Is there an issue? Send a MessageReason:
None
Changed line(s) 5,6 (click to see context) from:
The simplest version of an argument in formal logic is the syllogism: A set of premises, and then a conclusion that follows from the premises according to a set of standard relationships (which are too complex to go into for this article).
to:
The simplest version of an argument in formal logic is the syllogism: A set of at least two premises, and then a conclusion that follows from the premises according to a set of standard relationships (which are too complex to go into for this article).
Is there an issue? Send a MessageReason:
Changed line(s) 115,116 (click to see context) from:
Thus, science never gets the certainty of deductive logic because it always has inductive logic mixed in. However, we can have overwhelming confidence in a conclusion which we have built up enough evidence in. This is reflected in an argument by philosopher David Hume which proved that it is impossible to ever derive certain knowledge by observing the world. Hume argued that we observe the world and expect future events to play out similarly. I throw an apple in the air and it falls. I throw an orange in the air and it falls. I throw an elephant in the air and it falls. This idea, that things I throw into the air will fall, is a prediction based on an assumption. The future will resemble the past.
to:
Thus, science never gets the certainty of deductive logic because it always has inductive logic mixed in. However, we can have overwhelming confidence in a conclusion which we have built up enough evidence in. This is reflected in an argument by philosopher David Hume which proved that it is impossible to ever derive certain knowledge by observing the world. Hume argued that we observe the world and expect future events to play out similarly. I You throw an apple in the air and it falls. I You throw an orange in the air and it falls. I You throw an elephant in the air and it falls. This idea, that things I you throw into the air will fall, is a prediction based on an assumption. The future will resemble the past.
Is there an issue? Send a MessageReason:
None
Changed line(s) 107 (click to see context) from:
Thus we know for certain that the statement "All fish are aquatic creatures, but not all aquatic creatures are fish." is sound, valid, and true.
to:
Thus we know for certain that the statement "All fish are aquatic creatures, but not all aquatic creatures are fish." is sound, valid, and true.true.
!!Induction: A Part of Science
Induction allows us to make probabilistic conclusions about the world. If that makes you think of science, that's because it's part of the scientific method. The scientific method begins with a series of observations to learn about the world then uses inductive logic to reach a tentative conclusion about how that part of the world works. This tentative conclusion is your hypothesis.
The next step is to turn around and use deductive logic to see what would undermine the hypothesis, then run the experiment to test whether that is true. Ideally, you would test something necessary for your hypothesis. Or it may be something that should be true if your hypothesis is true. By testing this next idea, you have a new data point, and you return to inductive reasoning to shade your confidence in whether or not your hypothesis is true.
Thus, science never gets the certainty of deductive logic because it always has inductive logic mixed in. However, we can have overwhelming confidence in a conclusion which we have built up enough evidence in. This is reflected in an argument by philosopher David Hume which proved that it is impossible to ever derive certain knowledge by observing the world. Hume argued that we observe the world and expect future events to play out similarly. I throw an apple in the air and it falls. I throw an orange in the air and it falls. I throw an elephant in the air and it falls. This idea, that things I throw into the air will fall, is a prediction based on an assumption. The future will resemble the past.
How do you know the future will resemble the past? Because in the past, the future has resembled the past. This is circular reasoning, which makes it spurious. Thus, inductive logic and science can never give you certainty. No observation can ever give you certainty. The strength of science is that it has a means of continually reinforcing the confidence in its conclusions, not that it can ever remove all doubt.
Remember how in science, you try to disprove your hypothesis? Karl Popper, the philosopher of science, noted this is the key to science. Falsifiability is the core of a scientific statement. If you can't think of a way you might prove something wrong, it isn't science.
!!Induction: A Part of Science
Induction allows us to make probabilistic conclusions about the world. If that makes you think of science, that's because it's part of the scientific method. The scientific method begins with a series of observations to learn about the world then uses inductive logic to reach a tentative conclusion about how that part of the world works. This tentative conclusion is your hypothesis.
The next step is to turn around and use deductive logic to see what would undermine the hypothesis, then run the experiment to test whether that is true. Ideally, you would test something necessary for your hypothesis. Or it may be something that should be true if your hypothesis is true. By testing this next idea, you have a new data point, and you return to inductive reasoning to shade your confidence in whether or not your hypothesis is true.
Thus, science never gets the certainty of deductive logic because it always has inductive logic mixed in. However, we can have overwhelming confidence in a conclusion which we have built up enough evidence in. This is reflected in an argument by philosopher David Hume which proved that it is impossible to ever derive certain knowledge by observing the world. Hume argued that we observe the world and expect future events to play out similarly. I throw an apple in the air and it falls. I throw an orange in the air and it falls. I throw an elephant in the air and it falls. This idea, that things I throw into the air will fall, is a prediction based on an assumption. The future will resemble the past.
How do you know the future will resemble the past? Because in the past, the future has resembled the past. This is circular reasoning, which makes it spurious. Thus, inductive logic and science can never give you certainty. No observation can ever give you certainty. The strength of science is that it has a means of continually reinforcing the confidence in its conclusions, not that it can ever remove all doubt.
Remember how in science, you try to disprove your hypothesis? Karl Popper, the philosopher of science, noted this is the key to science. Falsifiability is the core of a scientific statement. If you can't think of a way you might prove something wrong, it isn't science.
Is there an issue? Send a MessageReason:
None
Changed line(s) 31,32 (click to see context) from:
'''Soundness''' refers to the argument as a whole. An argument is sound if the logic is valid ''and'' all the premises are true. If the argument is sound, then the conclusion must be accepted as true, by the definition of "valid". An unsound argument is one that contains a [[YouFailLogicForever logical fallacy]], making it invalid, or contains a false premise.
to:
'''Soundness''' refers to the argument as a whole. An argument is sound if the logic is valid ''and'' all the premises are true. If the argument is sound, then the conclusion must be accepted as true, by the definition of "valid". An unsound argument is one that contains a [[YouFailLogicForever logical fallacy]], LogicalFallacy, making it invalid, or contains a false premise.
Changed line(s) 66,67 (click to see context) from:
-->UsefulNotes/BarackObama is the President of the United States.
-->2.32% of Presidents of the United States are mixed-race.
-->2.32% of Presidents of the United States are mixed-race.
to:
-->UsefulNotes/BarackObama is was the President of the United States.
-->2.32% 22% of Presidents of the United States are mixed-race.
-->2.
Changed line(s) 74,75 (click to see context) from:
-->Barack Obama is the President of the United States.
-->97.68% of Presidents of the United States are white.
-->97.68% of Presidents of the United States are white.
to:
-->Barack Obama is was the President of the United States.
-->97.68% 7% of Presidents of the United States are white.
-->97.
Is there an issue? Send a MessageReason:
None
Changed line(s) 20,22 (click to see context) from:
--->Both of the premises are true, and the conclusion is true; all turtles are indeed animals. The truth of all three statements is not affected by the clearly invalid logic connecting them.
to:
Changed line(s) 28,30 (click to see context) from:
--->Although all three parts of this argument are obviously wrong, together they form a ''valid'' argument. IF all animals were dogs AND all dogs were terriers, then all animals would indeed be terriers.
to:
Changed line(s) 36,38 (click to see context) from:
--->The argument is sound, because the premises and conclusion are true and the logic is valid. This is a valid and factually correct argument.
to:
Deleted line(s) 61 (click to see context) :
Changed line(s) 65,66 (click to see context) from:
In the same way that an invalid deduction might still have a true conclusion (as with the turtles above), an inductive argument that is weak could still have a true conclusion. This should be fairly intuitive:
to:
In the same way that an invalid deduction might still have a true conclusion (as with the turtles above), an a weak inductive argument that is weak could still have a true conclusion. This should be fairly intuitive:
Is there an issue? Send a MessageReason:
The article as written makes use of the terms before it actually explains all of them, which makes it difficult to understand on a first reading, and also makes use of formal logic structures that are not explained in this document, which makes it hard to read for a lay-person. I'm trying to reorganize a little so each term is explained before it is used, and so it doesn't expect the reader to already know formal logic.
Changed line(s) 3,27 (click to see context) from:
In logic, "sound", "valid", and "true" ''[[YouKeepUsingThatWord are not synonymous]]''.
A set of premises and a conclusion is called a syllogism:
--> Premise: If X, then Y
--> Premise: If Y, then Z
--> Conclusion: Therefore if X then Z.
What makes syllogisms useful is that they reduce an argument to its simplest form, making it easy to examine for flaws. The premises and conclusion can be "true" or "false"; the chain of reasoning itself can be "valid" or "invalid"; the argument as a whole is either "sound" or "unsound".
'''Truth''' refers to the factual accuracy of each premise and conclusion of the argument. ''It has nothing to do with the validity of the argument''.
-->All dogs are animals. (True premise/All A are X.)
-->All cats are animals. (True premise/All B are X.)
-->Therefore, all turtles are animals. ([[BatDeduction True conclusion: All turtles ARE animals, HOWEVER - Invalid logic: If all A are X, and all B are X, then all C are not necessarily X.]])
---> (The argument as a whole is unsound, even though the premises and conclusion are true, because the logic is invalid. This is not a valid argument, even though it's factually correct.)
'''Validity''' refers to the chain of reasoning, the logical part of the argument. An argument is valid if it is impossible for its conclusion to be wrong and the premises true. ''It has nothing to do with the truth of the conclusion and premises.''
-->{{All animals are dogs}}. (False premise/All A are B.)
-->All dogs are terriers. (False premise/All B are C.)
-->Therefore, all animals are terriers. ([[EntertaininglyWrong False conclusion: All animals are not terriers, HOWEVER - Valid logic: If all A are B, and all B are C, then all A are C.]])
--->(The argument as a whole is unsound because the premises and conclusion are false, even though the logic is valid. This is a valid argument, even though it's factually wrong)
'''Soundness''' refers to the argument as a whole. The premises must be "true" ''and'' the logic must be "valid". (Using [[YouFailLogicForever a fallacy]] or false premises results in an unsound argument) If these conditions are met then conclusion must be true as well, by the above definition of "valid".
A set of premises and a conclusion is called a syllogism:
--> Premise: If X, then Y
--> Premise: If Y, then Z
--> Conclusion: Therefore if X then Z.
What makes syllogisms useful is that they reduce an argument to its simplest form, making it easy to examine for flaws. The premises and conclusion can be "true" or "false"; the chain of reasoning itself can be "valid" or "invalid"; the argument as a whole is either "sound" or "unsound".
'''Truth''' refers to the factual accuracy of each premise and conclusion of the argument. ''It has nothing to do with the validity of the argument''.
-->All dogs are animals. (True premise/All A are X.)
-->All cats are animals. (True premise/All B are X.)
-->Therefore, all turtles are animals. ([[BatDeduction True conclusion: All turtles ARE animals, HOWEVER - Invalid logic: If all A are X, and all B are X, then all C are not necessarily X.]])
---> (The argument as a whole is unsound, even though the premises and conclusion are true, because the logic is invalid. This is not a valid argument, even though it's factually correct.)
'''Validity''' refers to the chain of reasoning, the logical part of the argument. An argument is valid if it is impossible for its conclusion to be wrong and the premises true. ''It has nothing to do with the truth of the conclusion and premises.''
-->{{All animals are dogs}}. (False premise/All A are B.)
-->All dogs are terriers. (False premise/All B are C.)
-->Therefore, all animals are terriers. ([[EntertaininglyWrong False conclusion: All animals are not terriers, HOWEVER - Valid logic: If all A are B, and all B are C, then all A are C.]])
--->(The argument as a whole is unsound because the premises and conclusion are false, even though the logic is valid. This is a valid argument, even though it's factually wrong)
'''Soundness''' refers to the argument as a whole. The premises must be "true" ''and'' the logic must be "valid". (Using [[YouFailLogicForever a fallacy]] or false premises results in an unsound argument) If these conditions are met then conclusion must be true as well, by the above definition of "valid".
to:
In formal logic, "sound", "valid", and "true" ''[[YouKeepUsingThatWord are not synonymous]]''.
synonymous]]''.
The simplest version of an argument in formal logic is the syllogism: A set ofpremises premises, and then a conclusion is called that follows from the premises according to a set of standard relationships (which are too complex to go into for this article).
A classic example syllogism:
--> Premise:If X, then Y
All men are mortal.
--> Premise:If Y, then Z
Socrates is a man.
--> Conclusion:Therefore if X then Z.
What makes syllogismsTherefore, Socrates is mortal.
Syllogisms are usefulis that because they reduce an argument to its simplest form, making it easy easier to examine for flaws. The premises and conclusion can be "true" or "false"; the chain of reasoning itself can be "valid" or "invalid"; and the argument as a whole is either "sound" or "unsound".
"unsound".
'''Truth''' refers to the factual accuracy of each individual premise andconclusion of the argument. conclusion. ''It has nothing to do with whether the validity of the argument''.
-->All dogs are animals. (True premise/All A are X.)
-->All cats are animals. (True premise/All B are X.)
-->Therefore, all turtles are animals. ([[BatDeduction True conclusion: All turtles ARE animals, HOWEVER - Invalid logic: If all A are X, and all B are X, then all C are not necessarily X.]])
---> (Theargument as a whole is unsound, correct or not''; a statement can be true even though if it is used in an incoherent argument.
-->Premise: All dogs are animals.
-->Premise: All cats are animals.
-->Conclusion: Therefore, all turtles are animals.
--->Both of the premises are true, and the conclusion is true; all turtles aretrue, because the logic is invalid. This indeed animals. The truth of all three statements is not a valid argument, even though it's factually correct.)
affected by the clearly invalid logic connecting them.
'''Validity''' refers to whether the chain ofreasoning, reasoning that connects the premises and conclusion is logical part of the argument. or not. An argument is valid if it is impossible ''impossible'' for its conclusion to be wrong and false while the premises are true. ''It has nothing to do with whether the truth of the premises and conclusion and premises.''
are in fact true.''
-->{{All animals are dogs}}.(False premise/All A are B.(This is a false premise.)
-->All dogs are terriers.(False premise/All B are C.(This is also a false premise.)
-->Therefore, all animals are terriers. ([[EntertaininglyWrongFalse conclusion: All The conclusion is likewise false: Not all animals are not terriers, HOWEVER - Valid logic: If all A are B, and all B are C, then all A are C.terriers.]])
--->(The --->Although all three parts of this argument as a whole is unsound because the premises and conclusion are false, even though the logic is valid. This is obviously wrong, together they form a valid argument, even though it's factually wrong)
''valid'' argument. IF all animals were dogs AND all dogs were terriers, then all animals would indeed be terriers.
'''Soundness''' refers to the argument as a whole.The premises must be "true" An argument is sound if the logic is valid ''and'' all the logic premises are true. If the argument is sound, then the conclusion must be accepted as true, by the definition of "valid". (Using An unsound argument is one that contains a [[YouFailLogicForever a fallacy]] logical fallacy]], making it invalid, or contains a false premises results in an unsound argument) If these conditions are met then conclusion must be true as well, by the above definition of "valid".
premise.
The simplest version of an argument in formal logic is the syllogism: A set of
A classic example syllogism:
--> Premise:
--> Premise:
--> Conclusion:
What makes syllogisms
Syllogisms are useful
'''Truth''' refers to the factual accuracy of each individual premise and
-->All dogs are animals. (True premise/All A are X.)
-->All cats are animals. (True premise/All B are X.)
-->Therefore, all turtles are animals. ([[BatDeduction True conclusion: All turtles ARE animals, HOWEVER - Invalid logic: If all A are X, and all B are X, then all C are not necessarily X.]])
---> (The
-->Premise: All dogs are animals.
-->Premise: All cats are animals.
-->Conclusion: Therefore, all turtles are animals.
--->Both of the premises are true, and the conclusion is true; all turtles are
'''Validity''' refers to whether the chain of
-->{{All animals are dogs}}.
-->All dogs are terriers.
-->Therefore, all animals are terriers. ([[EntertaininglyWrong
'''Soundness''' refers to the argument as a whole.
Changed line(s) 31,34 (click to see context) from:
--->(The argument as a whole is sound because the premises and conclusion are true and the logic is valid. This is a valid and factually correct argument.)
A perfect (deductive) argument. It is true and valid, and therefore sound. In other words, the argument must be based on accurate information and not contain any errors in logic.
A perfect (deductive) argument. It is true and valid, and therefore sound. In other words, the argument must be based on accurate information and not contain any errors in logic.
to:
A perfect (deductive) argument. It is true and valid, and therefore sound. In other words, the argument must be based on accurate information and not contain any errors in logic.
Changed line(s) 37,40 (click to see context) from:
The above only refers to deductive logic. When it comes to induction, things get a bit more dicey. (See what we did there?)
The first thing to note is that all inductive arguments are, by their nature, invalid: induction, by its nature, relies on probability as a central element. Since the definition of validity is that, given true premises, you always end up with a true conclusion, and the definition of a probabilistic premise is that you can feed in true data and still come up with a false answer, inductive arguments are always invalid according to the strict standards of logic. This doesn't make them any less useful. For instance:
The first thing to note is that all inductive arguments are, by their nature, invalid: induction, by its nature, relies on probability as a central element. Since the definition of validity is that, given true premises, you always end up with a true conclusion, and the definition of a probabilistic premise is that you can feed in true data and still come up with a false answer, inductive arguments are always invalid according to the strict standards of logic. This doesn't make them any less useful. For instance:
to:
The above only refers to deductive logic. When it comes to induction, things get a bit more dicey. (See what we did there?)
The first thing to notecomplicated.
Inductive logic isthat all drawing ''likely'' conclusions from true premises. All inductive arguments are, by their nature, invalid: induction, by its nature, invalid; induction relies on probability as a central element. Since the definition of validity is that, given element rather than certainty. Validity requires that true premises, you always end up with premises NEVER lead to a true false conclusion, and the definition of but a probabilistic premise is specifically breaks that you can feed in true data and still come up with a false answer, inductive arguments are always invalid according to the strict standards of logic. rule. This doesn't make them any less useful. For instance:
useful, and in fact most of the logic people make use of on a day to day basis is inductive, based on previous experience and 'rules of thumb' rather than strict, unbreakable truths.
As an example:
The first thing to note
Inductive logic is
As an example:
Changed line(s) 45,48 (click to see context) from:
This is what is called a ''strong'' inductive argument: more likely to be true than false. It's invalid: even if both premises are true, the only thing we know for certain is that Brahim is Moroccan.[[note]]And male -- from his name: "Brahim" being the Moroccan pronunciation of "Ibrahim", the Arabic equivalent of "Abraham"-- but let's ignore that.[[/note]] Assuming that he is Moroccan, Brahim could still be one of the 1.1% of Moroccans who are Christian, or one of the 0.2% of Moroccans who are Jewish. Nevertheless, it is highly likely, given no data about Brahim other than that he is Moroccan, that Brahim is in fact Muslim.
If it is true that Brahim is Moroccan and that 98.7% of Moroccans are Muslim, this argument is also ''cogent''. A cogent argument is a strong argument with true premises.
If it is true that Brahim is Moroccan and that 98.7% of Moroccans are Muslim, this argument is also ''cogent''. A cogent argument is a strong argument with true premises.
to:
This argument is what is called a ''strong'' inductive argument: more likely to be true than false. It's invalid: ''invalid'': even if both premises are true, the only thing we know for certain is that Brahim is Moroccan.[[note]]And male -- from his name: "Brahim" being the Moroccan pronunciation of "Ibrahim", the Arabic equivalent of "Abraham"-- but let's ignore that.[[/note]] Assuming that he is Moroccan, Brahim could still be one of the 1.1% of Moroccans who are Christian, or one of the 0.2% of Moroccans who are Jewish. Nevertheless, it is highly likely, given no other data about Brahim other than that he is Moroccan, it is highly likely that Brahim is in fact Muslim.
IfMuslim.
So for inductive arguments, we don't worry about validity; instead we say the argument is '''strong''' if it is ''unlikely'' to have a false conclusion, provided the premises are true. And instead of saying the argument is sound, we say it is '''cogent''' if the logic is strong and the premises are all true.
''If'' it is true that Brahim isMoroccan and Moroccan, ''and'' it is true that 98.7% of Moroccans are Muslim, then this argument is also ''cogent''. A cogent argument and we can safely assume Brahim is a strong argument with true premises.
Muslim unless and until we find specific information to the contrary.
If
So for inductive arguments, we don't worry about validity; instead we say the argument is '''strong''' if it is ''unlikely'' to have a false conclusion, provided the premises are true. And instead of saying the argument is sound, we say it is '''cogent''' if the logic is strong and the premises are all true.
''If'' it is true that Brahim is
Changed line(s) 55,58 (click to see context) from:
This is theoretically "strong", and if the premises are correct then it is cogent, but one wouldn't want to rely on that.
Conversely, simply because an inductive argument is weak does not mean that it isn't true. This should be fairly intuitive:
Conversely, simply because an inductive argument is weak does not mean that it isn't true. This should be fairly intuitive:
to:
This is theoretically "strong", a "strong" argument, and if the premises are correct then it is cogent, but cogent. But as it's only a tiny fraction past 50%, one wouldn't want to rely on that.
Conversely, simply becausethat conclusion.
In the same way that an invalid deduction might still have a true conclusion (as with the turtles above), an inductive argument that is weakdoes not mean that it isn't true.could still have a true conclusion. This should be fairly intuitive:
Conversely, simply because
In the same way that an invalid deduction might still have a true conclusion (as with the turtles above), an inductive argument that is weak
Changed line(s) 63,64 (click to see context) from:
This is a weak argument, and therefore not cogent, even though all its premises are true and has a true conclusion. On the other hand, this argument ''would'' be strong, and it is also cogent even though its conclusion is false:
to:
This is a weak argument, and therefore not cogent, even though all its premises are true and has a true conclusion. conclusion.
On the other hand,this a strong argument ''would'' can easily be strong, and it is also cogent even though its conclusion is false:
while still producing a false conclusion:
On the other hand,
That's why inductive reasoning is less reliable than deduction.
Changed line(s) 77,78 (click to see context) from:
A valid deductive argument. However, the conclusion is known to be untrue; it is well documented that the Internet originated with United States military research in communications systems. Therefore, one or both of the premises must be false. Important: this technique does not tell you which premise is false, or whether both of them are, merely that at least one must be. In this example, it may be that good things can indeed come from military research; or that the Internet is not a good thing; or both (good things have come from military research, but the Internet is not one of them.)
to:
A valid deductive argument. However, the conclusion is known to be untrue; it is well documented that the Internet originated with United States military research in communications systems. Therefore, one or both of the premises must be false. Important: this technique does not tell you which ''which'' premise is false, or whether both ''both'' of them are, merely that at least one must be. In this example, it may be that good things can indeed come from military research; or that the Internet is not a good thing; or both (good things have come from military research, but the Internet is not one of them.)
them).
Is there an issue? Send a MessageReason:
None
Changed line(s) 16 (click to see context) from:
-->Therefore, all turtles are animals. ([[BatDeduction True conclusion: All turtles ARE animals, but - Invalid logic: If all A are X, and all B are X, then all C are not necessarily X.]])
to:
-->Therefore, all turtles are animals. ([[BatDeduction True conclusion: All turtles ARE animals, but HOWEVER - Invalid logic: If all A are X, and all B are X, then all C are not necessarily X.]])
Changed line(s) 23 (click to see context) from:
-->Therefore, all animals are terriers. ([[EntertaininglyWrong False conclusion: All animals are not terriers/Valid logic: If all A are B, and all B are C, then all A ARE C.]])
to:
-->Therefore, all animals are terriers. ([[EntertaininglyWrong False conclusion: All animals are not terriers/Valid terriers, HOWEVER - Valid logic: If all A are B, and all B are C, then all A ARE are C.]])
Is there an issue? Send a MessageReason:
None
Changed line(s) 16 (click to see context) from:
-->Therefore, all turtles are animals. ([[BatDeduction True conclusion: All turtles ARE animals/Invalid logic: If all A are X, and all B are X, then all C are not necessarily X.]])
to:
-->Therefore, all turtles are animals. ([[BatDeduction True conclusion: All turtles ARE animals/Invalid animals, but - Invalid logic: If all A are X, and all B are X, then all C are not necessarily X.]])
Is there an issue? Send a MessageReason:
None
Changed line(s) 81 (click to see context) from:
-->All fish are are aquatic creatures.
to:
-->All fish are are aquatic creatures.
Is there an issue? Send a MessageReason:
None
Changed line(s) 18,19 (click to see context) from:
'''Validity''' refers to the chain of reasoning, the logical part of the argument. An argument is valid if it is impossible for its conclusion to be wrong and the premises true. ''It has nothing to do with the factual truth of the conclusion or the premises.''
to:
'''Validity''' refers to the chain of reasoning, the logical part of the argument. An argument is valid if it is impossible for its conclusion to be wrong and the premises true. ''It has nothing to do with the factual truth of the conclusion or the and premises.''
Is there an issue? Send a MessageReason:
None
Changed line(s) 18,19 (click to see context) from:
'''Validity''' refers to the chain of reasoning, the logical part of the argument. ''It has nothing to do with the truth of the conclusion or the premises it is based upon.''
to:
'''Validity''' refers to the chain of reasoning, the logical part of the argument. An argument is valid if it is impossible for its conclusion to be wrong and the premises true. ''It has nothing to do with the factual truth of the conclusion or the premises it is based upon.premises.''
Changed line(s) 23,24 (click to see context) from:
--->(The argument as a whole is unsound because the premises and therefore the conclusion are false, even though the logic is valid. This is a valid argument, even though it's factually wrong)
to:
--->(The argument as a whole is unsound because the premises and therefore the conclusion are false, even though the logic is valid. This is a valid argument, even though it's factually wrong)
Is there an issue? Send a MessageReason:
None
Changed line(s) 16,17 (click to see context) from:
---> (The argument as a whole is unsound, even though the premises and conclusion are true, because the logic is invalid. This is a poor argument, even if it's factually correct.)
to:
---> (The argument as a whole is unsound, even though the premises and conclusion are true, because the logic is invalid. This is not a poor valid argument, even if though it's factually correct.)
Changed line(s) 23,24 (click to see context) from:
--->(The argument as a whole is unsound because the premises and therefore the conclusion are false, even though the logic is valid. This is a valid argument, even if it's factually wrong)
to:
--->(The argument as a whole is unsound because the premises and therefore the conclusion are false, even though the logic is valid. This is a valid argument, even if though it's factually wrong)
Is there an issue? Send a MessageReason:
None
Changed line(s) 16,17 (click to see context) from:
---> (The argument as a whole is unsound, even though the premises and conclusion are true, because the logic is invalid)
to:
---> (The argument as a whole is unsound, even though the premises and conclusion are true, because the logic is invalid)
invalid. This is a poor argument, even if it's factually correct.)
Changed line(s) 23,24 (click to see context) from:
--->(The argument as a whole is unsound because the premises and therefore the conclusion are false, even though the logic is valid)
to:
--->(The argument as a whole is unsound because the premises and therefore the conclusion are false, even though the logic is valid)
valid. This is a valid argument, even if it's factually wrong)
Changed line(s) 30,31 (click to see context) from:
--->(The argument as a whole is sound because the premises and conclusion are true and the logic is valid)
to:
--->(The argument as a whole is sound because the premises and conclusion are true and the logic is valid)
valid. This is a valid and factually correct argument.)
Is there an issue? Send a MessageReason:
None
Changed line(s) 9,12 (click to see context) from:
What makes syllogisms useful is that they reduce a statement to its simplest form, making it easy to examine for flaws. The premises and conclusion can be "true" or "false"; the chain of reasoning itself can be "valid" or "invalid"; the argument as a whole is either "sound" or "unsound".
'''Truth''' refers to the factual accuracy of each individual premise and the conclusion. It's exactly what it sounds like, but ''it does not address the validity of the logic''.
'''Truth''' refers to the factual accuracy of each individual premise and the conclusion. It's exactly what it sounds like, but ''it does not address the validity of the logic''.
to:
What makes syllogisms useful is that they reduce a statement an argument to its simplest form, making it easy to examine for flaws. The premises and conclusion can be "true" or "false"; the chain of reasoning itself can be "valid" or "invalid"; the argument as a whole is either "sound" or "unsound".
'''Truth''' refers to the factual accuracy of eachindividual premise and conclusion of the conclusion. It's exactly what it sounds like, but ''it does not address argument. ''It has nothing to do with the validity of the logic''.
argument''.
'''Truth''' refers to the factual accuracy of each
Changed line(s) 16,19 (click to see context) from:
---> (The argument as a whole is unsound.)
'''Validity''' refers to the chain of reasoning, the logical part of the argument. An argument is valid only if it is impossible for all of the premises to be true and for the conclusion to be false. ''It does not rely on the truth of the premises or of the conclusion.''
'''Validity''' refers to the chain of reasoning, the logical part of the argument. An argument is valid only if it is impossible for all of the premises to be true and for the conclusion to be false. ''It does not rely on the truth of the premises or of the conclusion.''
to:
---> (The argument as a whole is unsound.)
unsound, even though the premises and conclusion are true, because the logic is invalid)
'''Validity''' refers to the chain of reasoning, the logical part of the argument.An argument is valid only if it is impossible for all of the premises to be true and for the conclusion to be false. ''It does not rely on has nothing to do with the truth of the conclusion or the premises or of the conclusion.it is based upon.''
'''Validity''' refers to the chain of reasoning, the logical part of the argument.
Changed line(s) 23,26 (click to see context) from:
--->(The argument as a whole is unsound.)
'''Soundness''' refers to the argument as a whole. The premises must be "true" ''and'' the logic must be "valid". (Using [[YouFailLogicForever a fallacy]] results in an unsound argument, as does using false premises.) If these conditions are met, the conclusion must be true as well, by the above definition of "valid".
'''Soundness''' refers to the argument as a whole. The premises must be "true" ''and'' the logic must be "valid". (Using [[YouFailLogicForever a fallacy]] results in an unsound argument, as does using false premises.) If these conditions are met, the conclusion must be true as well, by the above definition of "valid".
to:
--->(The argument as a whole is unsound.)
unsound because the premises and therefore the conclusion are false, even though the logic is valid)
'''Soundness''' refers to the argument as a whole. The premises must be "true" ''and'' the logic must be "valid". (Using [[YouFailLogicForever a fallacy]] or false premises results in an unsoundargument, as does using false premises.) argument) If these conditions are met, the met then conclusion must be true as well, by the above definition of "valid".
'''Soundness''' refers to the argument as a whole. The premises must be "true" ''and'' the logic must be "valid". (Using [[YouFailLogicForever a fallacy]] or false premises results in an unsound
Changed line(s) 30 (click to see context) from:
to:
--->(The argument as a whole is sound because the premises and conclusion are true and the logic is valid)
Is there an issue? Send a MessageReason:
None
Changed line(s) 57 (click to see context) from:
-->BarackObama is the President of the United States.
to:
Is there an issue? Send a MessageReason:
None
Changed line(s) 3,4 (click to see context) from:
In logic, "sound", "valid", and "true" ''are not synonymous''.
to:
In logic, "sound", "valid", and "true" ''are ''[[YouKeepUsingThatWord are not synonymous''.synonymous]]''.
Is there an issue? Send a MessageReason:
None
Changed line(s) 11,12 (click to see context) from:
"Truth" refers to the factual accuracy of each individual premise and the conclusion. It's exactly what it sounds like, but ''it does not address the validity of the logic''.
to:
Changed line(s) 18,19 (click to see context) from:
"Validity" refers to the chain of reasoning, the logical part of the argument. An argument is valid only if it is impossible for all of the premises to be true and for the conclusion to be false. ''It does not rely on the truth of the premises or of the conclusion.''
to:
Changed line(s) 25,26 (click to see context) from:
"Soundness" refers to the argument as a whole. The premises must be "true" ''and'' the logic must be "valid". (Using [[YouFailLogicForever a fallacy]] results in an unsound argument, as does using false premises.) If these conditions are met, the conclusion must be true as well, by the above definition of "valid".
to:
Is there an issue? Send a MessageReason:
None
Changed line(s) 5 (click to see context) from:
In logic, a set of premises and a conclusion is called a syllogism:
to:
Changed line(s) 9,10 (click to see context) from:
What makes syllogisms useful is that they reduce a chain of logic to its simplest form, making it easy to examine the logic for flaws. The premises and conclusion can be "true" or "false"; the chain of reasoning itself can be "valid" or "invalid"; the argument as a whole is either "sound" or "unsound".
to:
What makes syllogisms useful is that they reduce a chain of logic statement to its simplest form, making it easy to examine the logic for flaws. The premises and conclusion can be "true" or "false"; the chain of reasoning itself can be "valid" or "invalid"; the argument as a whole is either "sound" or "unsound".
Is there an issue? Send a MessageReason:
None
Changed line(s) 91,92 (click to see context) from:
-->Therefore, All aquatic creatures are ''not'' fish.
to:
-->Therefore, All aquatic creatures are ''not'' all aquatic creatures are fish.
Is there an issue? Send a MessageReason:
None
Changed line(s) 3,4 (click to see context) from:
In logic, "sound", "valid", and "true" ''are not synonymous''. The premises and conclusion can be "true" or "false"; the chain of reasoning itself can be "valid" or "invalid"; the argument as a whole is either "sound" or "unsound".
to:
In logic, "sound", "valid", and "true" ''are not synonymous''. The premises and conclusion can be "true" or "false"; the chain of reasoning itself can be "valid" or "invalid"; the argument as a whole is either "sound" or "unsound".\n
Changed line(s) 6,9 (click to see context) from:
--> All X are Y
--> All Y are Z
--> Therefore all X are Z
--> All Y are Z
--> Therefore all X are Z
to:
--> All X are Premise: If X, then Y
-->All Y are Premise: If Y, then Z
--> Conclusion: Thereforeall if X are Z
then Z.
What makes syllogisms useful is that they reduce a chain of logic to its simplest form, making it easy to examine the logic for flaws. The premises and conclusion can be "true" or "false"; the chain of reasoning itself can be "valid" or "invalid"; the argument as a whole is either "sound" or "unsound".
-->
--> Conclusion: Therefore
What makes syllogisms useful is that they reduce a chain of logic to its simplest form, making it easy to examine the logic for flaws. The premises and conclusion can be "true" or "false"; the chain of reasoning itself can be "valid" or "invalid"; the argument as a whole is either "sound" or "unsound".
Changed line(s) 92 (click to see context) from:
-->Thus we know for certain that the statement "All fish are aquatic creatures, but not all aquatic creatures are fish." is sound, valid, and true.
to:
Is there an issue? Send a MessageReason:
None
Changed line(s) 8,9 (click to see context) from:
--> Therefore ll X are Z
to:
--> Therefore ll all X are Z
Is there an issue? Send a MessageReason:
None
In logic, a set of premises and a conclusion is called a syllogism:
--> All X are Y
--> All Y are Z
--> Therefore ll X are Z
--> All X are Y
--> All Y are Z
--> Therefore ll X are Z
Changed line(s) 69 (click to see context) from:
A valid deductive argument. However, the conclusion is known to be untrue; it is well documented that the Internet originated with United States military research in communications systems. Therefore, one or both of the premises must be false. Important: this technique does not tell you which premise is false, or whether both of them are, merely that at least one must be. In this example, it may be that good things can indeed come from military research; or that the Internet is not a good thing; or both (good things have come from military research, but the Internet is not one of them.)
to:
A valid deductive argument. However, the conclusion is known to be untrue; it is well documented that the Internet originated with United States military research in communications systems. Therefore, one or both of the premises must be false. Important: this technique does not tell you which premise is false, or whether both of them are, merely that at least one must be. In this example, it may be that good things can indeed come from military research; or that the Internet is not a good thing; or both (good things have come from military research, but the Internet is not one of them.))
By combining chains of logic using sets of syllogisms known to be sound, valid, and true, one can also prove the ''falsity'' of a hypothesis or logical fallacy with certainty, and establish larger absolute sound, valid, true statements:
-->All fish are are aquatic creatures.
-->Hypothesis: All aquatic creatures are fish. ''(ConverseError fallacy)''
-->All dolphins are aquatic creatures.
-->Therefore, all dolphins are fish. ''(AssociationFallacy)''
-->All dolphins are mammals.
-->Mammals are not fish.
-->Therefore, dolphins are not fish.
-->All dolphins are aquatic creatures.
-->Dolphins are not fish.
-->Therefore, All aquatic creatures are ''not'' fish.
-->Thus we know for certain that the statement "All fish are aquatic creatures, but not all aquatic creatures are fish." is sound, valid, and true.
By combining chains of logic using sets of syllogisms known to be sound, valid, and true, one can also prove the ''falsity'' of a hypothesis or logical fallacy with certainty, and establish larger absolute sound, valid, true statements:
-->All fish are are aquatic creatures.
-->Hypothesis: All aquatic creatures are fish. ''(ConverseError fallacy)''
-->All dolphins are aquatic creatures.
-->Therefore, all dolphins are fish. ''(AssociationFallacy)''
-->All dolphins are mammals.
-->Mammals are not fish.
-->Therefore, dolphins are not fish.
-->All dolphins are aquatic creatures.
-->Dolphins are not fish.
-->Therefore, All aquatic creatures are ''not'' fish.
-->Thus we know for certain that the statement "All fish are aquatic creatures, but not all aquatic creatures are fish." is sound, valid, and true.
Is there an issue? Send a MessageReason:
None
Changed line(s) 9 (click to see context) from:
-->Therefore, all turtles are animals. ([[BatDeduction True conclusion: All turtles ''are'' animals/Invalid logic: If all A are X, and all B are X, then all C are not necessarily X.]])
to:
-->Therefore, all turtles are animals. ([[BatDeduction True conclusion: All turtles ''are'' ARE animals/Invalid logic: If all A are X, and all B are X, then all C are not necessarily X.]])
Changed line(s) 16 (click to see context) from:
-->Therefore, all animals are terriers. ([[EntertaininglyWrong False conclusion: All animals are not terriers/Valid logic: If all A are B, and all B are C, then all A ''are'' C.]])
to:
-->Therefore, all animals are terriers. ([[EntertaininglyWrong False conclusion: All animals are not terriers/Valid logic: If all A are B, and all B are C, then all A ''are'' ARE C.]])
Is there an issue? Send a MessageReason:
Fixing the tropes. (In Right For The Wrong Reasons the premises are false.)
Changed line(s) 9 (click to see context) from:
-->Therefore, all turtles are animals. ([[RightForTheWrongReasons True conclusion: All turtles ''are'' animals/Invalid logic: If all A are X, and all B are X, then all C are not necessarily X.]])
to:
-->Therefore, all turtles are animals. ([[RightForTheWrongReasons ([[BatDeduction True conclusion: All turtles ''are'' animals/Invalid logic: If all A are X, and all B are X, then all C are not necessarily X.]])
Changed line(s) 16 (click to see context) from:
-->Therefore, all animals are terriers. (False conclusion: All animals are not terriers/Valid logic: If all A are B, and all B are C, then all A ''are'' C.)
to:
-->Therefore, all animals are terriers. (False ([[EntertaininglyWrong False conclusion: All animals are not terriers/Valid logic: If all A are B, and all B are C, then all A ''are'' C.)]])
Is there an issue? Send a MessageReason:
None
Changed line(s) 37,38 (click to see context) from:
This is what is called a ''strong'' inductive argument: more likely to be true than false. It's invalid: even if both premises are true, the only thing we know for certain is that Brahim is Moroccan.[[note]]And male -- from his name: "Brahim" being the Moroccan pronunciation of "Ibrahim", the Arabic equivalent of "Abraham"-- but let's ignore that.[[/note]] Brahim could be one of the 1.1% of Moroccans who are Christian, or one of the 0.2% of Moroccans who are Jewish. Nevertheless, it is highly likely, given no data about Brahim other than that he is Moroccan, that Brahim is in fact Muslim.
to:
This is what is called a ''strong'' inductive argument: more likely to be true than false. It's invalid: even if both premises are true, the only thing we know for certain is that Brahim is Moroccan.[[note]]And male -- from his name: "Brahim" being the Moroccan pronunciation of "Ibrahim", the Arabic equivalent of "Abraham"-- but let's ignore that.[[/note]] Assuming that he is Moroccan, Brahim could still be one of the 1.1% of Moroccans who are Christian, or one of the 0.2% of Moroccans who are Jewish. Nevertheless, it is highly likely, given no data about Brahim other than that he is Moroccan, that Brahim is in fact Muslim.
Is there an issue? Send a MessageReason:
None
Changed line(s) 37,40 (click to see context) from:
This is what is called a ''strong'' inductive argument: more likely to be true than false. It's invalid: we only know that Brahim is Moroccan.[[note]]And male -- from his name: "Brahim" being the Moroccan pronunciation of "Ibrahim", the Arabic equivalent of "Abraham"-- but let's ignore that.[[/note]] Brahim could be one of the 1.1% of Moroccans who are Christian, or one of the 0.2% of Moroccans who are Jewish. Nevertheless, it is highly likely, given no data about Brahim other than that he is Moroccan, that Brahim is in fact Muslim.
If Brahim is in fact Moroccan and is also in fact Muslim, this argument is also ''cogent''. A cogent argument is a strong argument with true premises.
If Brahim is in fact Moroccan and is also in fact Muslim, this argument is also ''cogent''. A cogent argument is a strong argument with true premises.
to:
This is what is called a ''strong'' inductive argument: more likely to be true than false. It's invalid: we even if both premises are true, the only thing we know for certain is that Brahim is Moroccan.[[note]]And male -- from his name: "Brahim" being the Moroccan pronunciation of "Ibrahim", the Arabic equivalent of "Abraham"-- but let's ignore that.[[/note]] Brahim could be one of the 1.1% of Moroccans who are Christian, or one of the 0.2% of Moroccans who are Jewish. Nevertheless, it is highly likely, given no data about Brahim other than that he is Moroccan, that Brahim is in fact Muslim.
If it is true that Brahim isin fact Moroccan and is also in fact that 98.7% of Moroccans are Muslim, this argument is also ''cogent''. A cogent argument is a strong argument with true premises.
If it is true that Brahim is
Is there an issue? Send a MessageReason:
None
Changed line(s) 37,38 (click to see context) from:
This is what is called a ''strong'' inductive argument: more likely to be true than false. It's invalid: we only know that Brahim is Moroccan.[[note]]And male -- from his name: "Brahim" being the Moroccan pronunciation of "Ibrahim", the Arabic equivalent of "Abraham"-- but let's ignore that.[[/note]] Brahim could be one of the 1.1% of Moroccans who are Christian, or one of the 0.2% of Moroccans who are Jewish. Nevertheless, it is highly likely, given no data about Brahim other than that he is Moroccan, that Brahim is in fact Muslim. This argument is also cogent, if the premises are true. A cogent argument is a strong argument with true premises.
to:
This is what is called a ''strong'' inductive argument: more likely to be true than false. It's invalid: we only know that Brahim is Moroccan.[[note]]And male -- from his name: "Brahim" being the Moroccan pronunciation of "Ibrahim", the Arabic equivalent of "Abraham"-- but let's ignore that.[[/note]] Brahim could be one of the 1.1% of Moroccans who are Christian, or one of the 0.2% of Moroccans who are Jewish. Nevertheless, it is highly likely, given no data about Brahim other than that he is Moroccan, that Brahim is in fact Muslim. This
If Brahim is in fact Moroccan and is also in fact Muslim, this argument is alsocogent, if the premises are true.''cogent''. A cogent argument is a strong argument with true premises.
If Brahim is in fact Moroccan and is also in fact Muslim, this argument is also
Is there an issue? Send a MessageReason:
corrected information on cogent arguments
Changed line(s) 37,38 (click to see context) from:
This is what is called a ''strong'' inductive argument: more likely to be true than false. It's invalid: we only know that Brahim is Moroccan.[[note]]And male -- from his name: "Brahim" being the Moroccan pronunciation of "Ibrahim", the Arabic equivalent of "Abraham"-- but let's ignore that.[[/note]] Brahim could be one of the 1.1% of Moroccans who are Christian, or one of the 0.2% of Moroccans who are Jewish. Nevertheless, it is highly likely, given no data about Brahim other than that he is Moroccan, that Brahim is in fact Muslim. If Brahim is in fact Muslim, then the argument becomes ''cogent'': not only strong, but true.
to:
This is what is called a ''strong'' inductive argument: more likely to be true than false. It's invalid: we only know that Brahim is Moroccan.[[note]]And male -- from his name: "Brahim" being the Moroccan pronunciation of "Ibrahim", the Arabic equivalent of "Abraham"-- but let's ignore that.[[/note]] Brahim could be one of the 1.1% of Moroccans who are Christian, or one of the 0.2% of Moroccans who are Jewish. Nevertheless, it is highly likely, given no data about Brahim other than that he is Moroccan, that Brahim is in fact Muslim. If Brahim is in fact Muslim, then the This argument becomes ''cogent'': not only strong, but true.
is also cogent, if the premises are true. A cogent argument is a strong argument with true premises.
Changed line(s) 45,46 (click to see context) from:
This is theoretically "strong", and if Pat really is male it would be cogent, but one wouldn't want to rely on that.
to:
This is theoretically "strong", and if Pat really the premises are correct then it is male it would be cogent, but one wouldn't want to rely on that.
Changed line(s) 53,54 (click to see context) from:
This is a weak argument, and therefore not cogent, even though all its premises are true and has a true conclusion. On the other hand, this argument ''would'' be strong, but it would also not be cogent:
to:
This is a weak argument, and therefore not cogent, even though all its premises are true and has a true conclusion. On the other hand, this argument ''would'' be strong, but and it would is also not be cogent:
cogent even though its conclusion is false:
Is there an issue? Send a MessageReason:
None
Changed line(s) 29,30 (click to see context) from:
The above only refers to deductive logic. When it comes to induction, things get a bit more dicey.
to:
The above only refers to deductive logic. When it comes to induction, things get a bit more dicey.
dicey. (See what we did there?)
Is there an issue? Send a MessageReason:
None
Changed line(s) 10,12 (click to see context) from:
The argument as a whole is unsound.
to:
Changed line(s) 18,22 (click to see context) from:
Technically speaking, even this breeds further distinctions, as "cogent" is the word you're properly supposed to use for inductive reasoning; only deductive arguments are "valid".
The argument as a whole is unsound. "Soundness" refers to the argument as a whole. The premises must be "true" ''and'' the logic must be "valid". (Using [[YouFailLogicForever a fallacy]] results in an unsound argument, as does using false premises.) If these conditions are met, the conclusion must be true as well, by the above definition of "valid".
to:
"Soundness" refers to the argument as a whole. The premises must be "true" ''and'' the logic must be "valid". (Using [[YouFailLogicForever a fallacy]] results in an unsound argument, as does using false premises.) If these conditions are met, the conclusion must be true as well, by the above definition of "valid".
Changed line(s) 31,32 (click to see context) from:
Of course, the above only refers to deductive logic. When it comes to induction, things get a bit more dicey.
to:
