How do we decide that A implies B?

[Speakpigeon]

How do we decide that A implies B?

Me, I accept that A and B implies A.
I accept for example that "It rains and I am Donald Trump" implies "I am Donald Trump".

I also accept that A or B doesn't imply A.
I accept for example that "Somebody started the fire or the fire was caused by lighting" doesn't imply "The fire was caused by lighting".

These are very simple cases and perhaps very easily decided by most people but there are complex arguments that are not so easy. We can decide on the simple cases without bothering to articulate any method because essentially we are all going to agree whether they are valid or not. More difficult and controversial cases, however, show that we would need all to have the same method.

If you think you have a method to decide whether something implies something else, could you try to articulate how it works by applying it to the following two example arguments?

A implies B and not B;
Therefore, not A.

Donald Trump is president of the European Union;
Therefore, God exists and religious education should be compulsory starting from kindergarten.​

Please also explain why your method would give us the correct answers.

Thanks to all.
EB

 

[Sarkus]

If I ask you to multiply 19 by 20, how many methods of achieving the right answer are there? Is it important that we agree on one method? And if one’s opinion on the answer is that it is the sound an elephant makes, is that legitimate?

 

[James R]

Speakpigeon:

Have you ever heard of Boolean algebra? If not, maybe now would be a good time to look it up.

 

[Speakpigeon]

Speakpigeon:

Have you ever heard of Boolean algebra? If not, maybe now would be a good time to look it up.

OK, thanks for the tip off.

So, given your vote, could you articulate why you think Boolean algebra is the correct method for deciding on the validity of logical arguments?
As you may have gathered by now, I'm desperate for a published justification by some well-known and esteemed logician that this or that method of logic used in mathematical logic is correct. So, since you clearly believe Boolean algebra is the correct method for deciding on the validity of logical arguments, how did you come to this conclusion? Do you actually know and understand one such justification? Or do you accept without such a justification that Boolean algebra is the correct method?
EB

 

[James R]

Boolean algebra is a systematic way to represent logical arguments. Logical conjunctions and disjunctions obey strict rules in the Boolean algebra, as do implications and the like. Any chain of logic that can be represented in the system can be evaluated for its overall truth value. In other words, given a set of premises, a chain of logic, and a conclusion, the algebra can be used to determine whether the set is valid.

If you have a better method that consistently works for evaluating the validity of logical arguments, or some reason you believe Boolean algebra can't do the job, I'm all ears.

 

[Write4U]

How do we decide that A implies B?

Mathematics.

 

[Speakpigeon]

Boolean algebra is a systematic way to represent logical arguments.

Yeah. But one can be systematically wrong. Indeed, mathematical logic is.

Logical conjunctions and disjunctions obey strict rules in the Boolean algebra,

Sure, I agree with you there.
Though, this is so easy that the first time I was presented with their truth tables, I thought, hey, why are we even talking about this?

as do implications and the like.

LOL. Well tried!
No. The material implication is a joke.

Any chain of logic that can be represented in the system can be evaluated for its overall truth value.

No.
Does it not even occur to you that you would need to be able to prove your claim here?!

In other words, given a set of premises, a chain of logic, and a conclusion, the algebra can be used to determine whether the set is valid.

No, it can't.

If you have a better method that consistently works for evaluating the validity of logical arguments, or some reason you believe Boolean algebra can't do the job, I'm all ears.

Sorry, I'm not for publication.
Beside, I don't need to prove anything. The mere fact that there are several methods of logic in mathematical logic proves they can't all be correct. But which one of them would be correct? And since only one could possibly be, why think any one of them would be?
Also, my point from the start, if you remember, is that I asked for a justification that mathematical logic is correct. No justification means it is irrational to just blindly accept that it is correct.
But no surprise here, people believe whatever suits them. I already told you, you are very naive.
And it's not just a few methods of logic. There is a new one everyday. There's no reason known to mathematicians that each of them couldn't invent his own.
EB

 

[Speakpigeon]

Mathematics.

So how did people do it before the invention of mathematics?!
Chicken and egg.
And Aristotle was well before mathematics.
Maybe you could try and think before you post?
EB

 

[Write4U]

So how did people do it before the invention of mathematics?!
Chicken and egg.
And Aristotle was well before mathematics.
Maybe you could try and think before you post?
EB

Maybe you should think before you reply. Man did not invent mathematics.
In a mathematical universe all things act in a mathematical fashion. That's why its called determinism.

Mathematical calculation is a fundamental skill of many animals especially predators, beginning with single celled organisms. Mathematics was practised long before man came along and invented the symbolic language of mathematics.

Lemurs are but one species tested for inherent math skills;

 

[Write4U]

And Aristotle was well before mathematics.

Does this count?

Aristotle uses mathematics and mathematical sciences in three important ways in his treatises. Contemporary mathematics serves as a model for his philosophy of science and provides some important techniques, e.g., as used in his logic. Throughout the corpus, he constructs mathematical arguments for various theses, especially in the physical writings, but also in the biology and ethics.

https://plato.stanford.edu/entries/aristotle-mathematics/

 

[Speakpigeon]

Does this count?
https://plato.stanford.edu/entries/aristotle-mathematics/

Excellent. Can't you then quote Aristotle explaining how to decide that a syllogism is valid from mathematical principles?
And given that he didn't do that, may be you could supply this explanation yourself. So, how do mathematical principles explain the validity of an implication?
EB

 

[Speakpigeon]

In a mathematical universe all things act in a mathematical fashion. That's why its called determinism.
Mathematical calculation is a fundamental skill of many animals especially predators, beginning with single celled organisms. Mathematics was practised long before man came along and invented the symbolic language of mathematics.
Lemurs are but one species tested for inherent math skills;

Your claim is trivial. You call everything "mathematics". You might just as well say that it is reality that makes us decide that A implies B.
I guess I should better than reply to your stupid posts.
EB

 

[Write4U]

Excellent. Can't you then quote Aristotle explaining how to decide that a syllogism is valid from mathematical principles?
And given that he didn't do that, may be you could supply this explanation yourself. So, how do mathematical principles explain the validity of an implication?
EB

Go argue with Stanford U.

Your claim is trivial. You call everything "mathematics". You might just as well say that it is reality that makes us decide that A implies B.
I guess I should better than reply to your stupid posts. EB

Are you in agreement that reality is based on mathematical patterns??? WOW!

But do you know the difference between "trivial" and "common denominator"? Just because mathematics is found all around you does not make it trivial, it makes it ubiquitous.

And yes, physical reality decides who does what, when, and where. That is determinism, which is the result of a mathematical function.

In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system.[1] A deterministic model will thus always produce the same output from a given starting condition or initial state.

In mathematics, The systems studied in chaos theory are deterministic. If the initial state were known exactly, then the future state of such a system could theoretically be predicted. However, in practice, knowledge about the future state is limited by the precision with which the initial state can be measured, and chaotic systems are characterized by a strong dependence on the initial conditions.[3] This sensitivity to initial conditions can be measured with Lyapunov exponents.

In physics, Physical laws that are described by differential equations represent deterministic systems, even though the state of the system at a given point in time may be difficult to describe explicitly.

In QM, In quantum mechanics, the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic.

https://en.wikipedia.org/wiki/Deterministic_system

Bohmian Mechanics rest on mathematical Implicates. Potential values which may become reality based on a prior state.

If mathematics do not decide that A implies B in essence, offer a better system if you can.

 

[Jeeves]

What, precisely, do you mean by "imply"?

 

[Write4U]

What, precisely, do you mean by "imply"?

In science, I relate the term "imply" to Bohm's Implicate Order, a concept based on a hierarchy of mathematical orders. (see David Bohm, "Wholeness and the Implicate order")
http://gci.org.uk/Documents/DavidBohm-WholenessAndTheImplicateOrder.pdf

It proposes that a given prior causal state determines a mathematical implicate of the next subsequent state.
i.e. 2 + 2 = ? (implicate 4).

I have no clue how SP perceives the implication of the term "imply".......

p.s. Last I heard he identifies "imply" with "trivial', but that just doesn't sound right...

Anil Seth explains how we create 'implications' as a product of sensory predictions.

 

[Jeeves]

It proposes that a given prior causal state determines a mathematical implicate of the next subsequent state.

Thanks. In that usage, it means a result or outcome determined by the given(s).
That's quite different from the way regular people use the word in ordinary life, where the implied result or outcome of a set of known circumstances is not certain but stands at some level of probability, from 'might be so' to 'is almost certain' - less than 100%.
In either case, the proposition is comprehensible only when the set of givens or known circumstances have some internal coherence, or relation to one another that can then lead to a next logical step.
If there is sufficient related information in the premises, they lead to a conclusion; if there is related information but not enough for a definitive conclusion, it leads to an inference, or at least narrows the focus of further inquiry. This is how forensic investigation works.
B is dead. B was killed violently. A had a motive. A had the means.
Not enough for a conclusion, but the givens imply that A killed B.
Therefore: Find out: Did A have opportunity?

However, I can't see mathematics, or formal logic or practical reasoning doing much with disparate statements regarding unrelated subjects.
A is a republican. Mrs. brown has five children. Fires in Spain destroyed 1000 hectares of forest.
Therefore - WTF?

 

[Write4U]

However, I can't see mathematics, or formal logic or practical reasoning doing much with disparate statements regarding unrelated subjects.
A is a republican. Mrs. brown has five children. Fires in Spain destroyed 1000 hectares of forest.
Therefore - WTF?

Perhaps you are making it to complicated.
Disparate statements have no implied relationship. No mathematical equation can be formulated. Therefore no implication as a result of combined statements can be formed.
It's just data.

IMO, it is essential that a mathematical equation of values can be drawn. Else there can be no implied (deterministic) result.

 

[Jeeves]

Then what's Pigeontoes on about?

 

[James R]

Speakpigeon:

Yeah. But one can be systematically wrong. Indeed, mathematical logic is.

Ah! A claim from you at last. But then later you say that you're not going to tell us why it's wrong. It's your private secret, I guess.

LOL. Well tried!
No. The material implication is a joke.

Why? Because of the secret error in mathematical logic that you're not telling anybody about?

No. Does it not even occur to you that you would need to be able to prove your claim here?!

Give me a counter-example, then. I dare you. It's your thread. You're the one who is claiming mathematical logic is systematically wrong, remember.

No, it can't.

Yes it can!

(Want to go another round of unsupported contradiction? I'm up for it if you are.)

Sorry, I'm not for publication.

This is kind of a pointless discussion thread, then, isn't it? You're making claims you refuse to support, so there's really nothing to discuss.

Beside, I don't need to prove anything.

Yeah you do. You need to prove your claim that mathematical logic is systematically wrong.

The mere fact that there are several methods of logic in mathematical logic proves they can't all be correct.

You're claiming they're all wrong. You didn't specify any particular one. More specifically, you have made the claim that Boolean algebra is wrong, but you refuse to support that claim. Which makes it just an unsupported opinion of yours, as things stand.

But which one of them would be correct? And since only one could possibly be, why think any one of them would be?

You haven't even specified what you're talking about here. I'm not about to flail about trying to guess what you might mean. If you've got something to discuss, you need to bring it.

Also, my point from the start, if you remember, is that I asked for a justification that mathematical logic is correct. No justification means it is irrational to just blindly accept that it is correct.

You'll notice that I didn't attempt to answer your question. I merely asked you if you were aware of Boolean algebra. I later asked if you could show that Boolean algebra is not a valid method for deciding if a logical argument is valid. Clearly, you couldn't. So, I'm happy to leave that particular topic, and you can keep discussing your original question with other people.

 

[Write4U]

W4U said,
IMO, it is essential that a mathematical equation of values can be drawn. Else there can be no implied (deterministic) result.

Jeeves said,
Then what's Pigeontoes on about?

Not sure, he made it complicated also....

I start with the simple definition of "implicate"

b (1): a logical relation between two propositions that fails to hold only if the first is true and the second is false— see TRUTH TABLE
(2): a logical relationship between two propositions in which if the first is true the second is true
(3): a statement exhibiting a relation of implication

https://www.merriam-webster.com/dictionary/implication

I mention David Bohm because he extended the concept of "the implicate" to a whole new universal "order" .

Bohm’s explanation of “manifest” is basically that in certain sub-orders, within the “whole set” of Implicate Order, there is a “totality of forms that have an approximate kind of recurrence, stability and separability.” These forms are capable of appearing tangible, solid, and thus make up our manifest world.

Bohm also declares that the “implicate order has to be extended into a multidimensional reality.” He proceeds: “In principle this reality is one unbroken whole, including the entire universe with all its fields and particles. Thus we have to say that the holomovement enfolds and unfolds in a multidimensional order, the dimensionality of which is effectively infinite. Thus the principle of relative autonomy of sub-totalities—is now seen to extend to the multi-dimensional order of reality.”

https://www.scienceandnonduality.com/article/david-bohm-implicate-order-and-holomovement

I'd like to see Tegmark's perspective on Bohm's (mathematically) deterministic universe.