Monday, May 25, 2009

Logic Primer 1: What Is Logic?

Logic studies the methods that we use to analyze information and draw valid conclusions. As Norman Geisler and Ronald Brooks put it, “Logic really means putting your thoughts in order.”1 They offer their formal definition: “Logic is the study of right reason or valid inferences and the attending fallacies, formal and informal.”2 Their 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.”3

According to Irving M. Copi and Carl Cohen in their Introduction to Logic, “Logic is the study of the methods and principles used to distinguish correct reasoning from incorrect reasoning.”4 Christian philosopher Gordon Clark puts it succinctly: “logic is the science of necessary inference.”5

We can see from these definitions that logic consists of ordering our thoughts so that we can reason correctly. Geisler and Brooks would add: “The next best thing besides godliness for a Christian is logic”6

The study of logic incorporates a number of elements. At the most basic level, logic examines propositions, arguments, premises, and conclusions. The focus is the use of right thinking to come to correct conclusions. Logic incorporates the study of proper thinking as well as mistakes in thinking (fallacies). Through processes of deduction and induction, inferences are made with the aim of coming to correct conclusions.

In addition, logic also deals with our use of language. The logical thinker is very concerned about precision and clarity in communication. He is concerned with the proper structure of arguments and the correct flow of thought. The student of logic seeks to be careful, methodical, and systematic.

Logic is built upon four undeniable laws:
1. The law of non-contradiction (A is not non-A)
2. The law of identity (A is A)
3. The law of excluded middle (either A or non-A)
4. The law of rational inference

These undeniable laws are foundational to all reason and thinking. One cannot object to the laws of logic without using them in his objection. Where did they foundational laws come from? Geisler and Brooks offer a Christian perspective: “From the standpoint of reality, we understand that God is the basis of all logic. As the ultimate reality, all truth is ultimately found in him.”7

In the next section, we will deal with the building blocks of logic. Terms will be defined and the basic foundation will be laid for further study.

Here are some resources that will get you started:
Audio resources:
- Princeton Review's LSAT Logic in Every Day Life podcast
- Reasons to Believe's Straight Thinking Podcast
- Greg Bahnsen's Critical Thinking course (logic) - uses Copi's textbook. Good only if you are using the book, but audio quality is poor.)
Helpful books:
- Copi and Cohen's Introduction to Logic - recommended for the serious student.
- Being Logical by D.Q. McInerny - recommended as the first read.
- Come Let Us Reason by Norman Geisler & Ronald Brooks
Some Web Links:
- Wikipedia on Logic
- Ken Samples article: Keep your thinking on track.
- Take a logic test here.

Tomorrow we look at the Building Blocks of Logic.

1 Norman Geisler & Ronald Brooks, Come Let Us Reason: An Introduction to Logical Thinking (Grand Rapids, MI: Baker Books, 1990), p. 11.
2 Ibid., p. 12.
3 Ibid.,p. 13.
4 Irving M. Copi & Carl Cohen, Introduction to Logic, 11th Edition (Upper Saddle River, NJ: Pearson Education, 2002), p. 3.
5 Gordon Clark, Logic (Jefferson, MD: The Trinity Foundation, 1985), p. 1.
6 Geisler & Brooks, p. 7.
7 Ibid., p. 17.

22 comments :

Lee said...

Nice post... thanks, I am looking forward to more.

Where did they foundational laws come from? Can’t we just say that the logic laws are “just just"?

They are what they are because they are what they are?

Isn't asking where they came implying they could be something else?

But didn't you just argue that they are "undeniable laws"?

So is your question a valid one?

Do I win a prize for asking 6 questions in a row?

Geisler and Brooks offer a Christian perspective: “From the standpoint of reality, we understand that God is the basis of all logic. As the ultimate reality, all truth is ultimately found in him.”From what you have just taught me, this isn’t a logical argument from Geisler and Brooks is it?

Thanks – Logic is fun. One day I might understand it.

Lee

Brian said...

Thanks for chiming in, Ranger. Your answer is right along the lines of what I would have responded with.

I also would agree that it would be good to hear a good non-theist account of logic that isn't circular.

Lee, if you say the laws of logic are "just there," were they there before the big bang or did they pop into existence out of no reason without cause as well?

The Christian account of logic, to me, seems a more consistent concept of reality than the idea that logic "just is."

I am out of the country at the moment, so I won't be able to do any heavy back and forth on this one.

Take care, Lee. I hope you enjoy the posts.

Lee said...

Hi Guys,

Glad I am predictable :-)

Just to say that I got myself a physics degree from uni, not philosophy so I am still working out the answers myself.

I will think about it though and get back to you – not tonight since I am watching a football game on the TV.

Off to work now.

Take care

Lee

Lee said...

Hello again,

So ‘the laws of logic’, where did they come from?

Well, I already asked why is it wrong to think that they are just a ‘brute fact’ – “they are what they are”.

Not sure yet why this is an invalid position to have?

I think it is also rather fundamental to my thoughts here so I would really love to hear where and why I am wrong.

I would also like to know why asserting that we require a god to provide these logical laws would be an improvement. For me it would be a backward step in our understanding.

I have two simple objections to the ‘god solution’ that I did touched on with my first reply but will repeat here in greater detail.

These are:-

1. By asserting a god the problem has merely been push back another level, the question where did God come from would have to be answered first to have any meaning. Any sort of reasoning (or ‘special pleading’ as it could be called) for God could equally apply to the problem we were first trying to solve.

All that would be achieved with asserting God would be to increase the level of uncertainty to a more mysterious unknown i.e. God. Why not try and solve the first unknown at hand rather than create a new one?

2. By asserting that God created these logical laws creates a new problem. It suggests that the laws could be something else if God willed it. So, what could these logical laws be if not what they already are? Or to put it another way – Could God make these laws something else? Can God make A = not A? (Remembering this is against the laws of logic as stated in the post.)

If the answer is no, then isn’t God also confined to the logical laws? Could it then be said that God is the author of these laws if God is confined to them?

If the laws cannot be changed, not even by God, then the laws are ‘outside the realms of God’ and God isn’t the solution to the problem.

... End of part 1

Lee said...

Part II

Jumping ahead of myself and answering a (strawman?) argument usually presented against what I have just wrote.

If a theist (as normally happens) agrees that God cannot make A=not A (or a 4 sided triangle) since this will indeed be logically impossible but then insists that this is because these logical laws are “part of God’s nature” . (“They have to be this way.”) Haven’t we just got ourselves back to the first solution I presented of a ‘brute fact’ – “They are what they are”? If God’s nature cannot be anything other than it is, it is just another ‘brute fact’. The only difference between my first solution and the god solution is that I didn’t need to assert a God for this brute fact.

God does not seem to be solution to the question at hand then – just an additional unknown.

So maybe another question is whether these logical laws are indeed laws and as such cannot be disputed - they cannot be anything else.

As I have discussed, if the laws cannot be anything else, then they could be just a ‘brute fact’ and we need to get over it.

If however the laws can be different, then firstly they are no-longer fixed laws just arbitrary, and maybe ‘we’ can only exist in a universe and think about the problem where the laws are as they are today. The universes where these laws are different cannot exist with minds to think…

I’m back to a ‘brute fact’ that “they are what they are for me to be able to think about the problem”.

End of Part II

Lee said...

Part III

Unless someone can reason me to a new position, I am again stuck with a brute fact

I cannot say I am happy about this ‘brute fact’ solution I presented since I have not been able to provide any explanation for it and it offers no exploratory power – that frustrates me, but such is life, that is what you have with ‘brute facts’ I guess.

A challenge remains of course that I have just talked around so far - How is this ‘brute fact’ any different to just saying ‘God did it’ and God is a ‘brute fact’?

Well, simply put there is more ‘baggage’ with God - more details to explain with any ‘god solution’.

The ‘brute fact’ of 4 logical laws is rather simpler than an “infinite, unphysical, timeless personal being with a mind that knows everything and has a nature that requires, as a brute fact, these 4 physical laws at its core” (Assuming that is a reasonable definition of a theistic god – no one has ever given me a good definition, so feel free to redefine it anyone so we have a better one for discussion).

The ‘principle of parsimony’ leads me to place my money on the 4 laws as brute fact and not God (which also requires a brute fact).

The solution that makes the least unknowable claims, the fewest assumptions is more likely correct.

I hope that was obvious :-)
(And no, I cannot prove the ‘principle of parsimony’ – it’s just a rule of thumb that seems to work in science. Call it a ‘faith’ I have)

Of course, there are a couple of further options open to me.

As Ranger pointed out, maybe these logical laws are just ‘all in the mind’ (as some atheists might argue)

Evolution got our brains (and hence minds) to where they are today – so maybe a ‘side effect’ of evolution also gave us our ‘logical minds’ and hence these logical laws?

At first glance this seems plausible, however as far as I see it, it answers only part of the question – it answers why we have our ‘logical models’ to explain the world around us.

It doesn’t answer anything about the ‘absolute logical laws’ that our models describe (if they are indeed absolute logical laws – I don’t know, it seems so at first glance).

So if the argument present by Ranger is a true reflection of Dan Barker’s position – I might be disagreeing with him that it is a full answer.

And the last option open to me?

I just don’t know :-)

Why is when you divide the circumference of a circle by its diameter you cannot ever write down the full answer? 3.1415926535897932384626433832795….. To infinity.

Why not just 3?

Just one of these things we may never know

Take care

Lee

Lee said...

WOW... sorry, that was a long post.

Won't happen again. Honest

Lee

Lee said...

Thanks Lee! Now that's the kind of response that I'm looking for! I thought I did go on a bit... it was too large to post in one hit. That's not happened before.

Thanks for your input, it's helpful. I hope my interaction can be helpful to you as well.Thank you for your input as well.

Bouncing ideas around really does help to get rid of the bad ideas

I want to know where I am wrong so I can change

Take care – time to go to work

Lee

Brian said...

As I said before, I don't have a lot of time to chime in on this one, so I will just say my bit for now.

I would say that right now we can agree that logic is a good tool to use to seek truth. We agree on the laws of logic, so that is some common ground.

Now when we ask the philosophical question of how these laws are grounded, the theist is really not in the position to prove anything, nor is the atheist. It seems to me that these are the presuppositions we bring to the question of philosophical grounding.

If we presume atheism, we may be forced into something along the lines of "brute facts." If we presume theism, then logic actually can fit nicely into that picture with God being the ontological grounding for immaterial laws like logic.

This is not something I am trying to demonstrate through deduction. Rather, this seems to be something that can be reasonably accepted by the theist by means of inference to the best explanation (abduction). The idea that God is the grounding of logic has more explanatory scope than the hypothesis "they are just there."

So I don't think it is that profitable to argue too much on this point, only to say that for me as a Christian, theism provides a satisfying solution to this kind of question; I don't find that from the atheistic perspective.

Take care for now! :)

Lee said...

Hi Ranger

Thanks again for your reply… I look forward to your future response after you have given it some further thought.

Who would have thought it, a physicist can talk philosophy with the best of them?

my initial response would be to become the skeptic Good start…I like being sceptical.

"Why is it a brute fact?"Does such a why question make sense?

Why is something A and not A?

"How do you know that?" "What reasons do you have for that statement?" I refer you to my last option I gave… “I don’t know”

The brute fact seems to be the only option left open to me with the information (and logic) to hand. Of course, ultimately I just don’t know.

Your questions are good ones, but can and should also be asked of your God solution.

As I said, even with God I am left with a brute fact – so why add the baggage of a god?

I actually believe that theists, pantheists, atheists and everyone in between has a circularity as the primary axiom of their interpretation of reality. In a sense, we are thus all irrational, haha!We are all on a big circle of life… I suppose that is why pi is an irrational number.

All makes sense now :-)

I completely understand your qualms with simply pushing it back another level to God, but at least it gives a viable reason for their regularity and constancy as an external source. I don’t think it does – just another level of complicity when none was there.

Even IF this all required a god, it would be more honest to think of it as a deistic god, not the theist God you believe in.

How can you explain/justify that leap of logic?

If there are other credible reasons to believe in God (which I would hold that there are)A very different debate that one… happy to have it, but as you might imagine – I have looked and found nothing- I remain sceptical.

I can explain my reasoning if you like – but not on this thread. It comes down to lack of evidence ultimately (my science training just kicks in…)

By the way, you are absolutely right that the theist would split the horns of your version of the Euthypro dilemma.I thought it was nice how I got to the Euthypro dilemma – I didn’t mean to when I started writing, I just drifted there so to speak. (Hence such a long response)

Laws are extensions of his nature, and thus I would agree that God must be a "brute fact" by definition.Bingo!!!

Now take a step back and join me on my step with one less unproven assumption.

When talking about God using the standard definition by theistic and atheistic philosophers you simply can't play, "Well who created God?" because the obvious answer would be "God.Wouldn’t that be a circular argument or special pleading?

This is why I don’t like this reasoning you are using - the same reasoning could equally apply to the laws of logic, or the universe… so why increase the unknowns?

Take care

Lee

Lee said...

Hi Brian

I would say that right now we can agree that logic is a good tool to use to seek truth. We agree on the laws of logic, so that is some common ground.It is a start… I got my education in science as you may know, so I feel we also need to test our reasoning to see that they fit with reality.

I’m sure it is perfectly possible to come up with a logically consistent model of ‘something’ but if it doesn’t match what we observe then for me it is just a model that can be left on the shelf waiting confirmation.

Now when we ask the philosophical question of how these laws are grounded, the theist is really not in the position to prove anything, nor is the atheist.My last option I gave to the question is the most honest one – I don’t know.

I don’t see any problems with that response at all :-)

Still, why is a brute fact solution wrong?

If we presume atheism, we may be forced into something along the lines of "brute facts."Hold on… can you please explain what you mean here.

How can someone assume atheism?

I can understand how someone can assume theism – that is a positive belief IN something.

Atheism is just not taking on that particular assumption – nothing more.

It is a lack of an assumption.

I don’t try and assume more than I have too.

If we presume theism, then logic actually can fit nicely into that picture with God being the ontological grounding for immaterial laws like logic.I refer you back to my earlier comment that it is possible to make a logically consistent model that is meaningless in reality.

Until positive evidence FOR God is provided, or indeed a logical requirement FOR God – then all that you have is an additional unproven assumption.

As I have tried to explain (in rather too much depth) the laws of logic do not seem to require God. Even the assumption of God, ultimately requires a ‘brute fact’ statement.

… that can be reasonably accepted by the theist by means of inference to the best explanation (abduction).Abduction? I thought that was when you kidnapped someone?

I am not sure you can claim it is the best explanation, it is ‘an’ explanation but it doesn’t make it correct.

What seems to be happening is a leap of “I don’t know so it has to be God”.

That makes no sense.

Why not just leave it as an unknown… or, if you like labels so much, why not call the brute fact of the laws of logic – “Fred”.

Using the term God is rather misleading – it comes with additional baggage none of which have been proven or shown as a requirement.

The idea that God is the grounding of logic has more explanatory scope than the hypothesis "they are just there." Fred offers just as much explanatory scope. I don’t see the difference.

Stating “God did it” offers nothing – I explained earlier it just leads to a brute fact that God’s nature requires these logical laws.

However the main problem really seems to be that the theist cannot accept “I don’t know” as an answer. Why is that?

Filling in the unknown with God – I truly don’t understand that. So another unknown to my list :-)

So I don't think it is that profitable to argue too much on this pointIf we could just both agree that we don’t know where the laws came from – then yes the discussion would be closed.

You have asserted God.

I just cannot see how God is any solution. Maybe we will have to differ on this one, but can we agree that it isn’t a positive claim FOR god?

only to say that for me as a Christian, theism provides a satisfying solution to this kind of question; I don't find that from the atheistic perspective.Can you show me then how God explains the laws of logic? I have just argued that He doesn’t.

Has it just come down to faith and the feeling it provides?

Thanks again for your input.

Lee

Brian said...

Again, this will be just a cursory response b/c of time constraints...

But my angle is not building from logic and then positing God. My point is that with certain presuppositions, the logic question is answered differently.

I am merely asserting here that it seems to me that if you approach it as a theist, it makes a lot of sense. If you approach it as an athiest, it offers less explanation -- very little.

Again, I am not starting with logic, then trying to ask a question of where it came from, and then positing God because he fills the gap (or Fred either).

No, I am starting with a presupposition (as is the atheist) or a certain world view by which I filter other things. This is not an argument for God. It is not positing unknowns. It is not trying to come up with a solution to anything. It is simply putting on the glasses of the thiest (or the atheist) and seeing how logic looks through those different glasses. From the theistic view, I see reason, sense, and order. From the atheistic view I see brute fact because logic, although foundational, has no causal power.

I hope that explains where I am coming from. I am not trying to use logic to prove God or try to posit God to answer a logic question --- this is just observing how each of those two well-established world views interprets the data.

Ok, lots to do... gotta run.
Take care. I'll let you have the last word and/or you can carry on with Ranger.

Lee said...

Hi Brian,

I'll let you have the last word and/or you can carry on with Ranger.Thanks for your input – I think I understand where you are coming from, but still feel you are making an additional assumption just to make yourself happy.

And I'm still not sure what it is you feel I am assuming - still missing that one.

You assume God - that's a positive assumption for something. Assumption 1 if you like.

I do not make that any such assumption on the god front.

I have not rejected God or assumed God.

Assumption count 0 on this front.

So I am missing where you are coming from

Getting late here... so all I will say as a 'last word' to you on this matter is that if you assume Fred - anything is possible :-)

Thanks

Lee

Lee said...

Hi Ranger,

Thanks for the long reply - it will take me time to read and to respond, assuming you would like me to respond and I have something new to add.

I think I have said I like can at the moment on the topic.

Lee

Lee said...

"I think I have said I like can at the moment on the topic."What was I typing this morning?

Mental note - don't write stuff when rushing for a train.

I think I have said all that I can at the moment on the topic would make a little more sense.

Oh well...

Lee

Lee said...

Hi Ranger,

First off – I think I am rather close to being a materialist (as I understand the term) I have never seen valid reason/justification to think any supernatural intervention has ever taken place to explain any observation.

I don’t however rule out the possibility of the supernatural – I could be wrong - but I am very wary about making conclusions that are not falsifiable, since once I accepted such a conclusion, how could I possible be changed from it? It would always appear true.

On aside note, many supernatural claims can be tested via the scientific method and with it shown that the most likely explanation is perfectly natural. Of course, creatures from the 14th dimension could be typing this reply, or it could be a silly Englishman stuck in Australia :-)

But I digress.

Back on point – I think at the core you don’t seem happy with an unknown and chose to fill it with a greater unknown just so a conclusion can be made.

Such methodology will surely mean the likelihood of selecting the wrong conclusion is high, especially when your conclusion is not falsifiable (how can you prove yourself wrong and change it?)

And as I pointed out, even by selecting God the actually question isn’t solved at all.

These pesky ‘brute facts’ remain. Redefining the words used to be “Fred” or “God” doesn’t help anyone find the truth (if indeed it can ever be found)

You say you think it is valid to ask why something is a brute fact, but this is just like asking why is A not not A – asking the question doesn’t mean there is a valid answer (or a valid question)

For example, can you tell me what is north of the North Pole? The structure of this question sounds valid, but it is a nonsensical question that is not answerable.

End of Part I

Lee said...

Part II

As for circular reasoning being used by the both of us – well, maybe.

However my repeated question remains, who is making the least number of assumptions?

And I am still not clear why saying something is a brute fact is actually logically wrong?

I would also advise against making phrases that include “I can’t imagine”, not sure what our imaginations have to do with the truth. As for a ‘multiverse’ – this would be a different topic, just to say that I don’t know of (and neither can I imagine) any reason why a multiverse isn’t possible :-)

As for testing for the multiverse, maybe there could be a test that is observable in this universe – don’t know until the theory is written first. Another time perhaps… cosmology is an interesting topic.

As for the mathematical rules/laws, these seem rather similar to the logical laws we are already discussing, so don’t see the need to expand on this.

Now onto you God point with regards to students of history, physics and philosopher.

Well, I am long past being a student of physics myself – just have a degree on the wall that’s all – but if the philosophers have been going back and forth for centuries without conclusion, maybe it is time for a historian and physicist to give it a go. I actually think the tools at our disposal are better at investigating the claims found within the Bible for example. This would take us off the topic of logic, but I am happy to continue it further if you are interested. We can setup a question and discuss it over at my blog (or yours) so not to mess Brian around to much.

This particular topic is probably coming to a closed – after all, I think you have just conceded that no positive argument FOR God can be made from the ‘unknown source’ of the laws of logic. The basis of your argument is “assuming the theistic God is true then…”

And that’s the problem, I don’t want to make such an assumption.

This isn’t because I have anything against gods, or that I don’t want to believe – but we should never assume what we are testing for when the assumption isn’t falsifiable.

Therefore, assuming God exists (for a moment) the only way I can rationally come to the conclusion that He does indeed exist is not to make the assumption first that He does. It is to assume no such thing. The evidence and reasoning will have to lead me there.

As a Christian, I think you should agree to this – if you don’t please tell me where I am going wrong.

Now I think it is possible to assume a characteristic of God and test that assumption via observations – but by assuming God first, and God not being falsifiable makes any test inconclusive for the believer.

OK – I think we have certainly moved away from the original topic, so I will closed

Take care, hope you, your mum and family has a good time.

Lee

Lee said...

Thanks Ranger,

It has been fun and educational. It seems I’ve learnt I might not be a materialist, but a naturalist.

Actually, I’m still not sure on either of these titles – but if you think I sound like a naturalist than that is good enough for me.

Enjoy the summer – it is cold and dark down here. Dark when I go to dark, dark when I get home.

I’ve got the winter blues already

Take care and I look forward to picking up future discussions with you.

Lee

Anonymous said...

Great series of post, I appreciate the work done.

Ray said...

By far, Peter Kreeft's, "Socratic Logic" is the best out there.

northierthanthou said...

It's an interesting start. I do think the multiple definitions you offer in the beginning muddle the waters a bit. I also think your treatment muddles the relationship between actual thought and thought as represented in argumentative form. Some of your treament seems fine on that, but in some areas you wander between them.

I would add that you seem to emphasize formal logic a bit here and along with it deductive argumentation. That's an interesting choice, but it undermines consideration of alternative reasoning strategies.

T&T 196th said...

By your statement it suggests you have exhausted all probabilities within the scope of your research and have arrived at your conclusion "brute fact".This being the case has in any research the mathematical formula,this is the discipline that proves something exists in reality or theory.A=A but does A=a? The triangle is three points in the second dimension while in the third what does it become?Bringing "God into the equation a formula does or doesn't make Him finite.I apologize but logic can logical be be understood by understanding the roots of language.There in from A perspective that has plagued humanity from the "time of the tower of babel".Which brings us all to a delimma about "God" and language's.Because the story makes no sense and that is fact,if you read it out loud than you will hear what you read bringing in another one of the senses to witness the story.It doesn't seem that"God"is all omnipotent at least in this story here's were I am not clear on understanding my belief system.That being the case truth comes under scrutiny.What is better understood logic or truth?Tell me and be brutal it doesn't hurt.

Post a Comment

Thanks for taking the time to comment. By posting your comment you are agreeing to the comment policy.

Blog Archive

Amz