you'll have to explain that in plain English to me (I'm not a maths student).
btw "logically consistent" is not the same as formal logic. Dialectical materialism is logically consistent, but it is anti-formal logic.
Formal logic
Formal logic is a set of rules for making deductions that seem self evident. Syllogisms like the following occur in every day conversation.
All humans are mortal.
Socrates is a human.
Therefore Socrates is mortal.
Mathematical logic formalizes such deductions with rules precise enough to program a computer to decide if an argument is valid.
This is facilitated by representing objects and relationships symbolically. For example we might use for the set of humans, for the set of mortal creatures and for Socrates. We use the symbolic expression `' to indicate that object is a member of set . Thus we represent `Socrates is a human' with . We use the `quantifier' to indicate that all objects satisfy some condition. For example all men are mortal can be written as . This reads that every that has the property of being human must also have the property of being mortal. Then we restate the syllogism as follows.
Logic assumes something cannot be both true and not true. It looks only at the truth value of a proposition. It involves simple relationships between these truth values. These can be represented by truth tables as shown in Table 3.1. The only logical operations required are the three in this figure. Others such as implication represented by `' can be constructed from these three. is the same as . implies requires that either both and are true or is false.
Determining the truth of a logical expression that contains no quantifiers (like ) is a straightforward application of simple rules. One can use a truth table to evaluate each subexpression starting with those at the root of the expression tree as shown in Table 3.2. If a logical expression contains quantifiers than we need to evaluate a logical relationship over a range of values to determine the truth of the expression. If the range is infinite then there is no general way to evaluate the expression. We can use induction3.2to prove that some statements hold for all integers but for that we need to go beyond logic to mathematics.
Formal logic
Basically it has been admitted that formal logic is inaqequate when it comes to higher maths and advanced physics. But people still try to apply it to history and politics.
you'll have to explain that in plain English to me (I'm not a maths student).
btw "logically consistent" is not the same as formal logic. Dialectical materialism is logically consistent, but it is anti-formal logic.
lolwat? How does formal logic break down if it is not by logical inconsistencies and wtf is "anti-formal logic"?
What does its application to higher maths and physics have to do with its application to history and politics? Fallacies and the application of certain basic logics (e.g., enthymemes, syllogistic) to discussions that take place in natural language is practical reasoning. What is the problem with using practical reason?
The response
What does its application to higher maths and physics have to do with its application to history and politics?
Basically it has been admitted that formal logic is inaqequate when it comes to higher maths and advanced physics. But people still try to apply it to history and politics.
Thank you, dear participants, for proving my point. G'night.
This is a different helios from the one who accidentally posted pictures of his testicles, right?
i think many of them use fancy words like that more than they normally would just to live up to the smartsy intp image
"anti-formal logic" is nothing. I just meant that dialectical materialism is opposed to formal logic.
Formal logic can break down if we can show if osmething can be both true and untrue at the same time. However dialectical logic does not break down if we show this, because "unity of opposites" is one of the three fundamental rules of dialectical materialism (the other two being "negation of the negation" and "quantity into quality").
So how, according to a formal logic x sometimes = -x, and sometimes not?
him said:Ok, at least he is correct on how formal logic breaks down, or to be precise how logical systems based on formal logic break down, to bad for him that is what is called logical inconsistencies, which he refused to acknowledge. This can only happen if the axioms lead to contradictory results(see Russel's paradox for an interesting development of the foundation of mathematics, as well as Frege's dreams being crushed). This does not mean that formal logic is at fault.
you said:So how, according to a formal logic x sometimes = -x, and sometimes not?:
him said:First of all, for all algebraic systems, including the real numbers 0 = -0, so this equation isn't faulty in any way. He probably is assuming x != 0, so ok, i'll give him an example of this. Take again the Z_2 or just any Z_(2k), where k \in N, the natural numbers(and the operation * is not a*b = a+b mod 2k). Then for, say k=2, we have the elements {0,1,2,3}. The operation table would be , like this:
0 * x = 0
1 * 0 = 1
1 * 1 = 2
1 * 2 = 3
1 * 3 = 0
2 * 1 = 3
2 * 2 = 0
..... and so on.
But here we have 2 * 2 = 0
if we denote the inverse element of the element x, by -x, we get: 2 = -2, and the equation x = -x has a non-zero solution.
I suspect he is just reading things that are way over his head and drawing bad conclusions. So formal logic is failing; for him.
someone else said:I don't have time for a full response, but I'd like to point out that the person cited by the OP's final point about how political or historical debates cannot be constrained within formal logic is wholly irrational. Similar to how Einstein's theories and Newton's laws work in the natural world despite quantum mechanics, the analysis of an understood system doesn't alter in truth based on obscure exceptions to the method of analysis. That only alludes to what we don't understand, but doesn't change the functionality or accuracy of an analytical system like formal logic, ESPECIALLY in a day-to-day sense.
:steam: :jofticon_1:
The fallacies are easy to remember. In fact, it was necessary for the written portion of the GRE (though admittedly they did not require that we memorize the Latin.) They're also used ALL THE TIME in academic writing.
I memorized them early on (in high school) because I was tired of coming across phrases like "post hoc" in my reading and either not knowing, or having to cross-reference, their meaning. It seems like I'd be missing a lot, or incompetent in some way, if I didn't know them (especially since they're simple and pretty easy to remember.) And once you know them, it's difficult not to use them for greater concision.