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What is Logic? (Logic 101)

Logic isn't really so tough. In fact, it's one of the simplest things to use because you use it all the time, though you may not realize it.

When you are at a supermarket and one brand of sugar is 3 cents per ounce, but another is 39 cents per lb. It it doesn't take long for you to pull out your calculator. You do that because you recognize that those ounces and pounds have to be put in the same catagory to be compared. That's logic. You use logic to do most everything. When you decide to take a shower after you work out instead of before, you don't necessarily go through all the formal steps it takes to reach that conclusion validly, but your decision rests on logic nonetheless.

Logic really means putting your thoughts in order.

So lets see how order works...

Order is the key word. It applies to all kinds of different disciplines. In nature, there is an order that reason discovers but does not produce. The patterns of quartz crystals, regularity of natural laws, movements of the planets, complext information in a single strand of DNA - they all show us an order that we can see but that we did nothing to put there, just as you are reading this post, but did not put the words here.

In art however, we do produce order. The artist imposes order on the things around him. He crafts the lines he wants to see, bends steel to suit his purpose, arranges the rhythms, the melodies, the harmonies to express a certain feeling. Art is created by a person imposing order on the things of the external world.

In philosophical thinking there is order also. Ethical order is order that reason produces in acts of the will. In other words, it is the ordering of our thoughts about the right and wrong of the things we choose. Whenever we ask a question about what we ought to do, we are ordering our choices by an ethical standard. That order tells us what we really think is good. It shows us what our values really are. Should I lie to save twenty bucks? Should I help the lady stranded on the freeway, or hurry home to watch football? How we answer depends on an ethical order that we produce about the choices we make. The best system of ethics is the one that best expresses the way things ought to be, ie., what really is good and valuable.

The order of logic is very similiar. It, too, is an ordering that we produce, but it is concerned with ordering our thoughts. Logic is reason looking at itself to see how good reason works. It studies the methods that we use to analyze information and draw valid conclusions. It puts all of these methods into an order that gives us the right way to draw conclusions. The best system of logic is one that is best suited to drawing proper conclusions from the premises.

To state this as a formal definition: Logic is the study of right reason or valid inferences and the attending fallacies, formal and informal.

Let's break it up...

Logic is the study of right reason. . . . That is the main point. Logic is a study, an ordering, of how to think rightly, or how to find truth. ie...logic is a way to think so that we come to correct conclusions..

. . . or valid inferences. . . . That means implications. Part of studying logic is recognizing when A implies B and when it does not. There are clear-cut rules to help us with this.

. . . and the attending fallacies, formal and informal. A fallacy is a mistake. Sometimes we make mistakes in the way we set up our thinking, or by using an implication that is not true. These are "formal fallacies", because they have to do w/ the form of the argument (more in a future post). Other times the mistakes are in the meaings of the terms we use. They might be unclear or misleading. Or, they might just not have anything to do with the subject at hand. Mistakes like these are "informal fallacies". Knowing the kinds of mistakes we can make helps us to avoid them.

If we put all of our paraphrases together, we get a simplified definition: Logic is a way to think so that we can come to correct conclusions by understanding implications and the mistakes people often make in thinking.

So regardless of the environment, circumstances, entities involved...logic is unchanging. While the variables may change, the way in that variables are determined to be true, untrue, valid or invalid do not change. Logic is is after all, putting our thoughts in order.

-=]Apokalupsis[=-Senior Administrator-------------------------I never considered a difference of opinion in politics, in religion, in philosophy, as cause for withdrawing from a friend. - Thomas Jefferson

Re: What is Logic? (Logic 101)

I have to quibble with your shopping example, that's not a real world application of logic but of arithmetic and units. A better one might be observing two people enter a room and three people leaving, and concluding that the third person must have been there before you arrived. The shower example is also a little contrived; one doesn't decide not to have a shower - the decision to have one only occurs after something changes with your body that requires one, i.e. the workout.

> Logic is a way to think so that we can come to correct conclusions by understanding implications and the mistakes people often make in thinking.

Yes, but a logical argument is only as good as the truth of the axioms or assumptions or the universe of discourse. So true and untrue is not really in the purview of logic - only valid or invalid. One great example is the Kalam's Cosmological Argument (and not to argue it here), which is indeed a sound argument but the axioms are wrong, its conclusion wrong and the universe of discourse, i.e. deities, nonsensical to an atheists mind.

Having a "correct conclusion" does not get one closer to the truth unless all three conditions are already met; hence KCA is only convincing for theists.

The only time a logical argument is indisputably "true" are those in the domains of mathematics, computing and science. In other domains - politics, religion, art and literature, everything is up for grabs.

Re: What is Logic? (Logic 101)

I have to quibble with your shopping example, that's not a real world application of logic but of arithmetic and units.

The notion of units and comparison are found within the discipline of philosophy as well as arithmetic.

Originally Posted by SharmaK

Yes, but a logical argument is only as good as the truth of the axioms or assumptions or the universe of discourse. So true and untrue is not really in the purview of logic - only valid or invalid. One great example is the Kalam's Cosmological Argument (and not to argue it here), which is indeed a sound argument but the axioms are wrong, its conclusion wrong and the universe of discourse, i.e. deities, nonsensical to an atheists mind.

By conventional definitions, an argument is "sound" if and only if it is valid and all of its premises are true.

The "axioms" of the Kalaam cosmological argument are simply the axioms of logic; you're disputing the truth of its premises, the specific claims it makes in the argument itself. The axioms of the KCM are rules about logical operators (like AND, OR, and implication).

I think you're just disputing how nuanced Apok needs to be. Logic is a way of deducing what must necessarily follow. Logic doesn't tell us whether "Barack Obama is president" is true. Logic tells us that if we accept what we perceive as real, and we perceive that Barack Obama is president, then we must accept that "Barack Obama is president" is true on pain of contradiction.

Logic, like other mathematical structures, is actually meaningless. It's just a way of manipulating symbols or ideas according to particular rules. What makes it meaningful is that humans have found that it faithfully maps the way that certain kinds of things actually work in the real world. It's like the use of math in physics: we do it because it's useful. So instead of working only with the real-world objects, which can be difficult and confusing, we can simply faithfully map the objects into logic-world, use logic-operations, come to a conclusion, then faithfully map back into the real world (as with the 'Barack Obama is president' example above).

If the mappings are truly faithful, then we can accept the real-world conclusion even if we only know how to get to it through logic-world operations.

If I am capable of grasping God objectively, I do not believe, but precisely because I cannot do this I must believe. - Soren Kierkegaard**** you, I won't do what you tell me

Re: What is Logic? (Logic 101)

The notion of units and comparison are found within the discipline of philosophy as well as arithmetic.

By conventional definitions, an argument is "sound" if and only if it is valid and all of its premises are true.

The "axioms" of the Kalaam cosmological argument are simply the axioms of logic; you're disputing the truth of its premises, the specific claims it makes in the argument itself. The axioms of the KCM are rules about logical operators (like AND, OR, and implication).

I think you're just disputing how nuanced Apok needs to be. Logic is a way of deducing what must necessarily follow. Logic doesn't tell us whether "Barack Obama is president" is true. Logic tells us that if we accept what we perceive as real, and we perceive that Barack Obama is president, then we must accept that "Barack Obama is president" is true on pain of contradiction.

Logic, like other mathematical structures, is actually meaningless. It's just a way of manipulating symbols or ideas according to particular rules. What makes it meaningful is that humans have found that it faithfully maps the way that certain kinds of things actually work in the real world. It's like the use of math in physics: we do it because it's useful. So instead of working only with the real-world objects, which can be difficult and confusing, we can simply faithfully map the objects into logic-world, use logic-operations, come to a conclusion, then faithfully map back into the real world (as with the 'Barack Obama is president' example above).

If the mappings are truly faithful, then we can accept the real-world conclusion even if we only know how to get to it through logic-world operations.

Yep, I agree with what you're saying. The word "true" unfortunately is ambiguous and in the other debate regarding what is science where we are discussing facts, he also states that philosophical arguments (e.g. KCA) is also a fact that informs his world-view. Which in a sense is true - KCA is a logical argument and taken as a whole, it is indeed a fact that such an argument exists and that it is logically sound. But in another sense, it cannot be true because, I being an atheist, have actual facts that point to deities most definitely not being true. It's like asserting that fairies exist at the bottom of a garden through some sound logical argument - it doesn't matter if its sound if fairies don't even exist in the first place.

It's good that you bring in the real-world in there because purely logical arguments and philosophical arguments aren't necessarily grounded in real-world facts (e.g. there is a single cause for the universe) but they end up producing non-facts (that universe was caused by a deity). And that's why I dispute, or ask for clarification, of what true means in the OP.

If it means a valid then I have no issue. If it means to make a statement about the actual universe then I do have an issue. The other discussion shows that he takes the latter meaning - a logical argument can indeed inform us of the existence of a deity; and not only that - only his own.

Re: What is Logic? (Logic 101)

Originally Posted by SharmaK

Yep, I agree with what you're saying. The word "true" unfortunately is ambiguous and in the other debate regarding what is science where we are discussing facts, he also states that philosophical arguments (e.g. KCA) is also a fact that informs his world-view. Which in a sense is true - KCA is a logical argument and taken as a whole, it is indeed a fact that such an argument exists and that it is logically sound. But in another sense, it cannot be true because, I being an atheist, have actual facts that point to deities most definitely not being true. It's like asserting that fairies exist at the bottom of a garden through some sound logical argument - it doesn't matter if its sound if fairies don't even exist in the first place.

I think you're confusing "sound" with "valid". If an argument is sound, its conclusions must be true. The existence of a sound argument for the existence of fairies would mean: 1) there is some set of premises which, if true, would mean that fairies exist; 2) these premises are, in fact, true.

It's good that you bring in the real-world in there because purely logical arguments and philosophical arguments aren't necessarily grounded in real-world facts (e.g. there is a single cause for the universe) but they end up producing non-facts (that universe was caused by a deity). And that's why I dispute, or ask for clarification, of what true means in the OP.

If it means a valid then I have no issue. If it means to make a statement about the actual universe then I do have an issue. The other discussion shows that he takes the latter meaning - a logical argument can indeed inform us of the existence of a deity; and not only that - only his own.

I'm surprised that you don't know what it means for a proposition to be true. You don't know what it means to say "The proposition 'God exists' is true"? You don't know what it means to say "The proposition 'God doesn't exist' is true"?

If I am capable of grasping God objectively, I do not believe, but precisely because I cannot do this I must believe. - Soren Kierkegaard**** you, I won't do what you tell me

Re: What is Logic? (Logic 101)

Originally Posted by CliveStaples

I think you're confusing "sound" with "valid". If an argument is sound, its conclusions must be true. The existence of a sound argument for the existence of fairies would mean: 1) there is some set of premises which, if true, would mean that fairies exist; 2) these premises are, in fact, true.

I think one has to include the universe of discourse in order for it to be valid. For example, it is a sound argument that Barak Obama is a Muslim because his father was a Muslim - the religion passes down through the paternal line in Islam. And it is also valid (and true) if we were in the universe of discourse of Islam. But the "reality" is that in a Christian universe of discourse, he is actually a Christian (to some).

Originally Posted by CliveStaples

I
I'm surprised that you don't know what it means for a proposition to be true. You don't know what it means to say "The proposition 'God exists' is true"? You don't know what it means to say "The proposition 'God doesn't exist' is true"?

I think this goes back to the universe of discourse. When some proves that "God exists", it doesn't make me believe that he does. It just informs me that these are the reasons why something believes he does. "True" means "taken to be true by someone who believes in the existence of deities". "True" for me means, actually existing in a physical way - my universe of discourse is the physical universe.

Re: What is Logic? (Logic 101)

Originally Posted by SharmaK

I think one has to include the universe of discourse in order for it to be valid. For example, it is a sound argument that Barak Obama is a Muslim because his father was a Muslim - the religion passes down through the paternal line in Islam. And it is also valid (and true) if we were in the universe of discourse of Islam. But the "reality" is that in a Christian universe of discourse, he is actually a Christian (to some).

No, that's not the universe of discourse. The universe of discourse would be something like the collection of all propositions that might be examined. What you're doing is something different; you're essentially forming a basis by which the soundness of arguments must be evaluated. You're doing something like this:

Take a subset, B, of the universal set of propositions, U. Then an argument A is B-sound if all of its premises are in B. In particular, if B includes the proposition "The Muslim religion passes down through the paternal line in Islam", then the argument "Barack Obama is a Muslim because his father was a Muslim" is B-sound.

Essentially, B is the set of things that are "true for the sake of argument" or "assumed to be true". But that's not what the definition of "sound" is talking about, nor is it what Apok was talking about. Truth, in the sense of the definition of 'sound' and, I suspect, in Apok's posts, makes no reference to 'belief' or 'assumption'. Hopefully we can all agree that there are truths about the universe that are true regardless of what anyone believes or assumes about those truths.

Or, to use the language above, there is a canonical subset B, namely the set of all observer-invariant facts about the universe; an argument A is said to be "sound" if all of its premises are in B.

I think this goes back to the universe of discourse. When some proves that "God exists", it doesn't make me believe that he does. It just informs me that these are the reasons why something believes he does. "True" means "taken to be true by someone who believes in the existence of deities". "True" for me means, actually existing in a physical way - my universe of discourse is the physical universe.

I understand what you're getting at, but I think your approach is too broad. We can agree that if someone proves "God exists", they've only shown that there is a collection of propositions which, if true, necessitate that God exists. In order to evaluate this argument (assuming it is valid), you must identify which of those propositions you think are false and why. Suppose I could prove that if you accept modern science as true, then God exists; it would be shoddy thinking for you to say, "Nah, God isn't in my universe of discourse, so I'm going to reject your conclusion." To do so would be unreasonable; you would either have to accept modern science, with all that it entails (including, in this hypothetical, the existence of God), or you would have to reject modern science.

Or, in the language above (because I love math): Suppose that A and B are subsets of U. (Think of A as "things CliveStaples believes" and B as "things SharmaK believes".) Let P be an argument proving that God exists. Suppose all of its premises are in a subset of B, B*. Then P is both B-sound and B*-sound. If B* is also a subset of A, then P is also A-sound. (Therefore, SharmaK should hold that P's conclusion is true within SharmaK's universe of discourse, A).

If I am capable of grasping God objectively, I do not believe, but precisely because I cannot do this I must believe. - Soren Kierkegaard**** you, I won't do what you tell me

Re: What is Logic? (Logic 101)

Originally Posted by CliveStaples

No, that's not the universe of discourse. The universe of discourse would be something like the collection of all propositions that might be examined. What you're doing is something different; you're essentially forming a basis by which the soundness of arguments must be evaluated. You're doing something like this:

Take a subset, B, of the universal set of propositions, U. Then an argument A is B-sound if all of its premises are in B. In particular, if B includes the proposition "The Muslim religion passes down through the paternal line in Islam", then the argument "Barack Obama is a Muslim because his father was a Muslim" is B-sound.

Essentially, B is the set of things that are "true for the sake of argument" or "assumed to be true". But that's not what the definition of "sound" is talking about, nor is it what Apok was talking about.

I don't have any dispute with the word "sound", "follows logically", "is logically valid". I had an issue with the word "true" because it seems sometimes to leak from be syntactically true to actually true.

So, is Barack Obama a Muslim or not?

Originally Posted by CliveStaples

Truth, in the sense of the definition of 'sound' and, I suspect, in Apok's posts, makes no reference to 'belief' or 'assumption'. Hopefully we can all agree that there are truths about the universe that are true regardless of what anyone believes or assumes about those truths.

Yes, pretty much all of mathematics are universally true.

Or, to use the language above, there is a canonical subset B, namely the set of all observer-invariant facts about the universe; an argument A is said to be "sound" if all of its premises are in B.

Originally Posted by CliveStaples

I understand what you're getting at, but I think your approach is too broad. We can agree that if someone proves "God exists", they've only shown that there is a collection of propositions which, if true, necessitate that God exists. In order to evaluate this argument (assuming it is valid), you must identify which of those propositions you think are false and why. Suppose I could prove that if you accept modern science as true, then God exists; it would be shoddy thinking for you to say, "Nah, God isn't in my universe of discourse, so I'm going to reject your conclusion." To do so would be unreasonable; you would either have to accept modern science, with all that it entails (including, in this hypothetical, the existence of God), or you would have to reject modern science.

If you can indeed prove that God exists within a scientific framework then I wouldn't be able to disregard it. But there hasn't been such an argument put forth. Indeed, these arguments explicitly reject that the universe works in a consistent way (i.e. miracles are not allowed) and that deities (sentient-beings that create universes) are possible. And then just around the corner there's all the other baggage that comes along with it.

Originally Posted by CliveStaples

Or, in the language above (because I love math): Suppose that A and B are subsets of U. (Think of A as "things CliveStaples believes" and B as "things SharmaK believes".) Let P be an argument proving that God exists. Suppose all of its premises are in a subset of B, B*. Then P is both B-sound and B*-sound. If B* is also a subset of A, then P is also A-sound. (Therefore, SharmaK should hold that P's conclusion is true within SharmaK's universe of discourse, A).

That's correct though I would argue that B is a super-set of A because I have already considered all the propositions of A in my rejections.

Re: What is Logic? (Logic 101)

Originally Posted by SharmaK

I don't have any dispute with the word "sound", "follows logically", "is logically valid". I had an issue with the word "true" because it seems sometimes to leak from be syntactically true to actually true.

So, is Barack Obama a Muslim or not?

What is the definition of "Muslim" that you're using?

Originally Posted by SharmaK

If you can indeed prove that God exists within a scientific framework then I wouldn't be able to disregard it. But there hasn't been such an argument put forth. Indeed, these arguments explicitly reject that the universe works in a consistent way (i.e. miracles are not allowed) and that deities (sentient-beings that create universes) are possible. And then just around the corner there's all the other baggage that comes along with it.

You're completely missing the point. This isn't a thread to talk about the strengths and weaknesses of arguments for God; this is a discussion about logic and philosophy. My point was about how we evaluate arguments, not about the strengths and weaknesses of a particular group of arguments.

That's correct though I would argue that B is a super-set of A because I have already considered all the propositions of A in my rejections.

Right, but you don't hold that the propositions in A are true, so they wouldn't be in B. So B wouldn't be a superset of A.

If I am capable of grasping God objectively, I do not believe, but precisely because I cannot do this I must believe. - Soren Kierkegaard**** you, I won't do what you tell me

Re: What is Logic? (Logic 101)

This is not the debate thread for the topic guys. The actual thread is very old, I didn't think I needed to link to it. I only recreated it as a member essay to make it easier to link someone to the op w/o being distracted by the rest of the discussion.

-=]Apokalupsis[=-Senior Administrator-------------------------I never considered a difference of opinion in politics, in religion, in philosophy, as cause for withdrawing from a friend. - Thomas Jefferson

Re: What is Logic? (Logic 101)

Originally Posted by CliveStaples

What is the definition of "Muslim" that you're using?

My point exactly.

Originally Posted by CliveStaples

You're completely missing the point. This isn't a thread to talk about the strengths and weaknesses of arguments for God; this is a discussion about logic and philosophy. My point was about how we evaluate arguments, not about the strengths and weaknesses of a particular group of arguments.

Agreed, I only bring in those arguments to show that the universe of discourse is necessary to interpret a logical series of statements. My point was that arguments for the existence of God are in a different universe of discourse from, say, reality.

Originally Posted by CliveStaples

Right, but you don't hold that the propositions in A are true, so they wouldn't be in B. So B wouldn't be a superset of A.

Not at all, all propositions in A are true within the universe of discourse of A - i.e. the universe that allows for deities, angels, demons, hell, miracles and all religious claims. B, reality, also contains all human ideas, so whilst propositions in A may not be true outside of A (where human inventions are not real), they are still true within A.