Matters pertaining to the likes of this post are quite simple for anyone with a preliminary background in philosophy, or any person with competence on scientific fundamentals. To begin our discussion, I think it would be fitting to attempt to find a simplistic understanding of the philosophy of science. This discipline within philosophy, is an important matter for understanding the function of scientific knowledge, explanation, prediction, and so forth. In respect to the totality of this discipline, I only wish to define what is meant by a “scientific law” and a “scientific fact” – which to some, might not seem very quite different.
However, in respect to the next section – Introduction to the Philosophy of Science – it is not required in order to better understand the section on Laws and Facts. For preliminary purposes, I have added the section for the interest of the reader who may want a brief introduction to what the philosophy of science entails.
Introduction to the Philosophy of Science
The Philosophy of Science is an interesting discipline within philosophy that is best to be understood in light of it’s close friend, science. Unlike science, which is itself both observational and experimental, the philosopher of science “is not so much interested in observation and experiment, at least not in the primary sense, as he is in the critical examination and evaluation of key scientific concepts and scientific methodology” . Therefore, within the philosophy of science, we are interested in questions such as (1) How should scientific theories be constructed and understood? (2) What is a scientific explanation? (3) Can induction be rationally justified? and questions of the like.
According to James Ladyman’s book, Understanding Philosophy of Science (2002) , he writes that “While there are other disciplines that study the sciences, the types of questions they address and their means of trying to answer them are different from those in the philosophy of science” . To quote him at length:
Questions about, for example, the development of particular scientiﬁc disciplines and theories need to be addressed by historians of science, not philosophers. On the other hand, questions like, ‘what sort of personality makes for a good scientist?’ or ‘what role do journals play in the communication and assessment of theories in physics?’ are matters for the psychology or sociology of science, respectively. Philosophical questions about science, like philosophical questions in general, cannot be answered by going out in the world and gathering information, and ﬁnding out what happened, or how a particular scientiﬁc community is, as a matter of fact, organised; rather, philosophical inquiry proceeds by analysis, argument and debate. (emphasis mine)
However, I found Ladyman’s last comment a bit crude in terms of his lack of clarity. Philosophical inquiry surely is “concerned with the critical reflection on justification and evidence,”  and that it is “often more concerned with method than with theoretical content” . Norman Geisler actually even goes so far as to name 8 characteristics associated with philosophical inquiry (2 of which have already been stated):
- Philosophical disputes are not caused by a lack of factual information.
- Philosophical problems are seldom solved by an appeal to facts.
- Philosophy is often more concerned with method than with theoretical content.
- One of philosophy’s chief goals is clarification.
- Philosophy is concerned with the critical reflection on justification and evidence.
- Philosophical inquiry centers on a quest for truth about crucial issues that are perennially discussed by thoughtful men.
- Philosophical analysis and explanation involves appeals to systems of principles.
- Some philosophy is concerned with the nature of “being” or reality. 
The importance of characteristic #5 may be quite conforming to the statement like that of Ladyman’s, namely, that “Philosophy evaluates arguments and assesses presuppositions and truth claims” . This is perhaps where the issue of philosophical argument/debate happens to step in.
More particularly, technical philosophical matters tend to come up as well in terms of epistemological justifications/warrants for scientific claims. Epistemology (from the Greek episteme, meaning “knowledge”), to remember, is the ”branch of philosophy that inquires into knowledge and justiﬁcation” . Even more so, when asking peculiar questions such as “what is science?”, another issue known as the demarcation problem that will often come up can be defined as the “problem of saying what is scientiﬁc and what is not” .
Therefore, in light of attempting to best understand how justified we are in terms of epistemically asserting certain claims to be the case, employing certain theories and forming other certain axioms, science even faces the issue most interested in by philosophers of science known as methodology, which, according to Ladyman, “is at the center of the philosophy of science” . Technical matters regarding methodology will not be addressed here (induction, nomological deduction, etc.).
What are Laws and Facts?
In our daily experience, we notice regularities. Day follows night, objects tend to fall when we drop them, and so on. In short, if “a certain regularity is observed at all times and all places, without exception, then the regularity is expressed in the form of a ‘universal law‘” . For instance, when the statement “All ice is cold” is furthered, we are suggesting that in all past, present, and future instances, ice is (was, or will be) cold. Of course, this is what’s known as a universal law. Laws that are not exactly universal, but are rather more probabilistic in scope are known as statistical laws. For example, “Approximately half the children born each year are boys” is a statistical law in that it only stipulates a certain percentage of cases that really occur.
These laws – both statistical and universal – are quite important in science. However, interestingly we convey universal laws more importantly under formal logic known as a “universal conditional statement”. For example, let us say that we have b, and if b is P, then whatever is b is also Q. This can be written as:
(b) (Pb ⊃ Qb)
The expression “(b)” on the left is what’s known as a “universal quantifier”. This basically means, that in all cases of b, Pb and Qb hold true. That symbol in between – “⊃” – is a connective used in symbolic logic. It links the term on its left to the term on its right. In corresponds in grammatical language as “If… then…” So, the above notation could be stated as:
In all instances of some material body b, if b has the property P, then it also has the property Q.
These could like saying that “for every body b, if that body were heated, then it will expand”. Here, we have the law of thermal expansion in its nonqualitative form. As Rudolf Carnap explains:
In physics, of course, one tries to obtain quantitative laws and to qualify them so as to exclude exceptions; but, if we forget about such refinements, then this universal conditional statement is the basic logical form of all universal laws. Sometimes we may say that, not only does [Qb] hold whenever [Pb] holds, but the reverse is also true; whenever [Qb] holds, [Pb] holds also. 
However, since we understand these matters of scientific laws, let us move to another logical form. A scientist for example may say, “Last Tuesday in the Galapagos Islands, Professor Smith discovered a new species of birds.” Of course, this does not fit under our usual understanding of a scientific law. This statement is about a particular time and place, or, is what’s known as a singular statement – since it states single facts. “Of course, all our knowledge”, says Carnap, “has its origin in singular statements – the particular observations of particular individuals” .
One of the big problems about the philosophy of science is trying to move from these singular statements to universal laws. The interesting thing however about these singular statements, is that it is how they are traditionally to be understood as “facts“. In other words, “Facts are particular events” . The importance of these facts is that “science begins with direct observations of single facts” . They are helpful in determining our justification of moving from the particular to the universal – or, in observing regularities to determine a new “law”. For more on this subject, see my other posts on the matter of Induction that touches on this universal and particular distinction.
To summarize, facts are seen as the particular while laws (in the universal sense) are seen as the universal. Laws are distinguished into (1) universal laws and (2) statistical laws along with (1a) empirical and (2a) theoretical laws. In respect to this post, we have only dealt with (1a) empirical laws in contrast to theoretical laws. Theoretical laws, which can be seen in examples of elementary particles and electromagnetic fields, are theoretical and nonobservable concepts. While, empirical concepts, are subject to observable and testable scrutiny.
For further reading into these subjects, see more posts of mine in the Philosophy of Science, as well as suggested readings in the “Recommended Books” section at the top of my page.
-  Norman Geisler, Introduction to Philosophy: A Christian Perspective (Grand Rapids: Mi, 1980) p. 33
-  James Ladyman, Understanding Philosophy of Science (Routledge: London, 2002)
-  Ibid. p. 3
-  Norman Geisler, Introduction to Philosophy: A Christian Perspective (Grand Rapids: Mi, 1980) p. 19
-  Ibid. p. 18
-  Ibid. pp. 18-20
-  Ibid. p. 19
-  James Ladyman, Understanding Philosophy of Science (Routledge: London, 2002) p. 5
-  Ibid. p. 4
-  Ibid. p. 4
-  Rudolf Carnap, An Introduction to the Philosophy of Science (Dover Edition: 1995) p. 3
-  Ibid. p. 4
-  Ibid. pp. 4-5
-  Ibid.
-  Ibid. p. 6