Logic

[Plain Simple]

I'd say it's a different language, utilizing the same word list.

Some of those aforementioned theorists have argued (ironically, in my opinion) that technical vocabularies exist primarily to reinforce the social status and exclusivity of the groups that use them: that, for example, the 'discourse of mathematics' exists primarily to increase the status-authority of mathematicians.

I'm not ordinarily a fan of such speculation. But based on what you've written here, I wonder if there isn't a grain of truth to what they say.

I cannot speak for other groups, but I don't think this is the case for mathematicians. Some might be overly fond of name dropping, using jargon where they could have sufficed with slightly simpler terms, but in general the language serves a specific purpose: to make precise unambiguous statements.

I'd hardly say that the definitions that logicians use are "loose and free". If anything they are strict and precise.

Ordinarily, I would agree with you. Just not in this case. Please note that I said "that word."

I don't think the word "therefore" is an exception, if anything the variety in meanings of the other words mentioned is reduced to fit with the (logical) meaning of "therefore".

But in reality mathematical logic usually deals not with "therefore" at all. It uses well defined symbols. "Therefore" might be used as a name or placeholder for one of these symbols for the ease of referencing it, but then the word gets its meaning (in logic) from the definition of the symbol, not from the Queen of England. There might be other forms of logic that (for example those that deal with natural languages) with which I'm not at all familiar for which this is not the case though?

 

[MarianLH]

I took a couple classes in logic when I was a college freshman. My professor summed it up this way: logic is a great tool for finding structural flaws in your reasoning, but not so good when it comes to the content.

A valid argument is structurally flawless. If the premises are true, then the conclusion cannot be false. If the premises are true. But in the real world, we can't always be certain what the truth is, and if one of the premises is off, then the result is garbage in, garbage out, despite being logically perfect.

That doesn't mean logic is useless. To extend the metaphor, logic does prevent "good stuff in, garbage out", which is otherwise a possibility. Applying logic to your reasoning will find and eliminate a lot of errors. Just not all of them.

Or so it was explained to me, longer ago than I care to admit and for only two semesters. And I got a C.


Marian

 

[TrekGuide.com]

If you say, "it's raining," and I say, "that's true," I am merely signalling my agreement with your statement. It's equivalent to nodding your head, or saying "yes, it is raining."

Thus, "truth" is merely every statement to which we should nod our heads, or which we should affirm.

Now wait a minute.

If you walk into a church on a Sunday morning, and say, "There is a God," then everyone will nod their head.

But if you walk across the street to the atheist convention and repeat the same statement, then zero people will nod.

I would think "truth" should be defined as something that is true no matter which building you are in.

Perhaps my definition of "truth" would be "something that can be supported by a repeatable scientific experiment, which would generate the same results whether performed in a church or in an atheist convention or in a meeting of the Flat Earth Society."

(As for my earlier examples, I guess they are more red herrings than attempts at logical statements. But that's why this thread was started: because people were citing "facts" to support opposite conclusions, and debating which conclusion was more "logical" or "true.")

 

[TrekGuide.com]

As to the debate over the word "Therefore," I think that word is frequently abused in debates to imply causality between two true statements, "therefore" reaching a false (or illogical) conclusion.

1. Ninety percent of children are vaccinated.
2. Three percent of vaccinated children are autistic.
3. Two percent of non-vaccinated children are autistic.
4. Therefore, vaccination causes autism.
5. I heard it on "Oprah," therefore it must be true.
​

Or this statement (which seems to prove what Mark Twain said about statistics):

1. Ninety percent of people who die this week have eaten carrots in the past month.
2. Ten percent of people who die this week have eaten a banana cream pie in the past month.
3. Therefore, you are more likely to die within a month of eating carrots than to die within a month of eating a banana cream pie.
​

(Perhaps the above statement is both true and logical, statistically speaking, but would make a poor scientific premise for a new diet book.)

 

[Jadzia]

I would think "truth" should be defined as something that is true no matter which building you are in.

Again, semantics: It depends how we each define the word "truth". It means something different to each of us.

Perhaps my definition of "truth" would be "something that can be supported by a repeatable scientific experiment, which would generate the same results whether performed in a church or in an atheist convention or in a meeting of the Flat Earth Society."

With my mathmatical background I can't agree with that concept of truth. You may say something is true only because you haven't toured to enough conventions. The only conventions you've visited are those where the goers nod their heads at your conjecture and make you feel that it is supported.

For example, in the scientific method, maybe you're simply doing the wrong experiments. Experiments a,b,c,d,...,x,y all seem to support your conjecture. So you believe it to be true. However, you never thought to do experiment z. Human limitations may even prevent you from doing experiment z, but if you did it would show the conjecture to be clearly false.

To me, quantity of evidence is irrelevant. Probability is irrelevant. Knowing is black or white: you either know something is true or you don't. There's no middle ground here. Even if you claim that you're 99% certain of a theory, it doesn't mean that it is 99% true. On the contrary, you could still be 100% wrong, and probability won't compensate you one iota for your error. Probable truths are not something I would call truth.

The scientific principle only makes testable predictions, with the purpose of guiding further thought. Scientific theories are a summary of the experiments done. It's important not to overgeneralise that. It doesn't say anything about the world outside of the experiments. We often do overgeneralise, because we believe we can and get away with it, but it is in fact making a leap of faith to take a theory from the lab and project it onto the universe.

Scientific truths are not carved in stone, and are not the blueprints of the universe. They are a flexible, adaptable summary of done experiments.

 

[Plain Simple]

^Can you name anything that can be considered a "true fact" where the use of "true" satisfies the conditions you outlined above? How can we ever know anything for 100% sure?

 

[Jadzia]

I know that I exist. I know that I have experiences. For example, I have am having an experience right now that I call 'trekbbs', and I am enjoying a conversation experience with 'plain simple'

I do assume a skeptical position Plain Simple, because of my rigorous concept of truth. Truth for me is something rare and special, and I like it that way

Like you, I started out with mathematics. I do enjoy the subject, but perhaps its greatest lesson was what it taught me about truth. It taught me how rigorous we need to be in order to declare something as true. I understand how making small even leaps of faith can introduce unforeseen errors. Even the possibility of of that is unacceptable to me, if I am to declare something as being true.

I can still enjoy the subjects of scientific study and speculation like everyone else. I don't restrict myself in what I put my mind to, but I am acutely aware of the limitations of theories; of where the truth ends and the faith begins.

 

[Plain Simple]

I think there are 'ways around' the truth of your examples, just like with every other statement. What does "I exist" even mean? How can we decide on the truth of that statement. And even if we somehow find a way to agree on the meaning and truth of "I exist and I have experiences" then everything beyond that is filtered through these experiences and limited by our senses. Like your examples seem to show you cannot find truth then beyond "I have an experience" (and you might lable that with for example 'trekbbs' or 'conversation with Plain Simple', but that has no meaning outside your own sensation of having an experience).

Btw, I do agree with you that we must be careful with the use of the term 'truth', but to restrict it that severely renders it almost useless. There seems to be a general agreement in society to what truth is though in most day-to-day cases and that is a very handy thing to have around. I exist, my table exists, I can't fly, the plane can, etc etc. I'll be the first to admit that all these things are not logically inevitable, but it is handy to have such a concept of truth around.

As for science, I don't think it has anything to do with truth in any "universal/eternal way". To me, the added value of science as opposed to any other way of describing (not explaining!) nature, is that (ideally) it is always clear what the assumptions are on which a theory is built, what the logical consequences are and what empirical evidence (or better, lack of empirical falsifications) there are for the assumptions and conclusions. Within the context of "day-to-day" truth as I explained above, I think "scientific truth" usually trickles down into "day-to-day" truth after a scientific theory has been around long enough, but that doesn't mean that we should add some ethereal extra quality to "scientific truth" that doesn't follow from the logic or assumptions.

 

[Smiley]

Here is how I would use truth in the logical and scientific context:

Conclusions derived from empirical data may or may not be truth. Anything proven through deductive reasoning is truth, given that all the postulates are true. There can be truth that may be impossible or impractical to prove with the methods available to us.

 

[Jadzia]

With the example of "I exist" it is something Descartes taught us.

Consciousness is something special where truth is concerned. Consciousness (knowledge of one's own existence) is perhaps the only real transcendental knowledge. That is, knowledge obtained without reasoning. Such knowledge is dependent on no other knowledge. It does not need logic or other truths to assert itself. To a mathematician I'm sure that sounds delightfully bizarre, for truth to appear from nowhere... Yet it does.

Such truths are the real foundations of knowledge, where the first implication begins, and from which the first real deduced truths are formed.

So how do I know that I exist? Why is there no way around that one? Because I am acutely aware of existing. "I" being the entity aware of it's state of being aware... "exists"... well that's a difficult to define concept, and is also somewhat relative But whatever it is, it is a necessary prerequisite to this 'trekbbs' experience I'm having right now. Perhaps what I mean is that existing is a state of experiencing. It's a subjective concept.

I'm not disputing that empirical/scientific truths are valuable, but that we shouldn't go around proclaiming them as truths in the same way as I proclaim "I exist" to be true, because it is on a different level entirely:

One is commonly accepted and generally unquestioned, yet we permit ourselves to revise it at a later date, as we learn more, and as we change our world view; the other has no malleability.

 

[Plain Simple]

To a mathematician I'm sure that sounds delightfully bizarre

Nah, not necessarily, depending on what definition of truth you use (and how narrow minded the mathematician is ). And within your concept of truth it seems to fit perfectly. Actually, like I said, I do agree with what you said, that most, if not all truths, are less unshakable then people tend to think. "I exist", or better perhaps "I experience" might be the only fundamental truth, but it only has value within the entity "I", since "you experience" is far from unshakable. Are there similarities here with a mathematical truth which only has value within the logical construct of mathematics?

 

[Jadzia]

Are there similarities here with a mathematical truth which only has value within the logical construct of mathematics?

The idea of truth being contained within a system/construct is common to both, yes. Deductive logic is common to both also. But I think that's where the similarity ends.

The foundations of mathematics lay with algebraic structures. I wouldn't say these structures are transcendental; they're essentially arbitrary constructs, although they do have empirical relevance to the real world.

Consciousness ("I exist", etc) isn't really as arbitrary. It's of boolean type: Either I experience or I don't. And if I didn't experience, then nothing else would be of consequence.

I understand what you're saying. The idealistic part of me would like to think that everything of importance can be deduced from transcendental truth.

But I don't think that's what mathematics is. I feel that the subject of mathematics is more about starting out with trivial equalities within an arbitrary axiomatic construct, then iterating them into complex relationships. Then finding the emergent patterns within those relationships, and making a theory of it.


Here's two nice quotes relevant to this thread:

Mathematicians are a species of Frenchmen: if you say something to them they translate it into their own language and presto! It is something entirely different.

– Johann Wolfgang Goethe

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long as the relations don't change. Matter is not important, only form interests them.

– Henri Poincaré

 

[Plain Simple]

I understand what you're saying. The idealistic part of me would like to think that everything of importance can be deduced from transcendental truth.

I'm not sure that's what I'm saying. But I do think 'logic' (whichever variant one chooses) is the most reasonable tool to try and derive statements about the world, since if we let go of that (i.e. if we do not adhere to a set of rules of reasoning) then everything goes. What does decide then which statement is more relevant or true (with respect to your starting point) then others?

But I don't think that's what mathematics is. I feel that the subject of mathematics is more about starting out with trivial equalities within an arbitrary axiomatic construct, then iterating them into complex relationships. Then finding the emergent patterns within those relationships, and making a theory of it.

I don't know about the "starting out with trivial equalities" part, since you can start with anything you like, but apart from that, yes, that is mathematics as far as I can see. (You might argue that what you start with should at least not be self-contradictory, since otherwise you're building a not very interesting structure.) Of course, what mathematicians try to do, is not just practice mathematics (otherwise I could make a career out of writing down statements like "1+1=2", "2+1=3", "3+1=4"... indefinitely, but practice 'interesting' mathematics. What that is, is often a lot harder to explain.

Here's two nice quotes relevant to this thread:

Mathematicians are a species of Frenchmen: if you say something to them they translate it into their own language and presto! It is something entirely different.

– Johann Wolfgang Goethe

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long as the relations don't change. Matter is not important, only form interests them.

– Henri Poincaré

Famous quotes. I always really liked Goethe's one. It's funny because it's true. Poincaré's quote certainly has some 'truth' in it, but is hardly without it's opponents when you delve into the philosophy of mathematics (although of course I cannot come up with a name of one of those opponents or one of their alternate theories ).