ANNOUNCEMENT OF FINAL TESTS
MONDAY TEST FOR BAMC AND BAJ STUDENTS
TUESDAY TEST FOR PR STUDENTS
Two main areas of concentration : categorical and hypothetical syllogisms :)-
-(((((((((((((((GOOD LUCK)))))))))))))))))))-
Friday, May 22, 2009
Wednesday, May 20, 2009
Rules for solving syllogisms
Rules for solving syllogistic arguments:
1. The term that the premises have in common is called the middle or common term and will never appear in the conclusion. The mathematical, LOGICAL nature of this reasoning should be stressed (cross out like terms).
2. In the conclusion, the subject term must come from one premise and the predicate term from the other premise. The conclusion cannot be identical to a premise.
3. The strength of a conclusion can be no greater than that of the weaker of the two premises. If one premise is universal (ALL, NO) and one is particular (SOME), the conclusion must be particular (SOME).
4. Only two affirmative premises can produce an affirmative conclusion. If one premise is negative, the conclusion will be negative. If both conclusions are negative, there will likely be NO conclusion.
1. The term that the premises have in common is called the middle or common term and will never appear in the conclusion. The mathematical, LOGICAL nature of this reasoning should be stressed (cross out like terms).
2. In the conclusion, the subject term must come from one premise and the predicate term from the other premise. The conclusion cannot be identical to a premise.
3. The strength of a conclusion can be no greater than that of the weaker of the two premises. If one premise is universal (ALL, NO) and one is particular (SOME), the conclusion must be particular (SOME).
4. Only two affirmative premises can produce an affirmative conclusion. If one premise is negative, the conclusion will be negative. If both conclusions are negative, there will likely be NO conclusion.
More on Deductive and Inductive Reasoning
Inductive reasoning goes from the specific to the general. Deductive reasoning goes from the general to the specific. Let me elaborate.
Deductive reasoning starts with a general rule, a premise, which we know to be true, or we accept it to be true for the circumstances. Then from that rule, we make a conclusion about something specific. Example:
All turtles have shells
The animal I have captured is a turtle
I conclude that the animal in my bag has a shell
A conclusion reached with deductive reasoning is logically sound, and airtight, assuming the premise is true. Deductive reasoning is fully convincing when it is based on a definition. If *by definition* a shilling is a flat disc, copper in color and has a profile of Nyerere on it, then I can be sure the shilling in my pocket has those qualities.
The obvious strength of deductive reasoning is that conclusions derived with it are fully certain. The weakness, which was illustrated in the most recent example, is that no new information is added. The fact that the shilling in my pocket is a copper disc with Nyerere on it was clear from the initial data, so the conclusion hasn't added any new information.
Inductive reasoning is making a conclusion based on a set of empirical data. If I observe that something is true many times, concluding that it will be true in all instances, is a use of inductive reasoning. Example:
All sheep that I've seen are white
All sheep must be white
This example makes inductive reasoning seem useless, but it is in fact very powerful. Most scientific discoveries are made with use of inductive reasoning. A majority of mathematical discoveries come about from conclusions made with inductive reasoning, or observation. But the key word is "discovery." With induction something can be discovered but not proven.
The general flow of events is like this: a)make observations b)form conclusions from empirical data c)prove conclusions with deductive reasoning. So if I notice that all triangles I come across have 180 degrees, through inductive reasoning I may form a hypothesis that *all* triangles have 180 degrees. But now that inductive reasoning has pointed me in the right direction, deductive reasoning allows me to prove my hypothesis as fact.
There is just too much data out there to gather, to just go around blindly using deductive reasoning. Induction allows us to mine the data, and points out significant bits of information. From there we can prove things and form hard facts.
Deductive reasoning starts with a general rule, a premise, which we know to be true, or we accept it to be true for the circumstances. Then from that rule, we make a conclusion about something specific. Example:
All turtles have shells
The animal I have captured is a turtle
I conclude that the animal in my bag has a shell
A conclusion reached with deductive reasoning is logically sound, and airtight, assuming the premise is true. Deductive reasoning is fully convincing when it is based on a definition. If *by definition* a shilling is a flat disc, copper in color and has a profile of Nyerere on it, then I can be sure the shilling in my pocket has those qualities.
The obvious strength of deductive reasoning is that conclusions derived with it are fully certain. The weakness, which was illustrated in the most recent example, is that no new information is added. The fact that the shilling in my pocket is a copper disc with Nyerere on it was clear from the initial data, so the conclusion hasn't added any new information.
Inductive reasoning is making a conclusion based on a set of empirical data. If I observe that something is true many times, concluding that it will be true in all instances, is a use of inductive reasoning. Example:
All sheep that I've seen are white
All sheep must be white
This example makes inductive reasoning seem useless, but it is in fact very powerful. Most scientific discoveries are made with use of inductive reasoning. A majority of mathematical discoveries come about from conclusions made with inductive reasoning, or observation. But the key word is "discovery." With induction something can be discovered but not proven.
The general flow of events is like this: a)make observations b)form conclusions from empirical data c)prove conclusions with deductive reasoning. So if I notice that all triangles I come across have 180 degrees, through inductive reasoning I may form a hypothesis that *all* triangles have 180 degrees. But now that inductive reasoning has pointed me in the right direction, deductive reasoning allows me to prove my hypothesis as fact.
There is just too much data out there to gather, to just go around blindly using deductive reasoning. Induction allows us to mine the data, and points out significant bits of information. From there we can prove things and form hard facts.
Friday, May 15, 2009
Complete the Syllogisms
Supply the conclusions of the following syllogisms: (just for fun) Enjoy them!
Wednesday, May 13, 2009
Categorical Syllogism
A form of deductive reasoning consisting of a major premise, a minor premise, and a conclusion; for example,
All humans are mortal, the major premise,
I am a human, the minor premise,
therefore, I am mortal, the conclusion.
Basic structure
A categorical syllogism consists of three parts: the major premise, the minor premise, and the conclusion, each part of which is a categorical proposition, and each categorical proposition containing two categorical terms.
Major premise: All humans are mortal.
Minor premise: Some animals are human.
Conclusion: Some animals are mortal.
Each of the three distinct terms represents a category, in this example, "human," "mortal," and "animal." "Mortal" is the major term; "animal," the minor term. The premises also have one term in common with each other, which is known as the middle term — in this example, "human." Here the major premise is universal and the minor particular, but this need not be so.
For example:
Major premise: All mortals die.
Minor premise: All men are mortals.
Conclusion: All men die.
The premises and conclusion of a syllogism can be any of four types, which are labelled by letters as follows. The meaning of the letters is given by the table:
By definition, S is the subject of the conclusion, P is the predicate of the conclusion, M is the middle term, the major premise links M with P and the minor premise links M with S.
However, the middle term can be either the subject or the predicate of each premise that it appears in. This gives rise to another classification of syllogisms known as the figure. Given that in each case the conclusion is S-P, the four figures are:
Putting it all together, there are 256 possible types of syllogisms (or 512 if the order of the major and minor premises is changed, although this makes no difference logically). Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures.
A syllogism can be described briefly by giving the letters for the premises and conclusion followed by the number for t he figure. For example, the syllogisms above are AAA-1.
Of course, the vast majority of the 256 possible forms of syllogism are invalid (the conclusion does not follow logically from the premises).
The letters A, E, I, O have been used since the medieval Schools to form mnemonic names for the forms as follows: 'Barbara' stands for AAA, 'Celarent' for EAE etc.
A sample syllogism of each type follows.
A form of deductive reasoning consisting of a major premise, a minor premise, and a conclusion; for example,
All humans are mortal, the major premise,
I am a human, the minor premise,
therefore, I am mortal, the conclusion.
Basic structure
A categorical syllogism consists of three parts: the major premise, the minor premise, and the conclusion, each part of which is a categorical proposition, and each categorical proposition containing two categorical terms.
Major premise: All humans are mortal.
Minor premise: Some animals are human.
Conclusion: Some animals are mortal.
Each of the three distinct terms represents a category, in this example, "human," "mortal," and "animal." "Mortal" is the major term; "animal," the minor term. The premises also have one term in common with each other, which is known as the middle term — in this example, "human." Here the major premise is universal and the minor particular, but this need not be so.
For example:
Major premise: All mortals die.
Minor premise: All men are mortals.
Conclusion: All men die.
The premises and conclusion of a syllogism can be any of four types, which are labelled by letters as follows. The meaning of the letters is given by the table:
By definition, S is the subject of the conclusion, P is the predicate of the conclusion, M is the middle term, the major premise links M with P and the minor premise links M with S.
However, the middle term can be either the subject or the predicate of each premise that it appears in. This gives rise to another classification of syllogisms known as the figure. Given that in each case the conclusion is S-P, the four figures are:
Putting it all together, there are 256 possible types of syllogisms (or 512 if the order of the major and minor premises is changed, although this makes no difference logically). Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures.
A syllogism can be described briefly by giving the letters for the premises and conclusion followed by the number for t he figure. For example, the syllogisms above are AAA-1.
Of course, the vast majority of the 256 possible forms of syllogism are invalid (the conclusion does not follow logically from the premises).
The letters A, E, I, O have been used since the medieval Schools to form mnemonic names for the forms as follows: 'Barbara' stands for AAA, 'Celarent' for EAE etc.
A sample syllogism of each type follows.
Monday, May 11, 2009
Deduction & Induction
Deductive and Inductive Thinking
________________________________________
In logic, we often refer to the two broad methods of reasoning as the deductive and inductive approaches.
Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a "top-down" approach.
We might begin with thinking up a theory about our topic of interest. We then narrow that down into more specific hypotheses that we can test. We narrow down even further when we collect observations to address the hypotheses. This ultimately leads us to be able to test the hypotheses with specific data - a confirmation (or not) of our original theories.
Inductive reasoning works the other way, moving from specific observations to broader generalizations and theories. Informally, we sometimes call this a "bottom up" approach (please note that it's "bottom up" and not "bottoms up" which is the kind of thing the bartender says to customers when he's trying to close for the night!).
In inductive reasoning, we begin with specific observations and measures, begin to detect patterns and regularities, formulate some tentative hypotheses that we can explore, and finally end up developing some general conclusions or theories.
These two methods of reasoning have a very different "feel" to them when you're conducting research.
Inductive reasoning, by its very nature, is more open-ended and exploratory, especially at the beginning.
Deductive reasoning is more narrow in nature and is concerned with testing or confirming hypotheses. Even though a particular study may look like it's purely deductive (e.g., an experiment designed to test the hypothesized effects of some treatment on some outcome), most social research involves both inductive and deductive reasoning processes at some time in the project.
Deductive and Inductive Thinking
________________________________________
In logic, we often refer to the two broad methods of reasoning as the deductive and inductive approaches.
Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a "top-down" approach.
We might begin with thinking up a theory about our topic of interest. We then narrow that down into more specific hypotheses that we can test. We narrow down even further when we collect observations to address the hypotheses. This ultimately leads us to be able to test the hypotheses with specific data - a confirmation (or not) of our original theories.
Inductive reasoning works the other way, moving from specific observations to broader generalizations and theories. Informally, we sometimes call this a "bottom up" approach (please note that it's "bottom up" and not "bottoms up" which is the kind of thing the bartender says to customers when he's trying to close for the night!).
In inductive reasoning, we begin with specific observations and measures, begin to detect patterns and regularities, formulate some tentative hypotheses that we can explore, and finally end up developing some general conclusions or theories.
These two methods of reasoning have a very different "feel" to them when you're conducting research.
Inductive reasoning, by its very nature, is more open-ended and exploratory, especially at the beginning.
Deductive reasoning is more narrow in nature and is concerned with testing or confirming hypotheses. Even though a particular study may look like it's purely deductive (e.g., an experiment designed to test the hypothesized effects of some treatment on some outcome), most social research involves both inductive and deductive reasoning processes at some time in the project.
Tuesday, May 5, 2009
Categorical Syllogisms
Standard Form Categorical Syllogisms
In order to understand standard form categorical syllogisms it will be helpful to define several words and phrases:
•Syllogism – a deductive argument in which the conclusion is drawn from two premises.
•Categorical syllogism – a deductive argument consisting of three categorical
propositions with exactly three shared terms, two terms per proposition.
•Standard form categorical syllogism – a categorical syllogism consisting of
standard form categorical propositions arranged in a specific order, with the major
premise stated first, then the minor premise, and then the conclusion.
•Major term – the term occurring in the predicate of the conclusion in a standard
form categorical syllogism.
•Minor term – the term occurring in the subject of the conclusion in a standard
form categorical syllogism.
•Middle term – the term occurring in both the major and minor premises of a
standard form categorical syllogism, but not in the conclusion.
•Major premise – the premise of a categorical syllogism that contains an instance
of the major term.
•Minor term – the premise of a categorical syllogism that contains an instance of
the minor term.
Note: the major and minor premises are not determined by their placement in a
categorical syllogism, but by terms that are contained within them.
Both premises of a syllogism contain the middle term, but only the major premise and the conclusion contain the major term, and only the minor premise and the conclusion contain the minor term.
In the following argument the minor premise is stated first, then the major premise, and then the conclusion:
All disciples are Saints.
Some disciples are preachers.
Therefore some saints are preachers.
The major term in this argument is “preachers,” because it is the term in the predicate of the conclusion.
The minor term is “saint,” because it is the term in the subject of the conclusion. The first premise contains the minor term, so it is the minor premise. The second premise contains the major term, so it is the major premise.
This is a valid categorical syllogism, but it is not a standard form syllogism, because the premises are not stated in the standard order with the major premise being stated first. It should be noted that “standard form” is simply a matter of convention or definition.
There is nothing that makes a standard form syllogism “better” than a non-standard form syllogism, and in fact arguments that are not in standard form are sometimes seen to be more persuasive, because they can be written or spoken in a more natural format.
Consider the standard form syllogism below,
Some disciples are preachers.
All disciples are Saints.
Therefore some saints are preachers.
With this more natural statement of the same argument:
It must be true that some saints are preachers, since all disciples are saints, and
some disciples are preachers.
Even in this form the argument is a bit stilted, since it still conforms to the rigors of standard form categorical propositions, but most would prefer the latter to the former in everyday language.
However, it is easier to work with standard form categorical syllogisms, so for this
purpose it is to be preferred over the less rigorous arguments.
Mood and Figure
All standard form categorical syllogisms can be described in terms of their mood and
figure. The mood of a syllogism is represented by the three letters that represent the type of each proposition in the syllogism. So a standard form syllogism with three universal affirmative propositions has a mood of AAA. However, the mood of a syllogism does not fully characterize its form. For example consider these two arguments each of which has a mood of AAA.
Major premise: All men are mortal.
Minor premise: All preachers are men.
Conclusion: All preachers are mortal.
Major premise: All Christians are men.
Minor premise: All preachers are men.
Conclusion: All preachers are Christians.
Both of these arguments have a mood of AAA, but they differ in how the middle term is
placed. The first argument places the middle term in the subject of the major premise, and the predicate of the minor premise, but the second argument places the middle term in the predicate of both major and minor premises. So, although both have the same mood, they differ in form.
Next time we will see the 4 Figures and how they work! keeping checking!
Subscribe to:
Posts (Atom)