# Is logic built on assumptions?

I'm sorry if this sounds like a stupid question, but how can we know that our logical approach to ideas is not in itself based on assumptions. For example, how can we know that the workings of the entire universe are consistent with what we observe? Do we know that the same laws of physics apply in a distant galaxy, or have we simply decided to take the leap of faith because finding any explanations would otherwise be impossible.

Perhaps a clearer example is addition. We have defined addition to simply represent the counting of the number of elements within a two distinct groups. For example, in order to recognize that 3 + 8 = 11, we can draw the following diagram:

| | | + | | | | | | | |

and count the total number of lines. Since nobody has "counted the number of lines" in an addition problem like 5893 + 2485, how can we be certain that our result will be 8378? How do know that consistency does not break down in addition specifically for these two numbers? Would it be fair to say that "addition works" is more of a conjecture than a proven axiom?

Ultimately, what I'm asking is how we can claim that consistency in the patterns we observe extends beyond what we observe. Is it possible to know that a tree will make a sound when it falls unheard or is that merely an attempt to bring continuity into a world that may or may not be? Is it just a practical, intuitive, unprovable assumption that is extremely convenient?

• A quick further point -- even assuming the physical laws are the same everywhere now, is there any "higher" law enforcing their consistency indefinitely into the future? (This is a question raised in Meillassoux's After Finitude, which might be interesting further reading here.) – Joseph Weissman May 29 '15 at 0:25
• What is a "proven axiom"? The whole point of an axiom is that it's unproven, but accepted. – user2953 May 29 '15 at 14:59
• Axioms are by definition undefined; but by even formulating them we are affirming that the body of knowledge that they elaborate is significant; that is what justifies the axiomatic approach is not only its logical structure of strict deduction; but also what is deduced; this looks like 'circular' logic; and in a way it is; this epistemology is called coherentism. – Mozibur Ullah May 31 '15 at 19:31
• That the universe has an intelligible order is an assumption; a metaphysical principle (from first principles); and is justified by thinking what it would mean to have no order at - despite popular notions of chaos theory - it isn't conceivable; try to write down what it means that the universe follows no law - it isn't possible when one has to give an account of 'follows no law'. – Mozibur Ullah May 31 '15 at 19:36

It seems that we have many questions in one here, and my answer is certainly one of many possible.

I'd like to quote Charles Sanders Peirce, from an article called "Some Consequences of Four Incapacities" (http://www.peirce.org/writings/p27.html), where he states his disagreement with the Cartesian principle of universal doubt:

We cannot begin with complete doubt. We must begin with all the prejudices which we actually have when we enter upon the study of philosophy. These prejudices are not to be dispelled by a maxim, for they are things which it does not occur to us can be questioned. Hence this initial skepticism will be a mere self-deception, and not real doubt; and no one who follows the Cartesian method will ever be satisfied until he has formally recovered all those beliefs which in form he has given up. It is, therefore, as useless a preliminary as going to the North Pole would be in order to get to Constantinople by coming down regularly upon a meridian. A person may, it is true, in the course of his studies, find reason to doubt what he began by believing; but in that case he doubts because he has a positive reason for it, and not on account of the Cartesian maxim. Let us not pretend to doubt in philosophy what we do not doubt in our hearts.

Even if your line of argument does not implicate universal doubt - only the doubt that comes from the absence of immediate evidence from the senses - it is a form of skepticism that can easily lead us to discredit even the "certainties" that come from direct testimony:

How can you be sure of having counted those eight bars correctly? And those other three on the left side, did you actually count them, or just subitized? Aren't your perceptual certainties also subjective, in the end? A result of insistence, mere beliefs? They certainly are beliefs too, even if that is not all what they are.

The starting point of knowledge - of science - for Peirce, is the inevitability of hypothetical thinking. Any mind is a factory of hypotheses, unproved assertions, first guesses. This is the ground zero, not doubt. How we respond to the hypotheses we are condemned to make, that's where the problem of method begins.

• Then, is there no legitimate claim in saying that philosophy is more a search for "truth" than any other subject? That is, that it only presents a certain set of biased relative truths based on certain predetermined ideas? That it can only act as an extrapolation or an extension of any other form of knowledge for that system, but not provide a message for everything in a way applicable beyond the self? What is the point of a philosophy that can not provide truth beyond a personal bias? Or does this view in itself make the claim that philosophy is an entirely personal matter? (1/2) – David Lalo May 31 '15 at 9:23
• How then, can it be a standardized field of knowledge? We find it possible to ascribe to the views of more well-thought people that are not ourselves, and, it seems to me, we base philosophy as work growing from that of previous thinkers, rather than a new field entirely redefined, with no ties to the past in each era. Or am I missing the whole point? Is this why there are so many different fields and views within philosophy? – David Lalo May 31 '15 at 9:31
• To extend Your geographic metaphor: philosophy can only tell us which cardinal direction to go in order to reach Constantinople, if we are not using a universal point of reference like the North Pole. So if a Polynesian girl tried to use a Frenchman's directions to get there (generally eastwards), she would obviously end up in the wrong place. Since in this case individual human context mirrors the different places from which different persons may arise, is it then a fair statement that the canon is useless? Obviously, people are capable of understanding the works of other philosophers. – David Lalo May 31 '15 at 9:37
• What Peirce suggests in this small fragment is not a method for reaching truth. He is speaking as a man of the XIX century, to his contemporaries, about what can be considered naive (even unethical) when trying to produce absolute truths from mere speculation. That does not diminish the importance of Descartes, but it is an argument against those who use his contributions unadvisedly and out of context. – André Souza Lemos May 31 '15 at 12:06
• Philosophy does advance, but not just the way science does - by mere refutation, or when a new and better explanatory model is proposed. It advances more often by reinterpretation. It is a creative activity, a little bit like poetry, in that regard. That is why there's so much hard work in philosophical writing. We cannot produce good philosophy out of wit and intelligence alone. – André Souza Lemos May 31 '15 at 12:12

Specifically regarding your numerical example, I think Mathematical Inducton explains it a bit:

Mathematical Induction wiki

From that point of view, the answer to your quesiton 'Would it be fair to say that "addition works" is more of a conjecture than a proven axiom?' does seem to be "Yes".

Or perhaps a more accurate way of viewing it is that our methods of logic and maths, and therefore proof, are based on the assumption that such things are true & that where a system can be extended to assume a general case, that assumpton is made.

There's also the notion that scientific method can only provide a hypothesis which is then demonstrated (repeatably) in reality. That means you can't ever prove anything in the real world, only provide theories as to how things will occur according to a model, so more conjecture.

• Ultimately, what I'm asking is how we can claim that consistency in the patterns we observe extends beyond what we observe.

We can't, we just have to assume that's the case in order to owrk with maths/logic. Theories do fall apart too - eg Newtonian physics was looking pretty decisive until Einstein & suchlike pointed out there's more to laws of physics than that.

• Is it possible to know that a tree will make a sound when it falls unheard or is that merely an attempt to bring continuity into a world that may or may not be?

No to "Know" but it is possible to make educated guesses (hypotheses) using assumptions above.

• Is it just a practical, intuitive, unprovable assumption that is extremely convenient?"

Yes, it would appear so :-)

This question is along similar lines :

Is everything just an opinion?

Yes, all logic is built on assumptions. 1 + 1 = 2 being logically correct assumes that we all hold the exact same understanding of 1, +, =, and 2. Logic is infallible, the only variance comes from assumptions and understanding of those assumptions.

I'd say that logic is based on observations, not assumptions. We observed our existence and therefore decided it true. Same way, when people observe something, they believe it true.

Then there are inferences. We make inferences about why something happens, didn't happen, or couldn't happen. These inferences can be wrong, but we make them anyways because they will be proven wrong later if so.

No logic isn't built from anything. Logic builds things though.

The truth of this statement is self-fulfilling, meaning the essence of a truth is its final teleological cause. Man does not possess logic but uses it. One may ask where does logic come from and that answer is out of order. And from where does order come from and that answer is out of chaos.

See Chaos Theory for a full clarification.

• What makes you say that? You might very well prove to be right, but you should provide a stronger argument. – James Kingsbery May 29 '15 at 21:48
• This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post - you can always comment on your own posts, and once you have sufficient reputation you will be able to comment on any post. – James Kingsbery May 29 '15 at 21:48
• @ James Kingsbery: I updated my argument. Hope that helps – Kris May 29 '15 at 22:01

Logic is based on premises which are assumed. For example, the premise that two is double one assumes that one is singular.

• The use of "premise" is a bit confusing here. Normally we use the term "axiom". – user2953 May 29 '15 at 17:16