Arguing that theism isn't necessarily irrational - Part 2: The Roots of Logic
Offline This is the second in my series of essays.
Again, this should be uncontroversial and I don't expect to get a huge amount of opposition here.
This one even involves an implicit refutation of some of the claims of pre-suppositionalist theology,
The idea is that the first two essays will remind us of some subtle points that will be picked up later on in the more controversial arguments.
The Roots of Logic
The last essay took at the root and purpose of reason.
This one concentrates on a particular method within reason - logic.
Once again, we'll be looking at root and purpose.
Not because logic needs justifying - logic needs to be in place before we can justify things, but so that we can recognise why logic is appropiate so judge when and where to apply it.
For logic to be applicable, only one thing has to be in place - language.
Once we have language, i.e. we grasp and understand the concepts involved (and that's pretty much necessary for any kind of questioning or debate to even start) logic comes out of it. The most famous rule of logic is the law of non-contradiction.
The Law of Non-Contradiction: 'P & not P' cannot be true
And why it holds in a debate[/b]
Consider the following conversation:
"You're an idiot."
"No I'm not!"
"I know you're not, but you're still an idiot."
"I told you, I'm not an idiot."
"I don't disagree, you're not an idiot but you're still an idiot."
The speaker on the right is using the word 'not', but he might as well not be as it doesn't seem to mean anything to the speaker on the left. It becomes quite clear that ignoring the law of non-contradiction makes the word 'not' meaningless. Seeing as we are reasoning in a language where we use the word 'not' as we do, the law of non-contradiction comes naturally.
Whatever our picture of the world, it can only be a picture if we are using language correctly to describe it. If we are abusing our language when what are we actually saying?
So if our position contains a contradiction then that shows a problem with our picture, that it doesn't really make sense as it stands.
That is why the law of non-contradiction holds within a debate.
Logical Inference
Alongside the law of non-contradiction there is another law.
The Law of the Excluded Middle: Either 'P' is true or 'not P' is true
This holds for the same reason as the law of non-contradiction.
It is another consequence of the meanings of the words 'or' and 'not'.
Using these two rules of logic we can build a method of logical inference.
A valid logical inference is when you prove that if some premises are true, then a conclusion is true.
For example:
Premise 1) Unicorns have horns
Premise 2) Sam is a unicorn
Conclusion: Sam has a horn
If you accept that premise 1 and premise 2 are true then the conclusion must also be true. This can be used to defend a statement against an opponent if it can be shown that it leads from premises that the opponent holds. By why is this. Why is a valid inference considered to be 'infallible'?
It's because that if an inference is valid, to accept the premises while denying the conclusion is to make a contradiction.
To deny that Sam has a horn while agreeing that Sam is a unicorn and that all unicorns have horns is to contradict yourself.
Methods of proof tend to work as follows:
1) Show that the premises contradict the denial of the conclusion.
2) By the Law of Non-Contradiction, if you hold these premises then the denial of the conclusion cannot be true.
3) By the Law of Excluded Middle, if the denial of the conclusion is false then the conclusion must be true.
4) So if you accept the premises then you must also accept the conclusion.
When and where is logic applicable?
Logic is best applied when the concepts in question are clearly defined.
Mathematics is the practice of logic.
Mathematical concepts are so well defined that mathematical problems can often be solved purely on logic, and when they can't, this too can be proved in advance using logic.
The language of Physics is very mathematical, and logic tends to be very applicable in science too. Once the concepts are defined it can be quite clear when there is a contradiction and problems can be spotted with relative ease.
Theories can be constructed from the ground up, starting from basic axioms as foundations.
Not all of our concepts are so crystal clear.
Our language has a whole range of concepts, ranging from mathematic ones that have very strict definitions to very loose ones that appear to elude strict definition altogether. Concept like 'love' tend to be so loose that an attempt to nail a strict definition will almost certainly be incorrect. 'Love' is a concept for poetry rather than logic, because rather than trying to nail strict rules, poetry lets the concept display it's true nature through loose examples.
This leads some people to prefer to avoid loose language in debate as it makes it much harder, maybe impossible, to get watertight conclusions. The thing is, are all questions worth asking supposed to have such definite answers? If we have a question that arises in the form of a loose language, would trying to re-phrase the question in a mathematical language lead us to a clear answer, or would it just change the question and lead the original question unanswered?
Like other methods, it seems that there is a time and place for strict logical method.
While some kind of logic will always applicable, it won't always give such definite answers, and it won't always be so obvious whether a contradiction is really a contradiction.
A circle is most certainly not a square, but whether love and hate are as incompatable isn't quite so obvious.
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In algebra, ten divided by three can be expressed as the number, x, which is required to make 3x = 10, or if you want it in words, three times a number which equals ten.
In calculus, you can represent it as an infinite series where 10/3 = the sum of the infinite series of 3(.1)^n from n=1 to infinity.
It can also be expressed as the integer ten, between the integers 9 and 11 divided by the integer 3, exactly between the ingeters 2 and 4.
All these definitions are correct, all the tautologies in math correspond exactly to every other tautology, since they are all determined by logic based on the base axioms and tautologies.
Seriously, this question was a waste of my time.
It doesn't matter if they consider it irrational, it was still rational for us to think it given then information given to us. It was rational for Newton to assume that time and space were not dependent on eachother. He was wrong, but he was still rational. Now it is rational to assume otherwise, but this doesn't change the fact that Newton was a very rational person. In fact, I would say that no one is irrational. We are all attempting to create answers given what we consider to be the best information. We may have an ineffective value system, and an innefective brain, but we are still always 100% rational as we can be when trying to extrapolate from that system of values. Someone who thinks that space aliens are invading will run around screaming, grabing his gun and shooting at the air--but these are entirely rational responses to a violent space alien invasion. The fact that he is crazy has nothing to do with whether or not he is acting rationally. Although his logic and senses may be screwy, he will always act as rationally as possible.
Defining rationality in such a way would make this argument too easy. It would make it obvious. No one actually uses the word "reason" or "rationality" this way.
? is that why you didn't answer it, true false or uncertain if you please
And once justified and accepted by the masses then you have a new social norm, but until then ..........
Soz
That would be arbitrarily limiting rationality to behavior, as opposed to belief. Newton's errors were established though information available objectively, not personal delusions.
“Soz?”
I meant that the majority of society can't be called abnormal, but its beliefs can be tested for rationality. If the majority can't justify their beliefs, they are being irrational, even if it's normal to be such. This isn't to say the belief is wrong -- a person can believe an empirically demonstrated thing, but be irrational because they lack the knowledge to defend, or even understand, the thing; in other words, not have the information to come to the conclusion they do, even if the conclusion is considered valid by those with the information. Returning to the topic of theism, it hasn't been demonstrated there's information to be had in this regard.
This completely misses the point of having the term 'rational', as applied to decisions, ie based on reason. This is to distinguish such decisions from those which are dominated by emotional drives, or instinctive or 'gut' reactions to events, etc. Typical decisions will have elements of all these things.
Seems like you may be conflating the use of the word 'reason' in the broad sense of whatever drove a particular decision, vs. the explicit conscious use of logical weighing of evidence, etc. Obviously there is a 'reason', or reasons, why we make a particular decision, but if that 'reason' is primarily an emotion, like fear or love or or hatred or anger, etc, that would not be classed as 'rational', or based ON 'reason'.
Oh and BTW, sum of an infinite series, especially in the simple example you gave, has damn all to do with calculus.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
wut? the answer to 10/3 is neither true, false, nor uncertain. It is all/any of the answers that I gave.
what does based on reason mean? Based on thought? Is not reason our attempt to reach a conclusion based on the means and the ends, i.e. based on our goals and the evidence available to us? Why is there so much push to equate "reason" with "logic," when they are quite often used in different concepts.
The only things which are not done using "reason" are instinct or gut reactions--but these often exist because we "pre-reasoned" them out. For instance, I have thought about what I would do if a car was comming straight at me on the highway, and have decided that I should swirve to teh right, no matter what damage would come to my car. This would be a gut reaction, but it would also be pre-reasoned.
Regardless, I do not see why you are so intent on making "reason" mean "logical thinking." We already have a word for "logical thinking." Reason should be related to the human attempts to reach conclusions using available pre-requisites.
Oh and BTW, sum of an infinite series, especially in the simple example you gave, has damn all to do with calculus.
I did not limit rationality in any such way, I was simply giving an example. I was simply reflecting his thoughts (beliefs) into his actions.
Your little snide remark missed the point. Because I extrapolate rationality to pursue ends that you find unworthy does not mean that I am not thinking rationally. I means that I have convinced myself that different ends in life are also important in addition to finding truth. The faculty I use to convince myself must be reason (even if flawed reason) since that is the faculty used to come to conclusions from desires and evidence.
For instance, the man seeing aliens had the desire to outlive the aliens, so he tried shooting them. Desire is a valid precept for reason to come to a conclusion.
No snide remark was intended, though it's interesting that you read it as an indictment. If the shoe fits, I suppose.
By your standard, anything is rational if it can be insulated from contradictory information, either by ignorance (where I agree), delusion, or sheer will (where I diverge).
I was not restricting 'reason' to refer to strictly 'logical thinking', but would include any conscious process of weighing up evidence of our senses, including allowances for knowledge of the limitations of such sensory data, as well as our memories of previous experience and acquired knowledge. Obviously this includes induction, and other even less formal ways of assessing relative likelihood of various propositions. These processes definitely go beyong the realm of what we normally mean when we refer to 'logical thinking'.
EDIT:
There is a continuum here, from rigorous application of formal logic rules and mathematical probability estimation and combination with Bayes Theorem, thru a more vague weighing up estimates of different factors, with increasing influence of our wants and desires, thru to instinctive reactions like 'fight or flight', and strong sexual reponses.
Obviously we are drawing the somewhat arbitrary line between 'rational' and emotional/instinctive decision-making processes at very different points.
There will be situations where a 'built-in' or gut reaction is entirely appropriate, which could be labelled 'rational', even though it involves nothing resembling a formal conscious assessment of the evidence. But such reactions can 'misfire' in circumstances very different to those in which these instincts evolved - this is where our rational thinking skills give us the capability to adjust to novel situations. /EDIT.
Many of our reactions are based on 'internalised' reasoning from earlier experience, this is true, but we definitely have many other reactions which come 'built-in', or are acquired from experience without necessarily having been thought through consciously.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me
From the sublime to the ridiculous: Science -> Philosophy -> Theology
Very well, I will expand the definition of rational a hair. You have convinced me that I must.
To be rational is to believe, as far as you know, in nothing that is contradictory. To be irrational is to believe in a single or many contradiction/s.
I still don't think there is hardly anyone that is "irrational" for very long, but I conceed that it may indeed be possible. Most people that believe in contradictions do so either becase a) they have not examined their belief, or b) they are going insane because they can not determine what is real. The person that has not examined their beliefs is still rational, although only through ignorance (as you pointed out). The person who believes in two contradictory things, however, is definately irrational.
Are we satisfied by this definition?