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[Pattern-chaser]

This topic concerns thought — serious and considered thought, wherever it occurs, and whatever it is applied to.
No other style or type of thinking is considered here.

Also, in this topic, "thought", "thinking", "reason" and "logic" are all effectively synonymous for our purposes here, and should be read as such.



Ever since I learned what axioms are, and what they're for, I sort of assumed that there are, somewhere, a number of axioms that lie behind reason (and logic), thinking and thought. So eventually, I went looking for them, and was surprised to discover that there are no such axioms. There are some laws and rules, but no axioms, no fundamental scaffolding upon which serious and considered thought might be based.

Many of you will already be aware of the so-called 'rules of thought', that I soon discovered in my search. No axioms, just some rules. And these rules do not seem to me to be sufficiently flexible to support all instances of serious and considered thought.

According to the 1999 Cambridge Dictionary of Philosophy, laws of thought are laws by which or in accordance with which valid thought proceeds, or that justify valid inference, or to which all valid deduction is reducible.

Laws of thought are rules that apply without exception to any subject matter of thought, etc.; sometimes they are said to be the object of logic. The term, rarely used in exactly the same sense by different authors, has long been associated with three equally ambiguous expressions:

• the law of identity (ID),
• the law of contradiction (or non-contradiction; NC), and
• the law of excluded middle (EM).

Sometimes, these three expressions are taken as propositions of formal ontology having the widest possible subject matter, propositions that apply to entities as such:

• (ID), everything is (i.e., is identical to) itself;
• (NC) no thing having a given quality also has the negative of that quality (e.g., no even number is non-even);
• (EM) every thing either has a given quality or has the negative of that quality (e.g., every number is either even or non-even).

Equally common in older works is the use of these expressions for principles of metalogic about propositions:

• (ID) every proposition implies itself;
• (NC) no proposition is both true and false;
• (EM) every proposition is either true or false.

To begin with, an empirical example. There are many real world situations where the law of the excluded middle is misleading, for it denies the part where most of the action takes place — in the middle, on a spectrum, away from the extremes (which might be TRUE and FALSE, but could as easily refer to YES and NO, or a different pair of 'opposites'). Serious and considered thought can often be — and often is — applied to such situations.

I observe that we humans use at least two 'types' of thought, binary thinking and what I have come to call network thinking (because I couldn't find a term for it that is already extant).

Binary thinking is instinctive in origin, the obvious example being 'fight or flight', when there is insufficient time for a complete analysis! But that isn't the only application of binary thought. Much scientific thinking is binary thinking, some of it even governed by Boolean Logic. There are many examples of the correct and useful application of binary thinking, to the extent that some feel it is the only acceptable mode of thought.

N.B. There are instances where the subject is not suited to binary thinking, and yet it is forced into that mould, to allow scientific-style thinking to be applied. Tactics such as "Well, X is either TRUE or FALSE, so which is it?", and others, might be used to avoid the (much) greater complexity and difficulty of network thinking? Whatever the reasons, if a subject is not suited to binary thinking — or to network thinking, in other circumstances — but we persist anyway, we can reasonably expect that our conclusions might not be all we hoped for.

There are occasions when a subject of study is not addressable via binary thinking, and yet serious and considered thought may be applied to it. What we use then is a more flexible style of thinking, network thinking. In network thinking, the progress of a chain of reasoning is not constrained by binary patterns and thinking. At each node in the chain, there might be any number of different possible outcomes, not just two.

The laws of thought are particularly unhelpful to network thinking. In fact, I suspect they were developed to support and promote binary, scientific, thinking? They seem so clearly matched, to me. In later posts, I have no doubt that these 'laws' of thought will be individually considered, so I will not try to anticipate every possible opinion that might be expressed.

I will end this first post by repeating the question that defines my search: what are the fundamental axioms of thought?

[thrasymachus]

Pattern-chaser wrote
I will end this first post by repeating the question that defines my search: what are the fundamental axioms of thought?

Logic IS its own presupposition! You can't get "behind" logic, because this assumes just what you are trying to get behind given that asking the question and answering it are all logically structured. Only logic can tell you what logic's foundation is, and that is question begging in the extreme.

What can logic say, then? See Aristotle categories, substance, quantity, quality. etc. Or Kant's take on this.

But pragmatists, for example, think logic is essentially, well, pragmatic, and this goes to an examination of Time. Heh, heh, there is no world....just "worlding". Logic is a temporal event, not to put too fine a point on it.

[The Beast]

Axiom of comprehension. The existence principle and how t is used. This principle correlates with thought as restricted or as unrestricted. Restricted thought provides a basis for a local reality. Unrestricted thought is reducible to a paradox. In the restricted thought the basic concept of class is introduced. The axiom of comprehension is also called the axiom of abstraction; term that is applied when using restricted thought to label it in a class paradox… (or metaphysical to use Kantian terminology). As for the term axiom, it is defined as a proposition of a theory. The propositions are logical or proper. All Kantian defined metaphysics are in the proper class. However. IMO, it is all about the axiom of constructability which to me is the TOM. The axiom of constructability is neither provable nor refutable. (TOM: always under construction)

[Pattern-chaser]

Axiom of comprehension. The existence principle and how t is used. This principle correlates with thought as restricted or as unrestricted. Restricted thought provides a basis for a local reality. Unrestricted thought is reducible to a paradox. In the restricted thought the basic concept of class is introduced. The axiom of comprehension is also called the axiom of abstraction; term that is applied when using restricted thought to label it in a class paradox… (or metaphysical to use Kantian terminology). As for the term axiom, it is defined as a proposition of a theory. The propositions are logical or proper. All Kantian defined metaphysics are in the proper class. However. IMO, it is all about the axiom of constructability which to me is the TOM. The axiom of constructability is neither provable nor refutable. (TOM: always under construction)

I'm afraid I've never heard of the various axioms you mention. Are these your terms, or are they more widely used than that? They sound interesting.

For example, the "axiom of comprehension" seems to be part of mathematical set theory? If so, it's hardly an axiom of the general concept of reason, thought, and thinking, is it?

[Pattern-chaser]

I will end this first post by repeating the question that defines my search: what are the fundamental axioms of thought?

Logic IS its own presupposition! You can't get "behind" logic, because this assumes just what you are trying to get behind given that asking the question and answering it are all logically structured. Only logic can tell you what logic's foundation is, and that is question begging in the extreme.

What can logic say, then? See Aristotle categories, substance, quantity, quality. etc. Or Kant's take on this.

But pragmatists, for example, think logic is essentially, well, pragmatic, and this goes to an examination of Time. Heh, heh, there is no world....just "worlding". Logic is a temporal event, not to put too fine a point on it.

But I'm not seeking, or asking for, the axioms of logic. I'm looking for something more general: the axioms of thought and thinking, which surely impact on reason? Yes, logic rears its ugly head, but in this topic, it only does so as a sort of sidekick to reason. I intend to avoid debating whether logic concerns only the structure of an argument (the traditional meaning), or whether it includes some or all of "reason" too (a more modern interpretation). In this topic, the split simply doesn't matter. The topic includes both, to ensure that all parts of reason/logic are captured.

Even more specific: this topic is only interested in logic and/or reason as a part of the search for the fundamental axioms of thought and thinking. Any other application/use of reason and logic is not considered or relevant.

[trarof]

The fundamental axioms of reason and thought are probably just facts about how the mind and perception operate. It's the fundamentals of metaphysics and epistemology.

[thrasymachus]

Pattern-chaser wrote
But I'm not seeking, or asking for, the axioms of logic. I'm looking for something more general: the axioms of thought and thinking, which surely impact on reason? Yes, logic rears its ugly head, but in this topic, it only does so as a sort of sidekick to reason. I intend to avoid debating whether logic concerns only the structure of an argument (the traditional meaning), or whether it includes some or all of "reason" too (a more modern interpretation). In this topic, the split simply doesn't matter. The topic includes both, to ensure that all parts of reason/logic are captured.

Even more specific: this topic is only interested in logic and/or reason as a part of the search for the fundamental axioms of thought and thinking. Any other application/use of reason and logic is not considered or relevant.

Not sure about what you are after. I think it is right to ask for something more fundamental than logic, even though one can be accused of absurdity (it takes logic to ask the question at all): I see a tree outside my window, and in the seeing itself there is an understanding already at work telling me it is a tree, belongs outside, tends to be green in the summer, and on and on. On the tree side, call it, one might say it is pure familiarity from years of exposure to trees and their environments. It is the familiarity that confirms the knowledge claim. This is also what is fundamental to an animal's "knowledge" of the world. But is familiarity the most basic analysis of knowledge? Familiarity occurs in time, that is, the past informs the present as to what to expect that things of that shape, size, color, appear, and this is what is behind familiarity, and what is up ahead, is an ummanifested future. So there we are, in the "middle" of a time dynamic in which past anticipates a future that is the "not yet" of experience. Time is, in this, a singular dynamic, for one doesn't ever actually witness the past or the future a such. The past is witnessed AS an anticipation of what is to come in a fleeting present. This present is just this recalled-anticipatory-into-the-not-yet. Time in the linear sense has no place here.

Logic, then, is to be seen as a "forward-looking" event. Inherently anticipatory. Logic, in the Aristotelian sense, on the other hand, as a set of categories, is just an abstraction of this seamless streaming actuality.

But as I see it, it does go deeper: logic is a concept about the the way judgment is structured in time, but judgment belongs to a primordial source, a generative "unseen". One may wants the reduction to brain activity to be foundational, but this simply falls apart on analysis almost instantly. the question turns to the spontaneous effusion of actuality which is shown, but never gotten behind.

[The Beast]

From a POV of getting an allowable answer to the posited question, a truth table method yields the desired tautology: True. So. From a hypothetical syllogism to the derived axiom thinking an De re/de dicto answer: Maybe true. (A decision or answeer from a thinking method of available facts).
What is an if/then/else method?
In an imaginary example we received twelve gold coins and a balance scale (axiom), and we are told of a false gold coin among the twelve. The exercise is to construct a method to find the false coin and if it weighs less or more. It must be done with three operations.
Prior to the start, the coins are numbered 1 to 12 and separated in 3 groups of 4.

Method:
12 is false.
1.- first group goes in one side of the scale and second group on the other plate of the scale.
If equal weight, then false coin is in the third group.
2 Coins 1 from the first group and coins 9 and 10 the third group go in one plate of the scale. Coin 11 of the third group and coins 2 and 3 of the first group go on the other plate of the scale.
If equal weight, then the false coin is 12.
3 Coin 1 goes on one plate of the scale and coin 12 on the other. If one weighs more, then 12 weighs less else 12 weighs more.
11 is false.
1.- first group goes in one side of the scale and second group on the other plate of the scale.
If equal weight, then false coin is in the third group.
2 Coins 1 from the first group and coins 9 and 10 the third group go in one plate of the scale. Coin 11 of the third group and coins 2 and 3 of the first group go on the other plate of the scale.
If different weight then note which side weighs more and the false coin is 9, 10 or 11
3.- 9 goes on one plate of the scale and 10 on the other if equal weight then the false coin is 11 and if in step 2 the plate weighs less then the coin weighs less else more.

Etc.…etc.…etc.

[Pattern-chaser]

From a POV of getting an allowable answer to the posited question, a truth table method yields the desired tautology: True. So. From a hypothetical syllogism to the derived axiom thinking an De re/de dicto answer: Maybe true. (A decision or answeer from a thinking method of available facts).
What is an if/then/else method?
In an imaginary example we received twelve gold coins and a balance scale (axiom), and we are told of a false gold coin among the twelve. The exercise is to construct a method to find the false coin and if it weighs less or more. It must be done with three operations.
Prior to the start, the coins are numbered 1 to 12 and separated in 3 groups of 4.

Method:
12 is false.
1.- first group goes in one side of the scale and second group on the other plate of the scale.
If equal weight, then false coin is in the third group.
2 Coins 1 from the first group and coins 9 and 10 the third group go in one plate of the scale. Coin 11 of the third group and coins 2 and 3 of the first group go on the other plate of the scale.
If equal weight, then the false coin is 12.
3 Coin 1 goes on one plate of the scale and coin 12 on the other. If one weighs more, then 12 weighs less else 12 weighs more.
11 is false.
1.- first group goes in one side of the scale and second group on the other plate of the scale.
If equal weight, then false coin is in the third group.
2 Coins 1 from the first group and coins 9 and 10 the third group go in one plate of the scale. Coin 11 of the third group and coins 2 and 3 of the first group go on the other plate of the scale.
If different weight then note which side weighs more and the false coin is 9, 10 or 11
3.- 9 goes on one plate of the scale and 10 on the other if equal weight then the false coin is 11 and if in step 2 the plate weighs less then the coin weighs less else more.

Etc.…etc.…etc.

You seem to be describing an old 'logic puzzle'. I don't understand what it has to do with the axioms of thought?

[The Beast]

The fundamental axioms of reason and thought are probably just facts about how the mind and perception operate. It's the fundamentals of metaphysics and epistemology.

Details?

I will end this first post by repeating the question that defines my search: what are the fundamental axioms of thought?

Yes. It is an old puzzle. I solved it long ago. But there are some questions. Why are there twelve gold coins? Why one is false? Why is there something instead of abstract numbers? Why is there a balance scale? Are these not your questions? The puzzle was as easy as my mother’s meal.

[thrasymachus]

trarof wrote
The fundamental axioms of reason and thought are probably just facts about how the mind and perception operate. It's the fundamentals of metaphysics and epistemology.

Wittgenstein tells us such things cannot be discussed at all, that they should be passed over in silence. And if you read analytic epistemology, you get just this kind of passing over. But is this a good idea? To draw a line where thought cannot go?

[Pattern-chaser]

But I'm not seeking, or asking for, the axioms of logic. I'm looking for something more general: the axioms of thought and thinking, which surely impact on reason? Yes, logic rears its ugly head, but in this topic, it only does so as a sort of sidekick to reason. I intend to avoid debating whether logic concerns only the structure of an argument (the traditional meaning), or whether it includes some or all of "reason" too (a more modern interpretation). In this topic, the split simply doesn't matter. The topic includes both, to ensure that all parts of reason/logic are captured.

Even more specific: this topic is only interested in logic and/or reason as a part of the search for the fundamental axioms of thought and thinking. Any other application/use of reason and logic is not considered or relevant.

Not sure about what you are after. I think it is right to ask for something more fundamental than logic, even though one can be accused of absurdity (it takes logic to ask the question at all)...

In other serious thought systems that we have and use, the foundation is the assumptions, the axioms, the things we hope are true, but cannot show to be true (if we could, we would). On top of that, we build, by deduction from those axioms, all the rest of the theory that applies to that discipline. If there are no axioms, there is nothing to build upon.

So I wonder what are the foundations of thought and reason? Where are those axioms, those initial assumptions upon which the rest of the edifice is built?





P.S. I asked repeatedly in my OP that we do not focus specifically on logic, and that logic only applies to this topic in the sense that it (logic) is the tool we use to decide if the structure of an argument is valid. I ask once again, can we please avoid focussing directly on logic. This is about thought, thinking, and reason; logic is the poor (and much less important) relation here, and has only a minor role to play. Thanks.

[Pattern-chaser]

The fundamental axioms of reason and thought are probably just facts about how the mind and perception operate. It's the fundamentals of metaphysics and epistemology.

Wittgenstein tells us such things cannot be discussed at all, that they should be passed over in silence. And if you read analytic epistemology, you get just this kind of passing over. But is this a good idea? To draw a line where thought cannot go?

I think there is only one place where thought cannot go, and that is the place where the 'rules of thought' are so incomprehensible to humans that our thoughts simply cannot follow. Otherwise, all venues are possible and acceptable, no?

[The Beast]

I am all for it. “What is” thought concerned with?
Language objectivity. I agree with “what is”. The axiom of “what is” (IMO) transcends language. However, it is formulated by language as ID and propositions (knowledge) to the understanding. It is what Kant said is the intuition of spacetime.
1.- Axiom of “what is.”

[thrasymachus]

Pattern-chaser wrote
I think there is only one place where thought cannot go, and that is the place where the 'rules of thought' are so incomprehensible to humans that our thoughts simply cannot follow. Otherwise, all venues are possible and acceptable, no?

There are many who hold that truth is made, not discovered. They don't bother to question where thought cannot go. They instead tell us that where it CAN go is really not "going" anywhere. They resist the idea that there is a "beyond" out of which reason doesn't apply. Rather, it is simply impossible to conceive of such a thing, and to try to do so is in the same league as uttering pure nonsense.

So when you are walking along and registering tree here, cloud there, this idea that you have some grasp of what something is outside of the conditions outside the conditions of propositional truth is just wrong. I am a thing. The cloud is a thing. The knowing is over here, my knowing, and the cloud "out there" is only an out there vis a vis me. Remove truth conditions, and there is simply nothing to say.