
Most people would say you would turn over the card with the vowel and the card with the even number. Because you want to check both directions — if there is a vowel then there is an even number, and if there is an even number then there is a vowel. But that is NOT what this rule is saying! It doesn’t say anything about what type of letter must be on the other side if there is an even number. So this is incorrect, we will not be able to draw any valid conclusions from that second card (though the first one would be correct).
The correct two cards to chose would be the vowel and the odd number. If there is an odd number, you want to confirm that there is no vowel on the other side, because this rule says if there is a vowel on one side, then there must be an even number on the other side. So if you don’t find this, the rule would be invalid.
In addition, you want to prove that if there is a vowel on one side, then there is an even number on the other side, which is what most people got right.
So the correct two cards to chose would be:
1. Modus ponens: affirming the antecedent
2. Modus tollens: denying the consequent
Only 4% turned over E and 7, and 46% turned over E and 4. Clearly people were optimistic and wanted to turn over the affirming statements.